id	sid	tid	token	lemma	pos
ejpam-4824	1	1	european	european	PROPN
ejpam-4824	1	2	journal	journal	PROPN
ejpam-4824	1	3	of	of	ADP
ejpam-4824	1	4	pure	pure	ADJ
ejpam-4824	1	5	and	and	CCONJ
ejpam-4824	1	6	applied	apply	VERB
ejpam-4824	1	7	mathematics	mathematic	NOUN
ejpam-4824	1	8	vol	vol	NOUN
ejpam-4824	1	9	.	.	PUNCT
ejpam-4824	2	1	16	16	NUM
ejpam-4824	2	2	,	,	PUNCT
ejpam-4824	2	3	no	no	INTJ
ejpam-4824	2	4	.	.	NOUN
ejpam-4824	2	5	3	3	NUM
ejpam-4824	2	6	,	,	PUNCT
ejpam-4824	2	7	2023	2023	NUM
ejpam-4824	2	8	,	,	PUNCT
ejpam-4824	2	9	1695	1695	NUM
ejpam-4824	2	10	-	-	SYM
ejpam-4824	2	11	1704	1704	NUM
ejpam-4824	2	12	issn	issn	PROPN
ejpam-4824	2	13	1307	1307	NUM
ejpam-4824	2	14	-	-	SYM
ejpam-4824	2	15	5543	5543	NUM
ejpam-4824	2	16	–	–	PUNCT
ejpam-4824	2	17	ejpam.com	ejpam.com	X
ejpam-4824	2	18	published	publish	VERB
ejpam-4824	2	19	by	by	ADP
ejpam-4824	2	20	new	new	PROPN
ejpam-4824	2	21	york	york	PROPN
ejpam-4824	2	22	business	business	PROPN
ejpam-4824	3	1	global	global	PROPN
ejpam-4824	3	2	a	a	DET
ejpam-4824	3	3	note	note	NOUN
ejpam-4824	3	4	on	on	ADP
ejpam-4824	3	5	quantum	quantum	NOUN
ejpam-4824	3	6	gates	gate	NOUN
ejpam-4824	3	7	swap	swap	NOUN
ejpam-4824	3	8	and	and	CCONJ
ejpam-4824	3	9	iswap	iswap	NOUN
ejpam-4824	3	10	in	in	ADP
ejpam-4824	3	11	higher	high	ADJ
ejpam-4824	3	12	dimensions	dimension	NOUN
ejpam-4824	3	13	arash	arash	PROPN
ejpam-4824	3	14	pourkia	pourkia	PROPN
ejpam-4824	3	15	college	college	PROPN
ejpam-4824	3	16	of	of	ADP
ejpam-4824	3	17	engineering	engineering	NOUN
ejpam-4824	3	18	and	and	CCONJ
ejpam-4824	3	19	technology	technology	NOUN
ejpam-4824	3	20	,	,	PUNCT
ejpam-4824	3	21	american	american	PROPN
ejpam-4824	3	22	university	university	PROPN
ejpam-4824	3	23	of	of	ADP
ejpam-4824	3	24	the	the	DET
ejpam-4824	3	25	middle	middle	PROPN
ejpam-4824	3	26	east	east	PROPN
ejpam-4824	3	27	,	,	PUNCT
ejpam-4824	3	28	kuwait	kuwait	PROPN
ejpam-4824	3	29	abstract	abstract	NOUN
ejpam-4824	3	30	.	.	PUNCT
ejpam-4824	4	1	we	we	PRON
ejpam-4824	4	2	present	present	VERB
ejpam-4824	4	3	explicit	explicit	ADJ
ejpam-4824	4	4	descriptions	description	NOUN
ejpam-4824	4	5	for	for	ADP
ejpam-4824	4	6	the	the	DET
ejpam-4824	4	7	swap	swap	NOUN
ejpam-4824	4	8	gate	gate	NOUN
ejpam-4824	4	9	and	and	CCONJ
ejpam-4824	4	10	the	the	DET
ejpam-4824	4	11	iswap	iswap	PROPN
ejpam-4824	4	12	gate	gate	NOUN
ejpam-4824	4	13	in	in	ADP
ejpam-4824	4	14	any	any	DET
ejpam-4824	4	15	arbitrary	arbitrary	ADJ
ejpam-4824	4	16	dimension	dimension	NOUN
ejpam-4824	4	17	d	d	X
ejpam-4824	4	18	≥	≥	NUM
ejpam-4824	4	19	2	2	NUM
ejpam-4824	4	20	,	,	PUNCT
ejpam-4824	4	21	in	in	ADP
ejpam-4824	4	22	terms	term	NOUN
ejpam-4824	4	23	of	of	ADP
ejpam-4824	4	24	permutation	permutation	NOUN
ejpam-4824	4	25	matrices	matrix	NOUN
ejpam-4824	4	26	.	.	PUNCT
ejpam-4824	5	1	moreover	moreover	ADV
ejpam-4824	5	2	,	,	PUNCT
ejpam-4824	5	3	we	we	PRON
ejpam-4824	5	4	unify	unify	VERB
ejpam-4824	5	5	these	these	DET
ejpam-4824	5	6	gates	gate	NOUN
ejpam-4824	5	7	by	by	ADP
ejpam-4824	5	8	introducing	introduce	VERB
ejpam-4824	5	9	a	a	DET
ejpam-4824	5	10	more	more	ADV
ejpam-4824	5	11	general	general	ADJ
ejpam-4824	5	12	gate	gate	NOUN
ejpam-4824	5	13	xswap	xswap	PROPN
ejpam-4824	5	14	which	which	PRON
ejpam-4824	5	15	includes	include	VERB
ejpam-4824	5	16	swap	swap	NOUN
ejpam-4824	5	17	and	and	CCONJ
ejpam-4824	5	18	iswap	iswap	NOUN
ejpam-4824	5	19	for	for	ADP
ejpam-4824	5	20	x	x	SYM
ejpam-4824	5	21	=	=	SYM
ejpam-4824	5	22	1	1	NUM
ejpam-4824	5	23	and	and	CCONJ
ejpam-4824	5	24	x	x	X
ejpam-4824	6	1	=	=	VERB
ejpam-4824	6	2	i	i	PRON
ejpam-4824	6	3	(	(	PUNCT
ejpam-4824	6	4	i.e.	i.e.	X
ejpam-4824	6	5	√	√	NUM
ejpam-4824	6	6	−1	−1	NOUN
ejpam-4824	6	7	)	)	PUNCT
ejpam-4824	6	8	,	,	PUNCT
ejpam-4824	6	9	respectively	respectively	ADV
ejpam-4824	6	10	.	.	PUNCT
ejpam-4824	7	1	the	the	DET
ejpam-4824	7	2	higher	higher	ADV
ejpam-4824	7	3	dimensional	dimensional	ADJ
ejpam-4824	7	4	xswap	xswap	NOUN
ejpam-4824	7	5	e.g.	e.g.	ADV
ejpam-4824	7	6	,	,	PUNCT
ejpam-4824	7	7	the	the	DET
ejpam-4824	7	8	swap	swap	NOUN
ejpam-4824	7	9	and	and	CCONJ
ejpam-4824	7	10	iswap	iswap	NOUN
ejpam-4824	7	11	gates	gate	NOUN
ejpam-4824	7	12	for	for	ADP
ejpam-4824	7	13	d	d	PROPN
ejpam-4824	7	14	>	>	X
ejpam-4824	7	15	2	2	NUM
ejpam-4824	7	16	serve	serve	VERB
ejpam-4824	7	17	as	as	ADP
ejpam-4824	7	18	quantum	quantum	NOUN
ejpam-4824	7	19	logic	logic	NOUN
ejpam-4824	7	20	gates	gate	NOUN
ejpam-4824	7	21	that	that	PRON
ejpam-4824	7	22	operate	operate	VERB
ejpam-4824	7	23	on	on	ADP
ejpam-4824	7	24	two	two	NUM
ejpam-4824	7	25	d	d	ADJ
ejpam-4824	7	26	-	-	PUNCT
ejpam-4824	7	27	level	level	NOUN
ejpam-4824	7	28	qudits	qudit	NOUN
ejpam-4824	7	29	.	.	PUNCT
ejpam-4824	8	1	for	for	ADP
ejpam-4824	8	2	d	d	PROPN
ejpam-4824	8	3	=	=	SYM
ejpam-4824	8	4	2	2	NUM
ejpam-4824	8	5	,	,	PUNCT
ejpam-4824	8	6	it	it	PRON
ejpam-4824	8	7	is	be	AUX
ejpam-4824	8	8	well	well	ADV
ejpam-4824	8	9	known	know	VERB
ejpam-4824	8	10	that	that	SCONJ
ejpam-4824	8	11	iswap	iswap	NOUN
ejpam-4824	8	12	unlike	unlike	ADP
ejpam-4824	8	13	swap	swap	NOUN
ejpam-4824	8	14	is	be	AUX
ejpam-4824	8	15	universal	universal	ADJ
ejpam-4824	8	16	for	for	ADP
ejpam-4824	8	17	quantum	quantum	NOUN
ejpam-4824	8	18	computing	computing	NOUN
ejpam-4824	8	19	.	.	PUNCT
ejpam-4824	9	1	we	we	PRON
ejpam-4824	9	2	will	will	AUX
ejpam-4824	9	3	prove	prove	VERB
ejpam-4824	9	4	this	this	DET
ejpam-4824	9	5	fact	fact	NOUN
ejpam-4824	9	6	for	for	ADP
ejpam-4824	9	7	xswap	xswap	PROPN
ejpam-4824	9	8	in	in	ADP
ejpam-4824	9	9	any	any	DET
ejpam-4824	9	10	dimension	dimension	NOUN
ejpam-4824	9	11	d	d	NOUN
ejpam-4824	9	12	,	,	PUNCT
ejpam-4824	9	13	when	when	SCONJ
ejpam-4824	9	14	x	x	SYM
ejpam-4824	9	15	̸=	̸=	PROPN
ejpam-4824	9	16	±1	±1	VERB
ejpam-4824	9	17	.	.	PUNCT
ejpam-4824	10	1	our	our	PRON
ejpam-4824	10	2	explicit	explicit	ADJ
ejpam-4824	10	3	representation	representation	NOUN
ejpam-4824	10	4	of	of	ADP
ejpam-4824	10	5	xswap	xswap	PROPN
ejpam-4824	10	6	by	by	ADP
ejpam-4824	10	7	a	a	DET
ejpam-4824	10	8	permutation	permutation	NOUN
ejpam-4824	10	9	matrix	matrix	NOUN
ejpam-4824	10	10	facilitates	facilitate	VERB
ejpam-4824	10	11	the	the	DET
ejpam-4824	10	12	proof	proof	NOUN
ejpam-4824	10	13	,	,	PUNCT
ejpam-4824	10	14	greatly	greatly	ADV
ejpam-4824	10	15	.	.	PUNCT
ejpam-4824	11	1	2020	2020	NUM
ejpam-4824	11	2	mathematics	mathematic	NOUN
ejpam-4824	11	3	subject	subject	NOUN
ejpam-4824	11	4	classifications	classification	NOUN
ejpam-4824	11	5	:	:	PUNCT
ejpam-4824	11	6	81p68	81p68	NUM
ejpam-4824	11	7	,	,	PUNCT
ejpam-4824	11	8	81p40	81p40	NUM
ejpam-4824	11	9	key	key	ADJ
ejpam-4824	11	10	words	word	NOUN
ejpam-4824	11	11	and	and	CCONJ
ejpam-4824	11	12	phrases	phrase	NOUN
ejpam-4824	11	13	:	:	PUNCT
ejpam-4824	11	14	qudits	qudit	NOUN
ejpam-4824	11	15	,	,	PUNCT
ejpam-4824	11	16	quantum	quantum	ADJ
ejpam-4824	11	17	logic	logic	NOUN
ejpam-4824	11	18	gates	gate	NOUN
ejpam-4824	11	19	,	,	PUNCT
ejpam-4824	11	20	universal	universal	ADJ
ejpam-4824	11	21	gates	gate	NOUN
ejpam-4824	11	22	,	,	PUNCT
ejpam-4824	11	23	entangling	entangle	VERB
ejpam-4824	11	24	gates	gate	NOUN
ejpam-4824	11	25	1	1	NUM
ejpam-4824	11	26	.	.	PUNCT
ejpam-4824	12	1	introduction	introduction	NOUN
ejpam-4824	12	2	applications	application	NOUN
ejpam-4824	12	3	of	of	ADP
ejpam-4824	12	4	d	d	NOUN
ejpam-4824	12	5	-	-	PUNCT
ejpam-4824	12	6	level	level	NOUN
ejpam-4824	12	7	qudits	qudit	NOUN
ejpam-4824	12	8	for	for	ADP
ejpam-4824	12	9	d	d	PROPN
ejpam-4824	12	10	≥	≥	NUM
ejpam-4824	12	11	3	3	NUM
ejpam-4824	12	12	have	have	AUX
ejpam-4824	12	13	been	be	AUX
ejpam-4824	12	14	found	find	VERB
ejpam-4824	12	15	to	to	PART
ejpam-4824	12	16	have	have	VERB
ejpam-4824	12	17	many	many	ADJ
ejpam-4824	12	18	advantages	advantage	NOUN
ejpam-4824	12	19	over	over	ADP
ejpam-4824	12	20	the	the	DET
ejpam-4824	12	21	conventional	conventional	ADJ
ejpam-4824	12	22	qubits	qubit	NOUN
ejpam-4824	12	23	(	(	PUNCT
ejpam-4824	12	24	d	d	NOUN
ejpam-4824	12	25	=	=	SYM
ejpam-4824	12	26	2	2	NUM
ejpam-4824	12	27	)	)	PUNCT
ejpam-4824	12	28	in	in	ADP
ejpam-4824	12	29	quantum	quantum	NOUN
ejpam-4824	12	30	computing	computing	NOUN
ejpam-4824	12	31	and	and	CCONJ
ejpam-4824	12	32	quantum	quantum	NOUN
ejpam-4824	12	33	information	information	NOUN
ejpam-4824	12	34	.	.	PUNCT
ejpam-4824	13	1	[	[	X
ejpam-4824	13	2	7–9	7–9	NUM
ejpam-4824	13	3	,	,	PUNCT
ejpam-4824	13	4	11–13	11–13	NUM
ejpam-4824	13	5	,	,	PUNCT
ejpam-4824	13	6	17	17	NUM
ejpam-4824	13	7	]	]	PUNCT
ejpam-4824	13	8	.	.	PUNCT
ejpam-4824	14	1	as	as	ADP
ejpam-4824	14	2	in	in	ADP
ejpam-4824	14	3	the	the	DET
ejpam-4824	14	4	case	case	NOUN
ejpam-4824	14	5	of	of	ADP
ejpam-4824	14	6	d	d	PROPN
ejpam-4824	14	7	=	=	SYM
ejpam-4824	14	8	2	2	NUM
ejpam-4824	14	9	,	,	PUNCT
ejpam-4824	14	10	to	to	PART
ejpam-4824	14	11	make	make	VERB
ejpam-4824	14	12	it	it	PRON
ejpam-4824	14	13	possible	possible	ADJ
ejpam-4824	14	14	to	to	PART
ejpam-4824	14	15	work	work	VERB
ejpam-4824	14	16	with	with	ADP
ejpam-4824	14	17	any	any	DET
ejpam-4824	14	18	d	d	ADJ
ejpam-4824	14	19	-	-	PUNCT
ejpam-4824	14	20	level	level	NOUN
ejpam-4824	14	21	qudits	qudit	VERB
ejpam-4824	14	22	one	one	NUM
ejpam-4824	14	23	needs	need	NOUN
ejpam-4824	14	24	to	to	PART
ejpam-4824	14	25	have	have	VERB
ejpam-4824	14	26	quantum	quantum	ADJ
ejpam-4824	14	27	logic	logic	NOUN
ejpam-4824	14	28	gates	gate	NOUN
ejpam-4824	14	29	that	that	PRON
ejpam-4824	14	30	could	could	AUX
ejpam-4824	14	31	operate	operate	VERB
ejpam-4824	14	32	on	on	ADP
ejpam-4824	14	33	them	they	PRON
ejpam-4824	14	34	.	.	PUNCT
ejpam-4824	15	1	the	the	DET
ejpam-4824	15	2	familiar	familiar	ADJ
ejpam-4824	15	3	swap	swap	NOUN
ejpam-4824	15	4	gate	gate	NOUN
ejpam-4824	15	5	(	(	PUNCT
ejpam-4824	15	6	swap	swap	NOUN
ejpam-4824	15	7	)	)	PUNCT
ejpam-4824	15	8	and	and	CCONJ
ejpam-4824	15	9	iswap	iswap	PROPN
ejpam-4824	15	10	gate	gate	PROPN
ejpam-4824	15	11	(	(	PUNCT
ejpam-4824	15	12	iswap	iswap	PROPN
ejpam-4824	15	13	)	)	PUNCT
ejpam-4824	15	14	are	be	AUX
ejpam-4824	15	15	among	among	ADP
ejpam-4824	15	16	most	most	ADV
ejpam-4824	15	17	important	important	ADJ
ejpam-4824	15	18	quantum	quantum	ADJ
ejpam-4824	15	19	gates	gate	NOUN
ejpam-4824	15	20	in	in	ADP
ejpam-4824	15	21	quantum	quantum	NOUN
ejpam-4824	15	22	computing	computing	NOUN
ejpam-4824	15	23	(	(	PUNCT
ejpam-4824	15	24	for	for	ADP
ejpam-4824	15	25	d	d	PROPN
ejpam-4824	15	26	=	=	SYM
ejpam-4824	15	27	2	2	NUM
ejpam-4824	15	28	)	)	PUNCT
ejpam-4824	15	29	.	.	PUNCT
ejpam-4824	16	1	their	their	PRON
ejpam-4824	16	2	generalization	generalization	NOUN
ejpam-4824	16	3	from	from	ADP
ejpam-4824	16	4	different	different	ADJ
ejpam-4824	16	5	point	point	NOUN
ejpam-4824	16	6	of	of	ADP
ejpam-4824	16	7	views	view	NOUN
ejpam-4824	16	8	,	,	PUNCT
ejpam-4824	16	9	and	and	CCONJ
ejpam-4824	16	10	their	their	PRON
ejpam-4824	16	11	physical	physical	ADJ
ejpam-4824	16	12	implementation	implementation	NOUN
ejpam-4824	16	13	are	be	AUX
ejpam-4824	16	14	active	active	ADJ
ejpam-4824	16	15	topics	topic	NOUN
ejpam-4824	16	16	of	of	ADP
ejpam-4824	16	17	research	research	NOUN
ejpam-4824	16	18	[	[	X
ejpam-4824	16	19	2	2	NUM
ejpam-4824	16	20	,	,	PUNCT
ejpam-4824	16	21	4	4	NUM
ejpam-4824	16	22	–	–	PUNCT
ejpam-4824	16	23	6	6	NUM
ejpam-4824	16	24	,	,	PUNCT
ejpam-4824	16	25	10	10	NUM
ejpam-4824	16	26	,	,	PUNCT
ejpam-4824	16	27	14–16	14–16	NUM
ejpam-4824	16	28	]	]	PUNCT
ejpam-4824	16	29	.	.	PUNCT
ejpam-4824	17	1	our	our	PRON
ejpam-4824	17	2	aim	aim	NOUN
ejpam-4824	17	3	in	in	ADP
ejpam-4824	17	4	this	this	DET
ejpam-4824	17	5	work	work	NOUN
ejpam-4824	17	6	is	be	AUX
ejpam-4824	17	7	to	to	PART
ejpam-4824	17	8	explicitly	explicitly	ADV
ejpam-4824	17	9	extend	extend	VERB
ejpam-4824	17	10	the	the	DET
ejpam-4824	17	11	well	well	ADV
ejpam-4824	17	12	known	know	VERB
ejpam-4824	17	13	swap	swap	NOUN
ejpam-4824	17	14	and	and	CCONJ
ejpam-4824	17	15	iswap	iswap	NOUN
ejpam-4824	17	16	gates	gate	NOUN
ejpam-4824	17	17	from	from	ADP
ejpam-4824	17	18	dimension	dimension	NOUN
ejpam-4824	17	19	d	d	NOUN
ejpam-4824	17	20	=	=	SYM
ejpam-4824	17	21	2	2	NUM
ejpam-4824	17	22	to	to	ADP
ejpam-4824	17	23	any	any	DET
ejpam-4824	17	24	dimension	dimension	NOUN
ejpam-4824	17	25	d	d	X
ejpam-4824	17	26	≥	≥	NUM
ejpam-4824	17	27	2	2	NUM
ejpam-4824	17	28	,	,	PUNCT
ejpam-4824	17	29	from	from	ADP
ejpam-4824	17	30	the	the	DET
ejpam-4824	17	31	point	point	NOUN
ejpam-4824	17	32	of	of	ADP
ejpam-4824	17	33	view	view	NOUN
ejpam-4824	17	34	of	of	ADP
ejpam-4824	17	35	their	their	PRON
ejpam-4824	17	36	representations	representation	NOUN
ejpam-4824	17	37	in	in	ADP
ejpam-4824	17	38	terms	term	NOUN
ejpam-4824	17	39	of	of	ADP
ejpam-4824	17	40	permutation	permutation	NOUN
ejpam-4824	17	41	matrices	matrix	NOUN
ejpam-4824	17	42	.	.	PUNCT
ejpam-4824	18	1	to	to	PART
ejpam-4824	18	2	do	do	VERB
ejpam-4824	18	3	this	this	PRON
ejpam-4824	18	4	we	we	PRON
ejpam-4824	18	5	first	first	ADV
ejpam-4824	18	6	unify	unify	VERB
ejpam-4824	18	7	these	these	DET
ejpam-4824	18	8	gates	gate	NOUN
ejpam-4824	18	9	by	by	ADP
ejpam-4824	18	10	introducing	introduce	VERB
ejpam-4824	18	11	a	a	DET
ejpam-4824	18	12	more	more	ADV
ejpam-4824	18	13	general	general	ADJ
ejpam-4824	18	14	gate	gate	NOUN
ejpam-4824	18	15	xswap	xswap	PROPN
ejpam-4824	18	16	which	which	PRON
ejpam-4824	18	17	includes	include	VERB
ejpam-4824	18	18	swap	swap	NOUN
ejpam-4824	18	19	and	and	CCONJ
ejpam-4824	18	20	iswap	iswap	NOUN
ejpam-4824	18	21	for	for	ADP
ejpam-4824	18	22	x	x	SYM
ejpam-4824	18	23	=	=	SYM
ejpam-4824	18	24	1	1	NUM
ejpam-4824	18	25	and	and	CCONJ
ejpam-4824	18	26	x	x	X
ejpam-4824	19	1	=	=	VERB
ejpam-4824	19	2	i	i	PRON
ejpam-4824	19	3	(	(	PUNCT
ejpam-4824	19	4	√	√	NUM
ejpam-4824	19	5	−1	−1	NOUN
ejpam-4824	19	6	)	)	PUNCT
ejpam-4824	19	7	,	,	PUNCT
ejpam-4824	19	8	respectively	respectively	ADV
ejpam-4824	19	9	.	.	PUNCT
ejpam-4824	20	1	these	these	DET
ejpam-4824	20	2	higher	high	ADJ
ejpam-4824	20	3	dimensional	dimensional	ADJ
ejpam-4824	20	4	gates	gate	NOUN
ejpam-4824	20	5	are	be	AUX
ejpam-4824	20	6	quantum	quantum	ADJ
ejpam-4824	20	7	logic	logic	NOUN
ejpam-4824	20	8	gates	gate	NOUN
ejpam-4824	20	9	for	for	ADP
ejpam-4824	20	10	d	d	NOUN
ejpam-4824	20	11	-	-	PUNCT
ejpam-4824	20	12	level	level	NOUN
ejpam-4824	20	13	qudit	qudit	NOUN
ejpam-4824	20	14	doi	doi	NOUN
ejpam-4824	20	15	:	:	PUNCT
ejpam-4824	20	16	https://doi.org/10.29020/nybg.ejpam.v16i3.4824	https://doi.org/10.29020/nybg.ejpam.v16i3.4824	DET
ejpam-4824	20	17	email	email	NOUN
ejpam-4824	20	18	address	address	NOUN
ejpam-4824	20	19	:	:	PUNCT
ejpam-4824	20	20	arash.pourkia@aum.edu.kw	arash.pourkia@aum.edu.kw	PROPN
ejpam-4824	20	21	(	(	PUNCT
ejpam-4824	20	22	a.	a.	NOUN
ejpam-4824	20	23	pourkia	pourkia	NOUN
ejpam-4824	20	24	)	)	PUNCT
ejpam-4824	20	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4824	20	26	1695	1695	NUM
ejpam-4824	20	27	©	©	PROPN
ejpam-4824	20	28	2023	2023	NUM
ejpam-4824	20	29	ejpam	ejpam	NOUN
ejpam-4824	20	30	all	all	DET
ejpam-4824	20	31	rights	right	NOUN
ejpam-4824	20	32	reserved	reserve	VERB
ejpam-4824	20	33	.	.	PUNCT
ejpam-4824	21	1	a.	a.	NOUN
ejpam-4824	21	2	pourkia	pourkia	PROPN
ejpam-4824	21	3	/	/	SYM
ejpam-4824	21	4	eur	eur	PROPN
ejpam-4824	21	5	.	.	PUNCT
ejpam-4824	22	1	j.	j.	PROPN
ejpam-4824	22	2	pure	pure	PROPN
ejpam-4824	22	3	appl	appl	PROPN
ejpam-4824	22	4	.	.	PROPN
ejpam-4824	22	5	math	math	PROPN
ejpam-4824	22	6	,	,	PUNCT
ejpam-4824	22	7	16	16	NUM
ejpam-4824	22	8	(	(	PUNCT
ejpam-4824	22	9	3	3	NUM
ejpam-4824	22	10	)	)	PUNCT
ejpam-4824	22	11	(	(	PUNCT
ejpam-4824	22	12	2023	2023	NUM
ejpam-4824	22	13	)	)	PUNCT
ejpam-4824	22	14	,	,	PUNCT
ejpam-4824	22	15	1695	1695	NUM
ejpam-4824	22	16	-	-	SYM
ejpam-4824	22	17	1704	1704	NUM
ejpam-4824	22	18	1696	1696	NUM
ejpam-4824	22	19	systems	system	NOUN
ejpam-4824	22	20	.	.	PUNCT
ejpam-4824	23	1	our	our	PRON
ejpam-4824	23	2	explicit	explicit	ADJ
ejpam-4824	23	3	representation	representation	NOUN
ejpam-4824	23	4	in	in	ADP
ejpam-4824	23	5	terms	term	NOUN
ejpam-4824	23	6	of	of	ADP
ejpam-4824	23	7	permutation	permutation	NOUN
ejpam-4824	23	8	matrix	matrix	NOUN
ejpam-4824	23	9	will	will	AUX
ejpam-4824	23	10	play	play	VERB
ejpam-4824	23	11	a	a	DET
ejpam-4824	23	12	crucial	crucial	ADJ
ejpam-4824	23	13	role	role	NOUN
ejpam-4824	23	14	in	in	ADP
ejpam-4824	23	15	helping	help	VERB
ejpam-4824	23	16	us	we	PRON
ejpam-4824	23	17	to	to	PART
ejpam-4824	23	18	prove	prove	VERB
ejpam-4824	23	19	that	that	SCONJ
ejpam-4824	23	20	for	for	SCONJ
ejpam-4824	23	21	x	x	SYM
ejpam-4824	23	22	̸=	̸=	PROPN
ejpam-4824	23	23	±1	±1	VERB
ejpam-4824	23	24	,	,	PUNCT
ejpam-4824	23	25	xswap	xswap	PROPN
ejpam-4824	23	26	is	be	AUX
ejpam-4824	23	27	a	a	DET
ejpam-4824	23	28	universal	universal	ADJ
ejpam-4824	23	29	quantum	quantum	NOUN
ejpam-4824	23	30	gate	gate	NOUN
ejpam-4824	23	31	,	,	PUNCT
ejpam-4824	23	32	analogous	analogous	ADJ
ejpam-4824	23	33	to	to	ADP
ejpam-4824	23	34	the	the	DET
ejpam-4824	23	35	well	well	ADV
ejpam-4824	23	36	known	know	VERB
ejpam-4824	23	37	fact	fact	NOUN
ejpam-4824	23	38	about	about	ADP
ejpam-4824	23	39	iswap	iswap	NOUN
ejpam-4824	23	40	for	for	ADP
ejpam-4824	23	41	d	d	PROPN
ejpam-4824	23	42	=	=	SYM
ejpam-4824	23	43	2	2	NUM
ejpam-4824	23	44	.	.	PUNCT
ejpam-4824	23	45	to	to	PART
ejpam-4824	23	46	do	do	VERB
ejpam-4824	23	47	this	this	PRON
ejpam-4824	23	48	we	we	PRON
ejpam-4824	23	49	will	will	AUX
ejpam-4824	23	50	use	use	VERB
ejpam-4824	23	51	the	the	DET
ejpam-4824	23	52	universality	universality	NOUN
ejpam-4824	23	53	criterion	criterion	NOUN
ejpam-4824	23	54	in	in	ADP
ejpam-4824	23	55	[	[	X
ejpam-4824	23	56	3	3	NUM
ejpam-4824	23	57	]	]	PUNCT
ejpam-4824	23	58	and	and	CCONJ
ejpam-4824	23	59	the	the	DET
ejpam-4824	23	60	non	non	ADJ
ejpam-4824	23	61	-	-	ADJ
ejpam-4824	23	62	entangling	entangle	VERB
ejpam-4824	23	63	criteria	criterion	NOUN
ejpam-4824	23	64	in	in	ADP
ejpam-4824	23	65	[	[	X
ejpam-4824	23	66	1	1	NUM
ejpam-4824	23	67	]	]	PUNCT
ejpam-4824	23	68	.	.	PUNCT
ejpam-4824	24	1	this	this	DET
ejpam-4824	24	2	paper	paper	NOUN
ejpam-4824	24	3	is	be	AUX
ejpam-4824	24	4	organized	organize	VERB
ejpam-4824	24	5	as	as	SCONJ
ejpam-4824	24	6	follows	follow	VERB
ejpam-4824	24	7	.	.	PUNCT
ejpam-4824	25	1	in	in	ADP
ejpam-4824	25	2	section	section	NOUN
ejpam-4824	25	3	2	2	NUM
ejpam-4824	25	4	,	,	PUNCT
ejpam-4824	25	5	we	we	PRON
ejpam-4824	25	6	recall	recall	VERB
ejpam-4824	25	7	some	some	DET
ejpam-4824	25	8	preliminary	preliminary	ADJ
ejpam-4824	25	9	notions	notion	NOUN
ejpam-4824	25	10	and	and	CCONJ
ejpam-4824	25	11	notations	notation	NOUN
ejpam-4824	25	12	.	.	PUNCT
ejpam-4824	26	1	in	in	ADP
ejpam-4824	26	2	section	section	NOUN
ejpam-4824	26	3	3	3	NUM
ejpam-4824	26	4	in	in	ADP
ejpam-4824	26	5	definition	definition	NOUN
ejpam-4824	26	6	1	1	NUM
ejpam-4824	26	7	,	,	PUNCT
ejpam-4824	26	8	we	we	PRON
ejpam-4824	26	9	give	give	VERB
ejpam-4824	26	10	an	an	DET
ejpam-4824	26	11	explicit	explicit	ADJ
ejpam-4824	26	12	description	description	NOUN
ejpam-4824	26	13	for	for	ADP
ejpam-4824	26	14	the	the	DET
ejpam-4824	26	15	higher	high	ADJ
ejpam-4824	26	16	dimensional	dimensional	ADJ
ejpam-4824	26	17	xswap	xswap	NOUN
ejpam-4824	26	18	(	(	PUNCT
ejpam-4824	26	19	hence	hence	ADV
ejpam-4824	26	20	swap	swap	NOUN
ejpam-4824	26	21	and	and	CCONJ
ejpam-4824	26	22	iswap	iswap	NOUN
ejpam-4824	26	23	)	)	PUNCT
ejpam-4824	26	24	in	in	ADP
ejpam-4824	26	25	terms	term	NOUN
ejpam-4824	26	26	of	of	ADP
ejpam-4824	26	27	permutation	permutation	NOUN
ejpam-4824	26	28	matrices	matrix	NOUN
ejpam-4824	26	29	.	.	PUNCT
ejpam-4824	27	1	in	in	ADP
ejpam-4824	27	2	section	section	NOUN
ejpam-4824	27	3	4	4	NUM
ejpam-4824	27	4	in	in	ADP
ejpam-4824	27	5	theorem	theorem	NOUN
ejpam-4824	27	6	1	1	NUM
ejpam-4824	27	7	,	,	PUNCT
ejpam-4824	27	8	we	we	PRON
ejpam-4824	27	9	prove	prove	VERB
ejpam-4824	27	10	that	that	SCONJ
ejpam-4824	27	11	the	the	DET
ejpam-4824	27	12	quantum	quantum	PROPN
ejpam-4824	27	13	gate	gate	NOUN
ejpam-4824	27	14	xswap	xswap	PROPN
ejpam-4824	27	15	is	be	AUX
ejpam-4824	27	16	universal	universal	ADJ
ejpam-4824	27	17	for	for	SCONJ
ejpam-4824	27	18	x	x	SYM
ejpam-4824	27	19	̸=	̸=	PROPN
ejpam-4824	27	20	±1	±1	VERB
ejpam-4824	27	21	.	.	PUNCT
ejpam-4824	28	1	we	we	PRON
ejpam-4824	28	2	will	will	AUX
ejpam-4824	28	3	finish	finish	VERB
ejpam-4824	28	4	this	this	DET
ejpam-4824	28	5	paper	paper	NOUN
ejpam-4824	28	6	with	with	ADP
ejpam-4824	28	7	concluding	conclude	VERB
ejpam-4824	28	8	remarks	remark	NOUN
ejpam-4824	28	9	in	in	ADP
ejpam-4824	28	10	section	section	NOUN
ejpam-4824	28	11	5	5	NUM
ejpam-4824	28	12	.	.	NOUN
ejpam-4824	28	13	2	2	NUM
ejpam-4824	28	14	.	.	NOUN
ejpam-4824	28	15	preliminaries	preliminary	NOUN
ejpam-4824	28	16	and	and	CCONJ
ejpam-4824	28	17	notations	notation	NOUN
ejpam-4824	28	18	let	let	VERB
ejpam-4824	28	19	us	we	PRON
ejpam-4824	28	20	recall	recall	VERB
ejpam-4824	28	21	that	that	SCONJ
ejpam-4824	28	22	in	in	ADP
ejpam-4824	28	23	quantum	quantum	NOUN
ejpam-4824	28	24	computing	compute	VERB
ejpam-4824	28	25	quantum	quantum	ADJ
ejpam-4824	28	26	logic	logic	NOUN
ejpam-4824	28	27	gates	gate	NOUN
ejpam-4824	28	28	can	can	AUX
ejpam-4824	28	29	be	be	AUX
ejpam-4824	28	30	represented	represent	VERB
ejpam-4824	28	31	by	by	ADP
ejpam-4824	28	32	unitary	unitary	ADJ
ejpam-4824	28	33	matrices	matrix	NOUN
ejpam-4824	28	34	on	on	ADP
ejpam-4824	28	35	a	a	DET
ejpam-4824	28	36	hilbert	hilbert	NOUN
ejpam-4824	28	37	space	space	NOUN
ejpam-4824	28	38	h	h	NOUN
ejpam-4824	28	39	with	with	ADP
ejpam-4824	28	40	dimension	dimension	NOUN
ejpam-4824	28	41	d.	d.	PROPN
ejpam-4824	28	42	the	the	DET
ejpam-4824	28	43	qubit	qubit	NOUN
ejpam-4824	28	44	is	be	AUX
ejpam-4824	28	45	a	a	DET
ejpam-4824	28	46	basic	basic	ADJ
ejpam-4824	28	47	unit	unit	NOUN
ejpam-4824	28	48	of	of	ADP
ejpam-4824	28	49	quantum	quantum	ADJ
ejpam-4824	28	50	information	information	NOUN
ejpam-4824	28	51	in	in	ADP
ejpam-4824	28	52	dimension	dimension	NOUN
ejpam-4824	28	53	d	d	X
ejpam-4824	28	54	=	=	SYM
ejpam-4824	28	55	2	2	X
ejpam-4824	28	56	.	.	PUNCT
ejpam-4824	29	1	the	the	DET
ejpam-4824	29	2	qudit	qudit	NOUN
ejpam-4824	29	3	is	be	AUX
ejpam-4824	29	4	a	a	DET
ejpam-4824	29	5	generalization	generalization	NOUN
ejpam-4824	29	6	of	of	ADP
ejpam-4824	29	7	the	the	DET
ejpam-4824	29	8	qubit	qubit	NOUN
ejpam-4824	29	9	to	to	ADP
ejpam-4824	29	10	a	a	DET
ejpam-4824	29	11	larger	large	ADJ
ejpam-4824	29	12	hilbert	hilbert	NOUN
ejpam-4824	29	13	space	space	NOUN
ejpam-4824	29	14	of	of	ADP
ejpam-4824	29	15	dimension	dimension	NOUN
ejpam-4824	29	16	d	d	X
ejpam-4824	29	17	≥	≥	NUM
ejpam-4824	29	18	2	2	NUM
ejpam-4824	29	19	.	.	PUNCT
ejpam-4824	30	1	in	in	ADP
ejpam-4824	30	2	dimension	dimension	NOUN
ejpam-4824	30	3	d	d	X
ejpam-4824	30	4	=	=	SYM
ejpam-4824	30	5	2	2	NUM
ejpam-4824	30	6	,	,	PUNCT
ejpam-4824	30	7	i.e.	i.e.	X
ejpam-4824	30	8	for	for	ADP
ejpam-4824	30	9	qubit	qubit	NOUN
ejpam-4824	30	10	systems	system	NOUN
ejpam-4824	30	11	,	,	PUNCT
ejpam-4824	30	12	two	two	NUM
ejpam-4824	30	13	very	very	ADV
ejpam-4824	30	14	important	important	ADJ
ejpam-4824	30	15	examples	example	NOUN
ejpam-4824	30	16	of	of	ADP
ejpam-4824	30	17	quantum	quantum	ADJ
ejpam-4824	30	18	logic	logic	NOUN
ejpam-4824	30	19	gates	gate	NOUN
ejpam-4824	30	20	are	be	AUX
ejpam-4824	30	21	the	the	DET
ejpam-4824	30	22	swap	swap	NOUN
ejpam-4824	30	23	gate	gate	NOUN
ejpam-4824	30	24	(	(	PUNCT
ejpam-4824	30	25	swap	swap	NOUN
ejpam-4824	30	26	)	)	PUNCT
ejpam-4824	30	27	denoted	denote	VERB
ejpam-4824	30	28	here	here	ADV
ejpam-4824	30	29	by	by	ADP
ejpam-4824	30	30	s	s	PRON
ejpam-4824	30	31	and	and	CCONJ
ejpam-4824	30	32	the	the	DET
ejpam-4824	30	33	iswap	iswap	PROPN
ejpam-4824	30	34	gate	gate	NOUN
ejpam-4824	30	35	(	(	PUNCT
ejpam-4824	30	36	iswap	iswap	PROPN
ejpam-4824	30	37	)	)	PUNCT
ejpam-4824	30	38	denoted	denote	VERB
ejpam-4824	30	39	here	here	ADV
ejpam-4824	30	40	by	by	ADP
ejpam-4824	30	41	is	be	AUX
ejpam-4824	30	42	.	.	PUNCT
ejpam-4824	31	1	they	they	PRON
ejpam-4824	31	2	are	be	AUX
ejpam-4824	31	3	defined	define	VERB
ejpam-4824	31	4	as	as	SCONJ
ejpam-4824	31	5	follows	follow	VERB
ejpam-4824	31	6	.	.	PUNCT
ejpam-4824	32	1	s	s	PART
ejpam-4824	32	2	:	:	PUNCT
ejpam-4824	32	3	h	h	PROPN
ejpam-4824	32	4	⊗	⊗	PROPN
ejpam-4824	32	5	h	h	PROPN
ejpam-4824	32	6	→	→	SYM
ejpam-4824	32	7	h	h	NOUN
ejpam-4824	32	8	⊗	⊗	PROPN
ejpam-4824	32	9	h	h	PROPN
ejpam-4824	32	10	(	(	PUNCT
ejpam-4824	32	11	1	1	NUM
ejpam-4824	32	12	)	)	PUNCT
ejpam-4824	32	13	s(u⊗	s(u⊗	NOUN
ejpam-4824	32	14	v	v	NOUN
ejpam-4824	32	15	)	)	PUNCT
ejpam-4824	32	16	=	=	SYM
ejpam-4824	33	1	v	v	ADP
ejpam-4824	33	2	⊗	⊗	PROPN
ejpam-4824	33	3	u	u	NOUN
ejpam-4824	33	4	is	be	AUX
ejpam-4824	33	5	:	:	PUNCT
ejpam-4824	33	6	h	h	PROPN
ejpam-4824	33	7	⊗	⊗	PROPN
ejpam-4824	33	8	h	h	PROPN
ejpam-4824	33	9	→	→	SYM
ejpam-4824	33	10	h	h	NOUN
ejpam-4824	33	11	⊗	⊗	PROPN
ejpam-4824	33	12	h	h	PROPN
ejpam-4824	33	13	(	(	PUNCT
ejpam-4824	33	14	2	2	NUM
ejpam-4824	33	15	)	)	PUNCT
ejpam-4824	33	16	s(u⊗	s(u⊗	NOUN
ejpam-4824	33	17	v	v	NOUN
ejpam-4824	33	18	)	)	PUNCT
ejpam-4824	33	19	=	=	SYM
ejpam-4824	34	1	i(v	i(v	X
ejpam-4824	34	2	⊗	⊗	PROPN
ejpam-4824	34	3	u	u	NOUN
ejpam-4824	34	4	)	)	PUNCT
ejpam-4824	34	5	,	,	PUNCT
ejpam-4824	34	6	when	when	SCONJ
ejpam-4824	34	7	v	v	ADP
ejpam-4824	34	8	̸=	̸=	PROPN
ejpam-4824	34	9	u	u	NOUN
ejpam-4824	34	10	and	and	CCONJ
ejpam-4824	34	11	,	,	PUNCT
ejpam-4824	34	12	s(u⊗	s(u⊗	NOUN
ejpam-4824	34	13	u	u	NOUN
ejpam-4824	34	14	)	)	PUNCT
ejpam-4824	34	15	=	=	PUNCT
ejpam-4824	34	16	u⊗	u⊗	NOUN
ejpam-4824	34	17	u	u	NOUN
ejpam-4824	34	18	for	for	ADP
ejpam-4824	34	19	all	all	DET
ejpam-4824	34	20	u	u	NOUN
ejpam-4824	34	21	and	and	CCONJ
ejpam-4824	34	22	v	v	NOUN
ejpam-4824	34	23	in	in	ADP
ejpam-4824	34	24	h	h	NOUN
ejpam-4824	34	25	.	.	PUNCT
ejpam-4824	35	1	for	for	ADP
ejpam-4824	35	2	our	our	PRON
ejpam-4824	35	3	purpose	purpose	NOUN
ejpam-4824	35	4	in	in	ADP
ejpam-4824	35	5	this	this	DET
ejpam-4824	35	6	paper	paper	NOUN
ejpam-4824	35	7	it	it	PRON
ejpam-4824	35	8	is	be	AUX
ejpam-4824	35	9	enough	enough	ADJ
ejpam-4824	35	10	to	to	PART
ejpam-4824	35	11	consider	consider	VERB
ejpam-4824	35	12	h	h	NOUN
ejpam-4824	35	13	=	=	SYM
ejpam-4824	35	14	cd	cd	PROPN
ejpam-4824	35	15	,	,	PUNCT
ejpam-4824	35	16	as	as	SCONJ
ejpam-4824	35	17	this	this	PRON
ejpam-4824	35	18	is	be	AUX
ejpam-4824	35	19	enough	enough	ADJ
ejpam-4824	35	20	for	for	ADP
ejpam-4824	35	21	quantum	quantum	NOUN
ejpam-4824	35	22	computing	computing	NOUN
ejpam-4824	35	23	.	.	PUNCT
ejpam-4824	36	1	throughout	throughout	ADP
ejpam-4824	36	2	this	this	DET
ejpam-4824	36	3	paper	paper	NOUN
ejpam-4824	36	4	we	we	PRON
ejpam-4824	36	5	will	will	AUX
ejpam-4824	36	6	use	use	VERB
ejpam-4824	36	7	the	the	DET
ejpam-4824	36	8	standard	standard	ADJ
ejpam-4824	36	9	basis	basis	NOUN
ejpam-4824	36	10	for	for	ADP
ejpam-4824	36	11	cd	cd	PROPN
ejpam-4824	36	12	alongside	alongside	ADP
ejpam-4824	36	13	the	the	DET
ejpam-4824	36	14	ket	ket	NOUN
ejpam-4824	36	15	from	from	ADP
ejpam-4824	36	16	bra	bra	NOUN
ejpam-4824	36	17	–	–	PUNCT
ejpam-4824	36	18	ket	ket	NOUN
ejpam-4824	36	19	notation	notation	NOUN
ejpam-4824	36	20	common	common	ADJ
ejpam-4824	36	21	in	in	ADP
ejpam-4824	36	22	quantum	quantum	NOUN
ejpam-4824	36	23	computing	computing	NOUN
ejpam-4824	36	24	literature	literature	NOUN
ejpam-4824	36	25	(	(	PUNCT
ejpam-4824	36	26	{	{	PUNCT
ejpam-4824	36	27	|0⟩	|0⟩	PROPN
ejpam-4824	36	28	,	,	PUNCT
ejpam-4824	36	29	|1⟩	|1⟩	PROPN
ejpam-4824	36	30	,	,	PUNCT
ejpam-4824	36	31	|2⟩	|2⟩	NOUN
ejpam-4824	36	32	,	,	PUNCT
ejpam-4824	36	33	·	·	PUNCT
ejpam-4824	36	34	·	·	PUNCT
ejpam-4824	36	35	·	·	PUNCT
ejpam-4824	36	36	,	,	PUNCT
ejpam-4824	36	37	|d−	|d−	PROPN
ejpam-4824	36	38	1⟩	1⟩	NUM
ejpam-4824	36	39	}	}	PUNCT
ejpam-4824	36	40	)	)	PUNCT
ejpam-4824	36	41	.	.	PUNCT
ejpam-4824	37	1	a.	a.	NOUN
ejpam-4824	37	2	pourkia	pourkia	PROPN
ejpam-4824	37	3	/	/	SYM
ejpam-4824	37	4	eur	eur	PROPN
ejpam-4824	37	5	.	.	PUNCT
ejpam-4824	38	1	j.	j.	PROPN
ejpam-4824	38	2	pure	pure	PROPN
ejpam-4824	38	3	appl	appl	PROPN
ejpam-4824	38	4	.	.	PROPN
ejpam-4824	38	5	math	math	PROPN
ejpam-4824	38	6	,	,	PUNCT
ejpam-4824	38	7	16	16	NUM
ejpam-4824	38	8	(	(	PUNCT
ejpam-4824	38	9	3	3	NUM
ejpam-4824	38	10	)	)	PUNCT
ejpam-4824	38	11	(	(	PUNCT
ejpam-4824	38	12	2023	2023	NUM
ejpam-4824	38	13	)	)	PUNCT
ejpam-4824	38	14	,	,	PUNCT
ejpam-4824	38	15	1695	1695	NUM
ejpam-4824	38	16	-	-	SYM
ejpam-4824	38	17	1704	1704	NUM
ejpam-4824	38	18	1697	1697	NUM
ejpam-4824	38	19	by	by	ADP
ejpam-4824	38	20	|ab⟩	|ab⟩	NOUN
ejpam-4824	38	21	we	we	PRON
ejpam-4824	38	22	mean	mean	VERB
ejpam-4824	38	23	|a⟩	|a⟩	PROPN
ejpam-4824	38	24	⊗	⊗	PROPN
ejpam-4824	38	25	|b⟩	|b⟩	PROPN
ejpam-4824	38	26	,	,	PUNCT
ejpam-4824	38	27	where	where	SCONJ
ejpam-4824	38	28	⊗	⊗	PROPN
ejpam-4824	38	29	stands	stand	VERB
ejpam-4824	38	30	for	for	ADP
ejpam-4824	38	31	the	the	DET
ejpam-4824	38	32	tensor	tensor	NOUN
ejpam-4824	38	33	product	product	NOUN
ejpam-4824	38	34	.	.	PUNCT
ejpam-4824	39	1	therefore	therefore	ADV
ejpam-4824	39	2	,	,	PUNCT
ejpam-4824	39	3	for	for	ADP
ejpam-4824	39	4	example	example	NOUN
ejpam-4824	39	5	in	in	ADP
ejpam-4824	39	6	dimension	dimension	NOUN
ejpam-4824	39	7	d	d	PROPN
ejpam-4824	39	8	=	=	SYM
ejpam-4824	39	9	2	2	NUM
ejpam-4824	39	10	,	,	PUNCT
ejpam-4824	39	11	for	for	ADP
ejpam-4824	39	12	c2	c2	PROPN
ejpam-4824	39	13	⊗c2	⊗c2	PROPN
ejpam-4824	39	14	,	,	PUNCT
ejpam-4824	39	15	we	we	PRON
ejpam-4824	39	16	use	use	VERB
ejpam-4824	39	17	the	the	DET
ejpam-4824	39	18	computational	computational	ADJ
ejpam-4824	39	19	basis	basis	NOUN
ejpam-4824	39	20	for	for	ADP
ejpam-4824	39	21	2	2	NUM
ejpam-4824	39	22	-	-	PUNCT
ejpam-4824	39	23	qubit	qubit	NOUN
ejpam-4824	39	24	states	state	NOUN
ejpam-4824	39	25	,	,	PUNCT
ejpam-4824	39	26	{	{	PUNCT
ejpam-4824	39	27	|00⟩	|00⟩	NOUN
ejpam-4824	39	28	,	,	PUNCT
ejpam-4824	39	29	|01⟩	|01⟩	ADJ
ejpam-4824	39	30	,	,	PUNCT
ejpam-4824	39	31	|10⟩	|10⟩	ADJ
ejpam-4824	39	32	,	,	PUNCT
ejpam-4824	39	33	|11⟩	|11⟩	NOUN
ejpam-4824	39	34	}	}	PUNCT
ejpam-4824	39	35	.	.	PUNCT
ejpam-4824	40	1	or	or	CCONJ
ejpam-4824	40	2	in	in	ADP
ejpam-4824	40	3	dimension	dimension	NOUN
ejpam-4824	40	4	d	d	X
ejpam-4824	40	5	=	=	SYM
ejpam-4824	40	6	3	3	NUM
ejpam-4824	40	7	,	,	PUNCT
ejpam-4824	40	8	for	for	ADP
ejpam-4824	40	9	c3	c3	PROPN
ejpam-4824	40	10	⊗	⊗	PROPN
ejpam-4824	40	11	c3	c3	PROPN
ejpam-4824	40	12	,	,	PUNCT
ejpam-4824	40	13	we	we	PRON
ejpam-4824	40	14	use	use	VERB
ejpam-4824	40	15	the	the	DET
ejpam-4824	40	16	computational	computational	ADJ
ejpam-4824	40	17	basis	basis	NOUN
ejpam-4824	40	18	for	for	ADP
ejpam-4824	40	19	2	2	NUM
ejpam-4824	40	20	-	-	PUNCT
ejpam-4824	40	21	qudit	qudit	NOUN
ejpam-4824	40	22	states	state	NOUN
ejpam-4824	40	23	,	,	PUNCT
ejpam-4824	40	24	{	{	PUNCT
ejpam-4824	40	25	|00⟩	|00⟩	NOUN
ejpam-4824	40	26	,	,	PUNCT
ejpam-4824	40	27	|01⟩	|01⟩	ADJ
ejpam-4824	40	28	,	,	PUNCT
ejpam-4824	40	29	|02⟩	|02⟩	NOUN
ejpam-4824	40	30	,	,	PUNCT
ejpam-4824	40	31	|10⟩	|10⟩	ADJ
ejpam-4824	40	32	,	,	PUNCT
ejpam-4824	40	33	|11⟩	|11⟩	NOUN
ejpam-4824	40	34	,	,	PUNCT
ejpam-4824	40	35	|12⟩	|12⟩	ADJ
ejpam-4824	40	36	,	,	PUNCT
ejpam-4824	40	37	|20⟩	|20⟩	X
ejpam-4824	40	38	,	,	PUNCT
ejpam-4824	40	39	|21⟩	|21⟩	VERB
ejpam-4824	40	40	,	,	PUNCT
ejpam-4824	40	41	|22⟩	|22⟩	X
ejpam-4824	40	42	}	}	PUNCT
ejpam-4824	40	43	.	.	PUNCT
ejpam-4824	41	1	let	let	VERB
ejpam-4824	41	2	us	we	PRON
ejpam-4824	41	3	also	also	ADV
ejpam-4824	41	4	recall	recall	VERB
ejpam-4824	41	5	the	the	DET
ejpam-4824	41	6	following	following	NOUN
ejpam-4824	41	7	.	.	PUNCT
ejpam-4824	42	1	a	a	DET
ejpam-4824	42	2	quantum	quantum	ADJ
ejpam-4824	42	3	logic	logic	NOUN
ejpam-4824	42	4	gate	gate	NOUN
ejpam-4824	42	5	must	must	AUX
ejpam-4824	42	6	be	be	AUX
ejpam-4824	42	7	unitary	unitary	ADJ
ejpam-4824	42	8	by	by	ADP
ejpam-4824	42	9	definition	definition	NOUN
ejpam-4824	42	10	.	.	PUNCT
ejpam-4824	43	1	a	a	DET
ejpam-4824	43	2	quantum	quantum	ADJ
ejpam-4824	43	3	logic	logic	NOUN
ejpam-4824	43	4	gate	gate	NOUN
ejpam-4824	43	5	is	be	AUX
ejpam-4824	43	6	entangling	entangle	VERB
ejpam-4824	43	7	if	if	SCONJ
ejpam-4824	43	8	it	it	PRON
ejpam-4824	43	9	can	can	AUX
ejpam-4824	43	10	produce	produce	VERB
ejpam-4824	43	11	entangled	entangle	VERB
ejpam-4824	43	12	states	state	NOUN
ejpam-4824	43	13	by	by	ADP
ejpam-4824	43	14	acting	act	VERB
ejpam-4824	43	15	on	on	ADP
ejpam-4824	43	16	unentangled	unentangled	ADJ
ejpam-4824	43	17	ones	one	NOUN
ejpam-4824	43	18	.	.	PUNCT
ejpam-4824	44	1	a	a	DET
ejpam-4824	44	2	2	2	NUM
ejpam-4824	44	3	-	-	PUNCT
ejpam-4824	44	4	qudit	qudit	NOUN
ejpam-4824	44	5	gate	gate	NOUN
ejpam-4824	44	6	g	g	PROPN
ejpam-4824	44	7	(	(	PUNCT
ejpam-4824	44	8	i.e.	i.e.	X
ejpam-4824	44	9	a	a	DET
ejpam-4824	44	10	gate	gate	NOUN
ejpam-4824	44	11	that	that	PRON
ejpam-4824	44	12	operates	operate	VERB
ejpam-4824	44	13	on	on	ADP
ejpam-4824	44	14	two	two	NUM
ejpam-4824	44	15	d	d	ADJ
ejpam-4824	44	16	-	-	PUNCT
ejpam-4824	44	17	level	level	NOUN
ejpam-4824	44	18	qudits	qudit	NOUN
ejpam-4824	44	19	)	)	PUNCT
ejpam-4824	44	20	is	be	AUX
ejpam-4824	44	21	universal	universal	ADJ
ejpam-4824	44	22	if	if	SCONJ
ejpam-4824	44	23	the	the	DET
ejpam-4824	44	24	set	set	NOUN
ejpam-4824	44	25	containing	contain	VERB
ejpam-4824	44	26	g	g	NOUN
ejpam-4824	44	27	and	and	CCONJ
ejpam-4824	44	28	all	all	DET
ejpam-4824	44	29	1	1	NUM
ejpam-4824	44	30	-	-	PUNCT
ejpam-4824	44	31	qudit	qudit	NOUN
ejpam-4824	44	32	gates	gate	NOUN
ejpam-4824	44	33	is	be	AUX
ejpam-4824	44	34	enough	enough	ADJ
ejpam-4824	44	35	to	to	PART
ejpam-4824	44	36	generate	generate	VERB
ejpam-4824	44	37	all	all	DET
ejpam-4824	44	38	qudit	qudit	NOUN
ejpam-4824	44	39	gates	gate	NOUN
ejpam-4824	44	40	.	.	PUNCT
ejpam-4824	45	1	it	it	PRON
ejpam-4824	45	2	is	be	AUX
ejpam-4824	45	3	well	well	ADV
ejpam-4824	45	4	known	know	VERB
ejpam-4824	45	5	that	that	SCONJ
ejpam-4824	45	6	,	,	PUNCT
ejpam-4824	45	7	a	a	DET
ejpam-4824	45	8	quantum	quantum	ADJ
ejpam-4824	45	9	logic	logic	NOUN
ejpam-4824	45	10	gate	gate	NOUN
ejpam-4824	45	11	operating	operate	VERB
ejpam-4824	45	12	on	on	ADP
ejpam-4824	45	13	two	two	NUM
ejpam-4824	45	14	d	d	ADJ
ejpam-4824	45	15	-	-	PUNCT
ejpam-4824	45	16	level	level	NOUN
ejpam-4824	45	17	qudits	qudit	NOUN
ejpam-4824	45	18	is	be	AUX
ejpam-4824	45	19	universal	universal	ADJ
ejpam-4824	45	20	for	for	ADP
ejpam-4824	45	21	quantum	quantum	NOUN
ejpam-4824	45	22	computing	computing	NOUN
ejpam-4824	46	1	[	[	X
ejpam-4824	46	2	6	6	NUM
ejpam-4824	46	3	]	]	PUNCT
ejpam-4824	46	4	,	,	PUNCT
ejpam-4824	46	5	if	if	SCONJ
ejpam-4824	46	6	and	and	CCONJ
ejpam-4824	46	7	only	only	ADV
ejpam-4824	46	8	if	if	SCONJ
ejpam-4824	46	9	it	it	PRON
ejpam-4824	46	10	is	be	AUX
ejpam-4824	46	11	entangling	entangle	VERB
ejpam-4824	46	12	[	[	X
ejpam-4824	46	13	3	3	NUM
ejpam-4824	46	14	]	]	PUNCT
ejpam-4824	46	15	.	.	PUNCT
ejpam-4824	47	1	3	3	X
ejpam-4824	47	2	.	.	X
ejpam-4824	47	3	swap	swap	NOUN
ejpam-4824	47	4	and	and	CCONJ
ejpam-4824	47	5	iswap	iswap	NOUN
ejpam-4824	47	6	in	in	ADP
ejpam-4824	47	7	higher	high	ADJ
ejpam-4824	47	8	dimensions	dimension	NOUN
ejpam-4824	47	9	and	and	CCONJ
ejpam-4824	47	10	general	general	ADJ
ejpam-4824	47	11	xswap	xswap	PROPN
ejpam-4824	47	12	for	for	ADP
ejpam-4824	47	13	d	d	PROPN
ejpam-4824	47	14	=	=	SYM
ejpam-4824	47	15	2	2	NUM
ejpam-4824	47	16	the	the	DET
ejpam-4824	47	17	swap	swap	NOUN
ejpam-4824	47	18	and	and	CCONJ
ejpam-4824	47	19	iswap	iswap	NOUN
ejpam-4824	47	20	defined	define	VERB
ejpam-4824	47	21	by	by	ADP
ejpam-4824	47	22	(	(	PUNCT
ejpam-4824	47	23	1	1	NUM
ejpam-4824	47	24	)	)	PUNCT
ejpam-4824	47	25	and	and	CCONJ
ejpam-4824	47	26	(	(	PUNCT
ejpam-4824	47	27	2	2	X
ejpam-4824	47	28	)	)	PUNCT
ejpam-4824	47	29	are	be	AUX
ejpam-4824	47	30	represented	represent	VERB
ejpam-4824	47	31	by	by	ADP
ejpam-4824	47	32	the	the	DET
ejpam-4824	47	33	following	follow	VERB
ejpam-4824	47	34	permutation	permutation	NOUN
ejpam-4824	47	35	matrices	matrix	NOUN
ejpam-4824	47	36	s4	s4	PROPN
ejpam-4824	47	37	and	and	CCONJ
ejpam-4824	47	38	is4	is4	NOUN
ejpam-4824	47	39	(	(	PUNCT
ejpam-4824	47	40	or	or	CCONJ
ejpam-4824	47	41	s	s	VERB
ejpam-4824	47	42	and	and	CCONJ
ejpam-4824	47	43	is	be	AUX
ejpam-4824	47	44	for	for	ADP
ejpam-4824	47	45	short	short	ADJ
ejpam-4824	47	46	if	if	SCONJ
ejpam-4824	47	47	there	there	PRON
ejpam-4824	47	48	is	be	VERB
ejpam-4824	47	49	no	no	DET
ejpam-4824	47	50	confusion	confusion	NOUN
ejpam-4824	47	51	about	about	ADP
ejpam-4824	47	52	the	the	DET
ejpam-4824	47	53	dimensions	dimension	NOUN
ejpam-4824	47	54	)	)	PUNCT
ejpam-4824	47	55	s4	s4	PROPN
ejpam-4824	47	56	=	=	SYM
ejpam-4824	47	57			PROPN
ejpam-4824	47	58	1	1	NUM
ejpam-4824	47	59	0	0	NUM
ejpam-4824	47	60	0	0	NUM
ejpam-4824	47	61	0	0	NUM
ejpam-4824	47	62	0	0	NUM
ejpam-4824	47	63	0	0	NUM
ejpam-4824	47	64	1	1	NUM
ejpam-4824	47	65	0	0	NUM
ejpam-4824	47	66	0	0	NUM
ejpam-4824	47	67	1	1	NUM
ejpam-4824	47	68	0	0	NUM
ejpam-4824	47	69	0	0	NUM
ejpam-4824	47	70	0	0	NUM
ejpam-4824	47	71	0	0	NUM
ejpam-4824	47	72	0	0	NUM
ejpam-4824	47	73	1	1	NUM
ejpam-4824	47	74			NOUN
ejpam-4824	47	75	,	,	PUNCT
ejpam-4824	47	76	is4	is4	NOUN
ejpam-4824	47	77	=	=	SYM
ejpam-4824	47	78			ADJ
ejpam-4824	48	1	1	1	NUM
ejpam-4824	48	2	0	0	NUM
ejpam-4824	48	3	0	0	NUM
ejpam-4824	48	4	0	0	NUM
ejpam-4824	48	5	0	0	NUM
ejpam-4824	48	6	0	0	NUM
ejpam-4824	48	7	i	i	NOUN
ejpam-4824	48	8	0	0	NUM
ejpam-4824	48	9	0	0	PUNCT
ejpam-4824	48	10	i	i	NOUN
ejpam-4824	48	11	0	0	NUM
ejpam-4824	48	12	0	0	NUM
ejpam-4824	48	13	0	0	NUM
ejpam-4824	48	14	0	0	NUM
ejpam-4824	48	15	0	0	NUM
ejpam-4824	48	16	1	1	NUM
ejpam-4824	48	17			NOUN
ejpam-4824	48	18	(	(	PUNCT
ejpam-4824	48	19	3	3	NUM
ejpam-4824	48	20	)	)	PUNCT
ejpam-4824	48	21	before	before	SCONJ
ejpam-4824	48	22	we	we	PRON
ejpam-4824	48	23	move	move	VERB
ejpam-4824	48	24	to	to	ADP
ejpam-4824	48	25	the	the	DET
ejpam-4824	48	26	higher	high	ADJ
ejpam-4824	48	27	dimensions	dimension	NOUN
ejpam-4824	48	28	let	let	VERB
ejpam-4824	48	29	us	we	PRON
ejpam-4824	48	30	first	first	ADV
ejpam-4824	48	31	unify	unify	VERB
ejpam-4824	48	32	these	these	DET
ejpam-4824	48	33	gates	gate	NOUN
ejpam-4824	48	34	by	by	ADP
ejpam-4824	48	35	introducing	introduce	VERB
ejpam-4824	48	36	a	a	DET
ejpam-4824	48	37	more	more	ADV
ejpam-4824	48	38	general	general	ADJ
ejpam-4824	48	39	gate	gate	NOUN
ejpam-4824	48	40	xswap	xswap	PROPN
ejpam-4824	48	41	(	(	PUNCT
ejpam-4824	48	42	denoted	denote	VERB
ejpam-4824	48	43	here	here	ADV
ejpam-4824	48	44	by	by	ADP
ejpam-4824	48	45	xs4	xs4	PROPN
ejpam-4824	48	46	or	or	CCONJ
ejpam-4824	48	47	xs	xs	PROPN
ejpam-4824	48	48	for	for	ADP
ejpam-4824	48	49	short	short	ADJ
ejpam-4824	48	50	)	)	PUNCT
ejpam-4824	48	51	as	as	SCONJ
ejpam-4824	48	52	follows	follow	VERB
ejpam-4824	48	53	:	:	PUNCT
ejpam-4824	48	54	xs4	xs4	X
ejpam-4824	48	55	=	=	PUNCT
ejpam-4824	48	56			VERB
ejpam-4824	48	57	1	1	NUM
ejpam-4824	48	58	0	0	NUM
ejpam-4824	48	59	0	0	NUM
ejpam-4824	48	60	0	0	NUM
ejpam-4824	48	61	0	0	NUM
ejpam-4824	48	62	0	0	NUM
ejpam-4824	49	1	x	x	SYM
ejpam-4824	49	2	0	0	NUM
ejpam-4824	49	3	0	0	NUM
ejpam-4824	49	4	x	x	SYM
ejpam-4824	49	5	0	0	NUM
ejpam-4824	49	6	0	0	NUM
ejpam-4824	49	7	0	0	NUM
ejpam-4824	49	8	0	0	NUM
ejpam-4824	49	9	0	0	NUM
ejpam-4824	49	10	1	1	NUM
ejpam-4824	49	11			NOUN
ejpam-4824	49	12	(	(	PUNCT
ejpam-4824	49	13	4	4	NUM
ejpam-4824	49	14	)	)	PUNCT
ejpam-4824	49	15	where	where	SCONJ
ejpam-4824	49	16	x	x	SYM
ejpam-4824	49	17	=	=	SYM
ejpam-4824	49	18	eiφ	eiφ	PROPN
ejpam-4824	49	19	and	and	CCONJ
ejpam-4824	49	20	φ	φ	PROPN
ejpam-4824	49	21	belongs	belong	VERB
ejpam-4824	49	22	to	to	ADP
ejpam-4824	49	23	the	the	DET
ejpam-4824	49	24	real	real	ADJ
ejpam-4824	49	25	numbers	number	NOUN
ejpam-4824	49	26	.	.	PUNCT
ejpam-4824	50	1	this	this	DET
ejpam-4824	50	2	choice	choice	NOUN
ejpam-4824	50	3	of	of	ADP
ejpam-4824	50	4	x	x	PUNCT
ejpam-4824	50	5	guarantees	guarantee	VERB
ejpam-4824	50	6	the	the	DET
ejpam-4824	50	7	unitarity	unitarity	NOUN
ejpam-4824	50	8	of	of	ADP
ejpam-4824	50	9	xs	xs	PROPN
ejpam-4824	50	10	.	.	PUNCT
ejpam-4824	51	1	clearly	clearly	ADV
ejpam-4824	51	2	,	,	PUNCT
ejpam-4824	51	3	x	x	SYM
ejpam-4824	51	4	=	=	SYM
ejpam-4824	51	5	1	1	NUM
ejpam-4824	51	6	and	and	CCONJ
ejpam-4824	51	7	x	x	X
ejpam-4824	52	1	=	=	NOUN
ejpam-4824	52	2	i	i	PRON
ejpam-4824	52	3	correspond	correspond	VERB
ejpam-4824	52	4	to	to	ADP
ejpam-4824	52	5	s	s	PRON
ejpam-4824	52	6	and	and	CCONJ
ejpam-4824	52	7	is	be	AUX
ejpam-4824	52	8	,	,	PUNCT
ejpam-4824	52	9	respectively	respectively	ADV
ejpam-4824	52	10	.	.	PUNCT
ejpam-4824	53	1	the	the	DET
ejpam-4824	53	2	representations	representation	NOUN
ejpam-4824	53	3	in	in	ADP
ejpam-4824	53	4	(	(	PUNCT
ejpam-4824	53	5	3	3	NUM
ejpam-4824	53	6	)	)	PUNCT
ejpam-4824	53	7	,	,	PUNCT
ejpam-4824	53	8	and	and	CCONJ
ejpam-4824	53	9	(	(	PUNCT
ejpam-4824	53	10	4	4	X
ejpam-4824	53	11	)	)	PUNCT
ejpam-4824	53	12	are	be	AUX
ejpam-4824	53	13	basically	basically	ADV
ejpam-4824	53	14	the	the	DET
ejpam-4824	53	15	results	result	NOUN
ejpam-4824	53	16	of	of	ADP
ejpam-4824	53	17	the	the	DET
ejpam-4824	53	18	following	follow	VERB
ejpam-4824	53	19	fact	fact	NOUN
ejpam-4824	53	20	.	.	PUNCT
ejpam-4824	54	1	from	from	ADP
ejpam-4824	54	2	(	(	PUNCT
ejpam-4824	54	3	1	1	NUM
ejpam-4824	54	4	)	)	PUNCT
ejpam-4824	54	5	and	and	CCONJ
ejpam-4824	54	6	(	(	PUNCT
ejpam-4824	54	7	2	2	NUM
ejpam-4824	54	8	)	)	PUNCT
ejpam-4824	54	9	,	,	PUNCT
ejpam-4824	54	10	for	for	ADP
ejpam-4824	54	11	x	x	SYM
ejpam-4824	54	12	=	=	SYM
ejpam-4824	54	13	1	1	NUM
ejpam-4824	54	14	and	and	CCONJ
ejpam-4824	54	15	x	x	X
ejpam-4824	54	16	=	=	SYM
ejpam-4824	54	17	i	i	PROPN
ejpam-4824	54	18	,	,	PUNCT
ejpam-4824	54	19	xs	xs	PROPN
ejpam-4824	54	20	must	must	AUX
ejpam-4824	54	21	satisfy	satisfy	VERB
ejpam-4824	54	22	xs(|00⟩	xs(|00⟩	NOUN
ejpam-4824	54	23	)	)	PUNCT
ejpam-4824	54	24	=	=	NUM
ejpam-4824	54	25	|00⟩	|00⟩	NOUN
ejpam-4824	54	26	xs(|01⟩	xs(|01⟩	ADJ
ejpam-4824	54	27	)	)	PUNCT
ejpam-4824	54	28	=	=	SYM
ejpam-4824	55	1	x|10⟩	x|10⟩	PROPN
ejpam-4824	55	2	xs(|10⟩	xs(|10⟩	PROPN
ejpam-4824	55	3	)	)	PUNCT
ejpam-4824	56	1	=	=	SYM
ejpam-4824	56	2	x|01⟩	x|01⟩	PROPN
ejpam-4824	56	3	xs(|11⟩	xs(|11⟩	NOUN
ejpam-4824	56	4	)	)	PUNCT
ejpam-4824	57	1	=	=	PUNCT
ejpam-4824	57	2	|11⟩	|11⟩	NOUN
ejpam-4824	57	3	a.	a.	NOUN
ejpam-4824	57	4	pourkia	pourkia	NOUN
ejpam-4824	57	5	/	/	SYM
ejpam-4824	57	6	eur	eur	PROPN
ejpam-4824	57	7	.	.	PUNCT
ejpam-4824	58	1	j.	j.	PROPN
ejpam-4824	58	2	pure	pure	PROPN
ejpam-4824	58	3	appl	appl	PROPN
ejpam-4824	58	4	.	.	PROPN
ejpam-4824	58	5	math	math	PROPN
ejpam-4824	58	6	,	,	PUNCT
ejpam-4824	58	7	16	16	NUM
ejpam-4824	58	8	(	(	PUNCT
ejpam-4824	58	9	3	3	NUM
ejpam-4824	58	10	)	)	PUNCT
ejpam-4824	58	11	(	(	PUNCT
ejpam-4824	58	12	2023	2023	NUM
ejpam-4824	58	13	)	)	PUNCT
ejpam-4824	58	14	,	,	PUNCT
ejpam-4824	58	15	1695	1695	NUM
ejpam-4824	58	16	-	-	SYM
ejpam-4824	58	17	1704	1704	NUM
ejpam-4824	58	18	1698	1698	NUM
ejpam-4824	58	19	now	now	ADV
ejpam-4824	58	20	going	go	VERB
ejpam-4824	58	21	one	one	NUM
ejpam-4824	58	22	step	step	NOUN
ejpam-4824	58	23	higher	higher	ADV
ejpam-4824	58	24	in	in	ADP
ejpam-4824	58	25	dimension	dimension	NOUN
ejpam-4824	58	26	,	,	PUNCT
ejpam-4824	58	27	for	for	ADP
ejpam-4824	58	28	d	d	PROPN
ejpam-4824	58	29	=	=	SYM
ejpam-4824	58	30	3	3	NUM
ejpam-4824	58	31	,	,	PUNCT
ejpam-4824	58	32	using	use	VERB
ejpam-4824	58	33	the	the	DET
ejpam-4824	58	34	same	same	ADJ
ejpam-4824	58	35	definitions	definition	NOUN
ejpam-4824	58	36	(	(	PUNCT
ejpam-4824	58	37	1	1	NUM
ejpam-4824	58	38	)	)	PUNCT
ejpam-4824	58	39	and	and	CCONJ
ejpam-4824	58	40	(	(	PUNCT
ejpam-4824	58	41	2	2	NUM
ejpam-4824	58	42	)	)	PUNCT
ejpam-4824	58	43	,	,	PUNCT
ejpam-4824	58	44	the	the	DET
ejpam-4824	58	45	unified	unify	VERB
ejpam-4824	58	46	xswap	xswap	PROPN
ejpam-4824	58	47	gate	gate	PROPN
ejpam-4824	58	48	xs9	xs9	PROPN
ejpam-4824	58	49	:	:	PUNCT
ejpam-4824	59	1	c3	c3	PROPN
ejpam-4824	59	2	⊗	⊗	PROPN
ejpam-4824	59	3	c3	c3	PROPN
ejpam-4824	59	4	→	→	PUNCT
ejpam-4824	59	5	c3	c3	PROPN
ejpam-4824	59	6	⊗	⊗	PROPN
ejpam-4824	59	7	c3	c3	PROPN
ejpam-4824	59	8	(	(	PUNCT
ejpam-4824	59	9	or	or	CCONJ
ejpam-4824	59	10	xs	xs	PROPN
ejpam-4824	59	11	for	for	ADP
ejpam-4824	59	12	short	short	ADJ
ejpam-4824	59	13	)	)	PUNCT
ejpam-4824	59	14	must	must	AUX
ejpam-4824	59	15	satisfy	satisfy	VERB
ejpam-4824	59	16	xs(|00⟩	xs(|00⟩	NOUN
ejpam-4824	59	17	)	)	PUNCT
ejpam-4824	59	18	=	=	NUM
ejpam-4824	59	19	|00⟩	|00⟩	NOUN
ejpam-4824	59	20	xs(|01⟩	xs(|01⟩	ADJ
ejpam-4824	59	21	)	)	PUNCT
ejpam-4824	59	22	=	=	SYM
ejpam-4824	60	1	x|10⟩	x|10⟩	PROPN
ejpam-4824	60	2	xs(|02⟩	xs(|02⟩	ADV
ejpam-4824	60	3	)	)	PUNCT
ejpam-4824	61	1	=	=	SYM
ejpam-4824	61	2	x|20⟩	x|20⟩	PROPN
ejpam-4824	61	3	xs(|10⟩	xs(|10⟩	PROPN
ejpam-4824	61	4	)	)	PUNCT
ejpam-4824	62	1	=	=	SYM
ejpam-4824	62	2	x|01⟩	x|01⟩	PROPN
ejpam-4824	62	3	xs(|11⟩	xs(|11⟩	NOUN
ejpam-4824	62	4	)	)	PUNCT
ejpam-4824	63	1	=	=	SYM
ejpam-4824	63	2	|11⟩	|11⟩	X
ejpam-4824	63	3	xs(|12⟩	xs(|12⟩	NOUN
ejpam-4824	63	4	)	)	PUNCT
ejpam-4824	64	1	=	=	SYM
ejpam-4824	65	1	x|21⟩	x|21⟩	NUM
ejpam-4824	65	2	xs(|20⟩	xs(|20⟩	NOUN
ejpam-4824	65	3	)	)	PUNCT
ejpam-4824	66	1	=	=	SYM
ejpam-4824	66	2	x|02⟩	x|02⟩	PROPN
ejpam-4824	66	3	xs(|21⟩	xs(|21⟩	VERB
ejpam-4824	66	4	)	)	PUNCT
ejpam-4824	67	1	=	=	SYM
ejpam-4824	67	2	x|12⟩	x|12⟩	NOUN
ejpam-4824	67	3	xs(|22⟩	xs(|22⟩	ADV
ejpam-4824	67	4	)	)	PUNCT
ejpam-4824	68	1	=	=	PRON
ejpam-4824	68	2	|22⟩	|22⟩	X
ejpam-4824	68	3	the	the	DET
ejpam-4824	68	4	above	above	ADJ
ejpam-4824	68	5	relations	relation	NOUN
ejpam-4824	68	6	easily	easily	ADV
ejpam-4824	68	7	imply	imply	VERB
ejpam-4824	68	8	that	that	PRON
ejpam-4824	68	9	for	for	ADP
ejpam-4824	68	10	x	x	SYM
ejpam-4824	68	11	=	=	PUNCT
ejpam-4824	68	12	eiφ	eiφ	NOUN
ejpam-4824	68	13	where	where	SCONJ
ejpam-4824	68	14	φ	φ	PROPN
ejpam-4824	68	15	is	be	AUX
ejpam-4824	68	16	a	a	DET
ejpam-4824	68	17	real	real	ADJ
ejpam-4824	68	18	number	number	NOUN
ejpam-4824	68	19	xs9	xs9	PUNCT
ejpam-4824	69	1	=	=	PUNCT
ejpam-4824	69	2			VERB
ejpam-4824	69	3	1	1	NUM
ejpam-4824	69	4	0	0	NUM
ejpam-4824	69	5	0	0	NUM
ejpam-4824	69	6	0	0	NUM
ejpam-4824	69	7	0	0	NUM
ejpam-4824	69	8	0	0	NUM
ejpam-4824	69	9	0	0	NUM
ejpam-4824	69	10	0	0	NUM
ejpam-4824	69	11	0	0	NUM
ejpam-4824	69	12	0	0	NUM
ejpam-4824	69	13	0	0	NUM
ejpam-4824	69	14	0	0	NUM
ejpam-4824	70	1	x	x	SYM
ejpam-4824	70	2	0	0	NUM
ejpam-4824	70	3	0	0	NUM
ejpam-4824	70	4	0	0	NUM
ejpam-4824	70	5	0	0	NUM
ejpam-4824	70	6	0	0	NUM
ejpam-4824	70	7	0	0	NUM
ejpam-4824	70	8	0	0	NUM
ejpam-4824	70	9	0	0	NUM
ejpam-4824	70	10	0	0	NUM
ejpam-4824	70	11	0	0	NUM
ejpam-4824	70	12	0	0	NUM
ejpam-4824	70	13	x	x	SYM
ejpam-4824	70	14	0	0	NUM
ejpam-4824	70	15	0	0	NUM
ejpam-4824	70	16	0	0	NUM
ejpam-4824	70	17	x	x	SYM
ejpam-4824	70	18	0	0	NUM
ejpam-4824	70	19	0	0	NUM
ejpam-4824	70	20	0	0	NUM
ejpam-4824	70	21	0	0	NUM
ejpam-4824	70	22	0	0	NUM
ejpam-4824	70	23	0	0	NUM
ejpam-4824	70	24	0	0	NUM
ejpam-4824	70	25	0	0	NUM
ejpam-4824	70	26	0	0	NUM
ejpam-4824	70	27	0	0	NUM
ejpam-4824	70	28	0	0	NUM
ejpam-4824	70	29	1	1	NUM
ejpam-4824	70	30	0	0	NUM
ejpam-4824	70	31	0	0	NUM
ejpam-4824	70	32	0	0	NUM
ejpam-4824	70	33	0	0	NUM
ejpam-4824	70	34	0	0	NUM
ejpam-4824	70	35	0	0	NUM
ejpam-4824	70	36	0	0	NUM
ejpam-4824	70	37	0	0	NUM
ejpam-4824	70	38	0	0	NUM
ejpam-4824	70	39	0	0	NUM
ejpam-4824	70	40	0	0	NUM
ejpam-4824	70	41	x	x	SYM
ejpam-4824	70	42	0	0	NUM
ejpam-4824	70	43	0	0	NUM
ejpam-4824	70	44	0	0	NUM
ejpam-4824	70	45	x	x	SYM
ejpam-4824	70	46	0	0	NUM
ejpam-4824	70	47	0	0	NUM
ejpam-4824	70	48	0	0	NUM
ejpam-4824	70	49	0	0	NUM
ejpam-4824	70	50	0	0	NUM
ejpam-4824	70	51	0	0	NUM
ejpam-4824	70	52	0	0	NUM
ejpam-4824	70	53	0	0	NUM
ejpam-4824	70	54	0	0	NUM
ejpam-4824	70	55	0	0	NUM
ejpam-4824	70	56	0	0	NUM
ejpam-4824	70	57	x	x	SYM
ejpam-4824	70	58	0	0	NUM
ejpam-4824	70	59	0	0	NUM
ejpam-4824	70	60	0	0	NUM
ejpam-4824	70	61	0	0	NUM
ejpam-4824	70	62	0	0	NUM
ejpam-4824	70	63	0	0	NUM
ejpam-4824	70	64	0	0	NUM
ejpam-4824	70	65	0	0	NUM
ejpam-4824	70	66	0	0	NUM
ejpam-4824	70	67	0	0	NUM
ejpam-4824	70	68	0	0	NUM
ejpam-4824	70	69	1	1	NUM
ejpam-4824	70	70			NOUN
ejpam-4824	70	71	this	this	PRON
ejpam-4824	70	72	is	be	AUX
ejpam-4824	70	73	xswap	xswap	ADJ
ejpam-4824	70	74	in	in	ADP
ejpam-4824	70	75	dimension	dimension	NOUN
ejpam-4824	71	1	d	d	PROPN
ejpam-4824	71	2	=	=	SYM
ejpam-4824	71	3	3	3	X
ejpam-4824	71	4	.	.	X
ejpam-4824	72	1	for	for	ADP
ejpam-4824	72	2	x	x	SYM
ejpam-4824	72	3	=	=	SYM
ejpam-4824	72	4	1	1	NUM
ejpam-4824	72	5	and	and	CCONJ
ejpam-4824	72	6	x	x	X
ejpam-4824	72	7	=	=	SYM
ejpam-4824	72	8	i	i	PROPN
ejpam-4824	72	9	,	,	PUNCT
ejpam-4824	72	10	it	it	PRON
ejpam-4824	72	11	provides	provide	VERB
ejpam-4824	72	12	the	the	DET
ejpam-4824	72	13	gates	gate	NOUN
ejpam-4824	72	14	swap	swap	NOUN
ejpam-4824	72	15	and	and	CCONJ
ejpam-4824	72	16	iswap	iswap	NOUN
ejpam-4824	72	17	in	in	ADP
ejpam-4824	72	18	dimension	dimension	NOUN
ejpam-4824	72	19	d	d	NOUN
ejpam-4824	72	20	=	=	SYM
ejpam-4824	72	21	3	3	NUM
ejpam-4824	72	22	(	(	PUNCT
ejpam-4824	72	23	s9	s9	VERB
ejpam-4824	72	24	and	and	CCONJ
ejpam-4824	72	25	is9	is9	PROPN
ejpam-4824	72	26	)	)	PUNCT
ejpam-4824	72	27	,	,	PUNCT
ejpam-4824	72	28	respectively	respectively	ADV
ejpam-4824	72	29	.	.	PUNCT
ejpam-4824	73	1	a	a	DET
ejpam-4824	73	2	similar	similar	ADJ
ejpam-4824	73	3	argument	argument	NOUN
ejpam-4824	73	4	for	for	ADP
ejpam-4824	73	5	d	d	NOUN
ejpam-4824	73	6	=	=	SYM
ejpam-4824	73	7	4	4	NUM
ejpam-4824	73	8	yields	yield	NOUN
ejpam-4824	73	9	xswap	xswap	NOUN
ejpam-4824	73	10	(	(	PUNCT
ejpam-4824	73	11	denoted	denote	VERB
ejpam-4824	73	12	below	below	ADP
ejpam-4824	73	13	by	by	ADP
ejpam-4824	73	14	xs16	xs16	PROPN
ejpam-4824	73	15	)	)	PUNCT
ejpam-4824	73	16	,	,	PUNCT
ejpam-4824	73	17	as	as	SCONJ
ejpam-4824	73	18	follows	follow	VERB
ejpam-4824	73	19	:	:	PUNCT
ejpam-4824	73	20	a.	a.	NOUN
ejpam-4824	73	21	pourkia	pourkia	NOUN
ejpam-4824	73	22	/	/	SYM
ejpam-4824	73	23	eur	eur	PROPN
ejpam-4824	73	24	.	.	PUNCT
ejpam-4824	74	1	j.	j.	PROPN
ejpam-4824	74	2	pure	pure	PROPN
ejpam-4824	74	3	appl	appl	PROPN
ejpam-4824	74	4	.	.	PROPN
ejpam-4824	74	5	math	math	PROPN
ejpam-4824	74	6	,	,	PUNCT
ejpam-4824	74	7	16	16	NUM
ejpam-4824	74	8	(	(	PUNCT
ejpam-4824	74	9	3	3	NUM
ejpam-4824	74	10	)	)	PUNCT
ejpam-4824	74	11	(	(	PUNCT
ejpam-4824	74	12	2023	2023	NUM
ejpam-4824	74	13	)	)	PUNCT
ejpam-4824	74	14	,	,	PUNCT
ejpam-4824	74	15	1695	1695	NUM
ejpam-4824	74	16	-	-	SYM
ejpam-4824	74	17	1704	1704	NUM
ejpam-4824	74	18	1699	1699	NUM
ejpam-4824	75	1	xs16	xs16	PROPN
ejpam-4824	75	2	=	=	PUNCT
ejpam-4824	75	3			NOUN
ejpam-4824	75	4	1	1	NUM
ejpam-4824	75	5	0	0	NUM
ejpam-4824	75	6	0	0	NUM
ejpam-4824	75	7	0	0	NUM
ejpam-4824	75	8	0	0	NUM
ejpam-4824	75	9	0	0	NUM
ejpam-4824	75	10	0	0	NUM
ejpam-4824	75	11	0	0	NUM
ejpam-4824	75	12	0	0	NUM
ejpam-4824	75	13	0	0	NUM
ejpam-4824	75	14	0	0	NUM
ejpam-4824	75	15	0	0	NUM
ejpam-4824	75	16	0	0	NUM
ejpam-4824	75	17	0	0	NUM
ejpam-4824	75	18	0	0	NUM
ejpam-4824	75	19	0	0	NUM
ejpam-4824	75	20	0	0	NUM
ejpam-4824	75	21	0	0	NUM
ejpam-4824	75	22	0	0	NUM
ejpam-4824	75	23	0	0	NUM
ejpam-4824	76	1	x	x	SYM
ejpam-4824	76	2	0	0	NUM
ejpam-4824	76	3	0	0	NUM
ejpam-4824	76	4	0	0	NUM
ejpam-4824	76	5	0	0	NUM
ejpam-4824	76	6	0	0	NUM
ejpam-4824	76	7	0	0	NUM
ejpam-4824	76	8	0	0	NUM
ejpam-4824	76	9	0	0	NUM
ejpam-4824	76	10	0	0	NUM
ejpam-4824	76	11	0	0	NUM
ejpam-4824	76	12	0	0	NUM
ejpam-4824	76	13	0	0	NUM
ejpam-4824	76	14	0	0	NUM
ejpam-4824	76	15	0	0	NUM
ejpam-4824	76	16	0	0	NUM
ejpam-4824	76	17	0	0	NUM
ejpam-4824	76	18	0	0	NUM
ejpam-4824	76	19	0	0	NUM
ejpam-4824	76	20	0	0	NUM
ejpam-4824	76	21	x	x	SYM
ejpam-4824	76	22	0	0	NUM
ejpam-4824	76	23	0	0	NUM
ejpam-4824	76	24	0	0	NUM
ejpam-4824	76	25	0	0	NUM
ejpam-4824	76	26	0	0	NUM
ejpam-4824	76	27	0	0	NUM
ejpam-4824	76	28	0	0	NUM
ejpam-4824	76	29	0	0	NUM
ejpam-4824	76	30	0	0	NUM
ejpam-4824	76	31	0	0	NUM
ejpam-4824	76	32	0	0	NUM
ejpam-4824	76	33	0	0	NUM
ejpam-4824	76	34	0	0	NUM
ejpam-4824	76	35	0	0	NUM
ejpam-4824	76	36	0	0	NUM
ejpam-4824	76	37	0	0	NUM
ejpam-4824	76	38	0	0	NUM
ejpam-4824	76	39	0	0	NUM
ejpam-4824	76	40	0	0	NUM
ejpam-4824	76	41	x	x	SYM
ejpam-4824	76	42	0	0	NUM
ejpam-4824	76	43	0	0	NUM
ejpam-4824	76	44	0	0	NUM
ejpam-4824	76	45	0	0	NUM
ejpam-4824	76	46	x	x	SYM
ejpam-4824	76	47	0	0	NUM
ejpam-4824	76	48	0	0	NUM
ejpam-4824	76	49	0	0	NUM
ejpam-4824	76	50	0	0	NUM
ejpam-4824	76	51	0	0	NUM
ejpam-4824	76	52	0	0	NUM
ejpam-4824	76	53	0	0	NUM
ejpam-4824	76	54	0	0	NUM
ejpam-4824	76	55	0	0	NUM
ejpam-4824	76	56	0	0	NUM
ejpam-4824	76	57	0	0	NUM
ejpam-4824	76	58	0	0	NUM
ejpam-4824	76	59	0	0	NUM
ejpam-4824	76	60	0	0	NUM
ejpam-4824	76	61	0	0	NUM
ejpam-4824	76	62	0	0	NUM
ejpam-4824	76	63	0	0	NUM
ejpam-4824	76	64	0	0	NUM
ejpam-4824	76	65	0	0	NUM
ejpam-4824	76	66	1	1	NUM
ejpam-4824	76	67	0	0	NUM
ejpam-4824	76	68	0	0	NUM
ejpam-4824	76	69	0	0	NUM
ejpam-4824	76	70	0	0	NUM
ejpam-4824	76	71	0	0	NUM
ejpam-4824	76	72	0	0	NUM
ejpam-4824	76	73	0	0	NUM
ejpam-4824	76	74	0	0	NUM
ejpam-4824	76	75	0	0	NUM
ejpam-4824	76	76	0	0	NUM
ejpam-4824	76	77	0	0	NUM
ejpam-4824	76	78	0	0	NUM
ejpam-4824	76	79	0	0	NUM
ejpam-4824	76	80	0	0	NUM
ejpam-4824	76	81	0	0	NUM
ejpam-4824	76	82	0	0	NUM
ejpam-4824	76	83	0	0	NUM
ejpam-4824	76	84	0	0	NUM
ejpam-4824	76	85	0	0	NUM
ejpam-4824	76	86	x	x	SYM
ejpam-4824	76	87	0	0	NUM
ejpam-4824	76	88	0	0	NUM
ejpam-4824	76	89	0	0	NUM
ejpam-4824	76	90	0	0	NUM
ejpam-4824	76	91	0	0	NUM
ejpam-4824	76	92	0	0	NUM
ejpam-4824	76	93	0	0	NUM
ejpam-4824	76	94	0	0	NUM
ejpam-4824	76	95	0	0	NUM
ejpam-4824	76	96	0	0	NUM
ejpam-4824	76	97	0	0	NUM
ejpam-4824	76	98	0	0	NUM
ejpam-4824	76	99	0	0	NUM
ejpam-4824	76	100	0	0	NUM
ejpam-4824	76	101	0	0	NUM
ejpam-4824	76	102	0	0	NUM
ejpam-4824	76	103	0	0	NUM
ejpam-4824	76	104	0	0	NUM
ejpam-4824	76	105	0	0	NUM
ejpam-4824	76	106	x	x	SYM
ejpam-4824	76	107	0	0	NUM
ejpam-4824	76	108	0	0	NUM
ejpam-4824	76	109	0	0	NUM
ejpam-4824	76	110	0	0	NUM
ejpam-4824	76	111	x	x	SYM
ejpam-4824	76	112	0	0	NUM
ejpam-4824	76	113	0	0	NUM
ejpam-4824	76	114	0	0	NUM
ejpam-4824	76	115	0	0	NUM
ejpam-4824	76	116	0	0	NUM
ejpam-4824	76	117	0	0	NUM
ejpam-4824	76	118	0	0	NUM
ejpam-4824	76	119	0	0	NUM
ejpam-4824	76	120	0	0	NUM
ejpam-4824	76	121	0	0	NUM
ejpam-4824	76	122	0	0	NUM
ejpam-4824	76	123	0	0	NUM
ejpam-4824	76	124	0	0	NUM
ejpam-4824	76	125	0	0	NUM
ejpam-4824	76	126	0	0	NUM
ejpam-4824	76	127	0	0	NUM
ejpam-4824	76	128	0	0	NUM
ejpam-4824	76	129	0	0	NUM
ejpam-4824	76	130	0	0	NUM
ejpam-4824	76	131	x	x	SYM
ejpam-4824	76	132	0	0	NUM
ejpam-4824	76	133	0	0	NUM
ejpam-4824	76	134	0	0	NUM
ejpam-4824	76	135	0	0	NUM
ejpam-4824	76	136	0	0	NUM
ejpam-4824	76	137	0	0	NUM
ejpam-4824	76	138	0	0	NUM
ejpam-4824	76	139	0	0	NUM
ejpam-4824	76	140	0	0	NUM
ejpam-4824	76	141	0	0	NUM
ejpam-4824	76	142	0	0	NUM
ejpam-4824	76	143	0	0	NUM
ejpam-4824	76	144	0	0	NUM
ejpam-4824	76	145	0	0	NUM
ejpam-4824	76	146	0	0	NUM
ejpam-4824	76	147	0	0	NUM
ejpam-4824	76	148	0	0	NUM
ejpam-4824	76	149	0	0	NUM
ejpam-4824	76	150	0	0	NUM
ejpam-4824	76	151	1	1	NUM
ejpam-4824	76	152	0	0	NUM
ejpam-4824	76	153	0	0	NUM
ejpam-4824	76	154	0	0	NUM
ejpam-4824	76	155	0	0	NUM
ejpam-4824	76	156	0	0	NUM
ejpam-4824	76	157	0	0	NUM
ejpam-4824	76	158	0	0	NUM
ejpam-4824	76	159	0	0	NUM
ejpam-4824	76	160	0	0	NUM
ejpam-4824	76	161	0	0	NUM
ejpam-4824	76	162	0	0	NUM
ejpam-4824	76	163	0	0	NUM
ejpam-4824	76	164	0	0	NUM
ejpam-4824	76	165	0	0	NUM
ejpam-4824	76	166	0	0	NUM
ejpam-4824	76	167	0	0	NUM
ejpam-4824	76	168	0	0	NUM
ejpam-4824	76	169	0	0	NUM
ejpam-4824	76	170	0	0	NUM
ejpam-4824	76	171	x	x	SYM
ejpam-4824	76	172	0	0	NUM
ejpam-4824	76	173	0	0	NUM
ejpam-4824	76	174	0	0	NUM
ejpam-4824	76	175	0	0	NUM
ejpam-4824	76	176	x	x	SYM
ejpam-4824	76	177	0	0	NUM
ejpam-4824	76	178	0	0	NUM
ejpam-4824	76	179	0	0	NUM
ejpam-4824	76	180	0	0	NUM
ejpam-4824	76	181	0	0	NUM
ejpam-4824	76	182	0	0	NUM
ejpam-4824	76	183	0	0	NUM
ejpam-4824	76	184	0	0	NUM
ejpam-4824	76	185	0	0	NUM
ejpam-4824	76	186	0	0	NUM
ejpam-4824	76	187	0	0	NUM
ejpam-4824	76	188	0	0	NUM
ejpam-4824	76	189	0	0	NUM
ejpam-4824	76	190	0	0	NUM
ejpam-4824	76	191	0	0	NUM
ejpam-4824	76	192	0	0	NUM
ejpam-4824	76	193	0	0	NUM
ejpam-4824	76	194	0	0	NUM
ejpam-4824	76	195	0	0	NUM
ejpam-4824	76	196	x	x	SYM
ejpam-4824	76	197	0	0	NUM
ejpam-4824	76	198	0	0	NUM
ejpam-4824	76	199	0	0	NUM
ejpam-4824	76	200	0	0	NUM
ejpam-4824	76	201	0	0	NUM
ejpam-4824	76	202	0	0	NUM
ejpam-4824	76	203	0	0	NUM
ejpam-4824	76	204	0	0	NUM
ejpam-4824	76	205	0	0	NUM
ejpam-4824	76	206	0	0	NUM
ejpam-4824	76	207	0	0	NUM
ejpam-4824	76	208	0	0	NUM
ejpam-4824	76	209	0	0	NUM
ejpam-4824	76	210	0	0	NUM
ejpam-4824	76	211	0	0	NUM
ejpam-4824	76	212	0	0	NUM
ejpam-4824	76	213	0	0	NUM
ejpam-4824	76	214	0	0	NUM
ejpam-4824	76	215	0	0	NUM
ejpam-4824	76	216	x	x	SYM
ejpam-4824	76	217	0	0	NUM
ejpam-4824	76	218	0	0	NUM
ejpam-4824	76	219	0	0	NUM
ejpam-4824	76	220	0	0	NUM
ejpam-4824	76	221	0	0	NUM
ejpam-4824	76	222	0	0	NUM
ejpam-4824	76	223	0	0	NUM
ejpam-4824	76	224	0	0	NUM
ejpam-4824	76	225	0	0	NUM
ejpam-4824	76	226	0	0	NUM
ejpam-4824	76	227	0	0	NUM
ejpam-4824	76	228	0	0	NUM
ejpam-4824	76	229	0	0	NUM
ejpam-4824	76	230	0	0	NUM
ejpam-4824	76	231	0	0	NUM
ejpam-4824	76	232	0	0	NUM
ejpam-4824	76	233	0	0	NUM
ejpam-4824	76	234	0	0	NUM
ejpam-4824	76	235	0	0	NUM
ejpam-4824	76	236	1	1	NUM
ejpam-4824	76	237			NOUN
ejpam-4824	76	238	here	here	ADV
ejpam-4824	76	239	x	x	X
ejpam-4824	76	240	=	=	SYM
ejpam-4824	76	241	1	1	NUM
ejpam-4824	76	242	and	and	CCONJ
ejpam-4824	76	243	x	x	X
ejpam-4824	77	1	=	=	NOUN
ejpam-4824	77	2	i	i	PRON
ejpam-4824	77	3	correspond	correspond	VERB
ejpam-4824	77	4	to	to	PART
ejpam-4824	77	5	swap	swap	VERB
ejpam-4824	77	6	and	and	CCONJ
ejpam-4824	77	7	iswap	iswap	NOUN
ejpam-4824	77	8	in	in	ADP
ejpam-4824	77	9	dimension	dimension	NOUN
ejpam-4824	77	10	d	d	X
ejpam-4824	77	11	=	=	SYM
ejpam-4824	77	12	4	4	NUM
ejpam-4824	77	13	,	,	PUNCT
ejpam-4824	77	14	respectively	respectively	ADV
ejpam-4824	77	15	.	.	PUNCT
ejpam-4824	78	1	at	at	ADP
ejpam-4824	78	2	this	this	DET
ejpam-4824	78	3	point	point	NOUN
ejpam-4824	78	4	it	it	PRON
ejpam-4824	78	5	is	be	AUX
ejpam-4824	78	6	not	not	PART
ejpam-4824	78	7	hard	hard	ADJ
ejpam-4824	78	8	to	to	PART
ejpam-4824	78	9	see	see	VERB
ejpam-4824	78	10	that	that	SCONJ
ejpam-4824	78	11	the	the	DET
ejpam-4824	78	12	matrix	matrix	NOUN
ejpam-4824	78	13	xsd2	xsd2	PROPN
ejpam-4824	78	14	(	(	PUNCT
ejpam-4824	78	15	or	or	CCONJ
ejpam-4824	78	16	xs	xs	PROPN
ejpam-4824	78	17	for	for	ADP
ejpam-4824	78	18	short	short	ADJ
ejpam-4824	78	19	)	)	PUNCT
ejpam-4824	78	20	defined	define	VERB
ejpam-4824	78	21	below	below	ADV
ejpam-4824	78	22	is	be	AUX
ejpam-4824	78	23	the	the	DET
ejpam-4824	78	24	xswap	xswap	PROPN
ejpam-4824	78	25	gate	gate	NOUN
ejpam-4824	78	26	for	for	ADP
ejpam-4824	78	27	any	any	DET
ejpam-4824	78	28	dimension	dimension	NOUN
ejpam-4824	78	29	d.	d.	PROPN
ejpam-4824	78	30	definition	definition	NOUN
ejpam-4824	78	31	1	1	NUM
ejpam-4824	78	32	(	(	PUNCT
ejpam-4824	78	33	xswap	xswap	PROPN
ejpam-4824	78	34	)	)	PUNCT
ejpam-4824	78	35	.	.	PUNCT
ejpam-4824	79	1	for	for	ADP
ejpam-4824	79	2	any	any	DET
ejpam-4824	79	3	d	d	PROPN
ejpam-4824	79	4	≥	≥	NUM
ejpam-4824	79	5	2	2	NUM
ejpam-4824	79	6	and	and	CCONJ
ejpam-4824	79	7	for	for	ADP
ejpam-4824	79	8	any	any	DET
ejpam-4824	79	9	x	x	NOUN
ejpam-4824	79	10	=	=	PRON
ejpam-4824	79	11	eiφ	eiφ	NOUN
ejpam-4824	79	12	in	in	ADP
ejpam-4824	79	13	which	which	PRON
ejpam-4824	79	14	φ	φ	PROPN
ejpam-4824	79	15	belongs	belong	VERB
ejpam-4824	79	16	to	to	ADP
ejpam-4824	79	17	the	the	DET
ejpam-4824	79	18	real	real	ADJ
ejpam-4824	79	19	numbers	number	NOUN
ejpam-4824	79	20	,	,	PUNCT
ejpam-4824	79	21	we	we	PRON
ejpam-4824	79	22	define	define	VERB
ejpam-4824	79	23	the	the	DET
ejpam-4824	79	24	xswap	xswap	NOUN
ejpam-4824	79	25	(	(	PUNCT
ejpam-4824	79	26	denoted	denote	VERB
ejpam-4824	79	27	by	by	ADP
ejpam-4824	79	28	xs	xs	PROPN
ejpam-4824	79	29	below	below	ADV
ejpam-4824	79	30	)	)	PUNCT
ejpam-4824	79	31	by	by	ADP
ejpam-4824	79	32	the	the	DET
ejpam-4824	79	33	following	follow	VERB
ejpam-4824	79	34	relations	relation	NOUN
ejpam-4824	79	35	:	:	PUNCT
ejpam-4824	79	36	xsi	xsi	PROPN
ejpam-4824	79	37	,	,	PUNCT
ejpam-4824	79	38	j	j	PROPN
ejpam-4824	80	1	=	=	SYM
ejpam-4824	80	2	x	x	PROPN
ejpam-4824	80	3	,	,	PUNCT
ejpam-4824	80	4	for	for	ADP
ejpam-4824	80	5	i	i	PRON
ejpam-4824	80	6	=	=	SYM
ejpam-4824	80	7	(	(	PUNCT
ejpam-4824	80	8	t−	t−	PROPN
ejpam-4824	80	9	1)d+	1)d+	NUM
ejpam-4824	80	10	s	s	NOUN
ejpam-4824	80	11	and	and	CCONJ
ejpam-4824	80	12	j	j	PROPN
ejpam-4824	81	1	=	=	PRON
ejpam-4824	81	2	(	(	PUNCT
ejpam-4824	81	3	s−	s−	PROPN
ejpam-4824	81	4	1)d+	1)d+	NUM
ejpam-4824	81	5	t	t	PROPN
ejpam-4824	81	6	,	,	PUNCT
ejpam-4824	81	7	(	(	PUNCT
ejpam-4824	81	8	5	5	NUM
ejpam-4824	81	9	)	)	PUNCT
ejpam-4824	81	10	where	where	SCONJ
ejpam-4824	81	11	1	1	NUM
ejpam-4824	81	12	≤	≤	NOUN
ejpam-4824	81	13	t	t	NOUN
ejpam-4824	81	14	≤	≤	NUM
ejpam-4824	81	15	d	d	PROPN
ejpam-4824	81	16	,	,	PUNCT
ejpam-4824	81	17	1	1	NUM
ejpam-4824	81	18	≤	≤	NOUN
ejpam-4824	81	19	s	s	PART
ejpam-4824	81	20	≤	≤	NUM
ejpam-4824	81	21	d	d	NOUN
ejpam-4824	81	22	and	and	CCONJ
ejpam-4824	81	23	t	t	PROPN
ejpam-4824	81	24	̸=	̸=	PROPN
ejpam-4824	81	25	s	s	PROPN
ejpam-4824	81	26	xsi	xsi	PROPN
ejpam-4824	81	27	,	,	PUNCT
ejpam-4824	81	28	j	j	PROPN
ejpam-4824	81	29	=	=	SYM
ejpam-4824	81	30	1	1	NUM
ejpam-4824	81	31	,	,	PUNCT
ejpam-4824	81	32	for	for	ADP
ejpam-4824	81	33	i	i	PRON
ejpam-4824	81	34	=	=	SYM
ejpam-4824	81	35	(	(	PUNCT
ejpam-4824	81	36	t−	t−	PROPN
ejpam-4824	81	37	1)d+	1)d+	NUM
ejpam-4824	81	38	s	s	NOUN
ejpam-4824	81	39	and	and	CCONJ
ejpam-4824	81	40	j	j	PROPN
ejpam-4824	81	41	=	=	PRON
ejpam-4824	81	42	(	(	PUNCT
ejpam-4824	81	43	s−	s−	PROPN
ejpam-4824	81	44	1)d+	1)d+	NUM
ejpam-4824	81	45	t	t	PROPN
ejpam-4824	81	46	,	,	PUNCT
ejpam-4824	81	47	where	where	SCONJ
ejpam-4824	81	48	t	t	NOUN
ejpam-4824	81	49	=	=	SYM
ejpam-4824	81	50	s	s	PART
ejpam-4824	81	51	=	=	SYM
ejpam-4824	81	52	1	1	NUM
ejpam-4824	81	53	,	,	PUNCT
ejpam-4824	81	54	2	2	NUM
ejpam-4824	81	55	,	,	PUNCT
ejpam-4824	81	56	·	·	PUNCT
ejpam-4824	81	57	·	·	PUNCT
ejpam-4824	81	58	·	·	PUNCT
ejpam-4824	81	59	,	,	PUNCT
ejpam-4824	82	1	d	d	PROPN
ejpam-4824	82	2	and	and	CCONJ
ejpam-4824	82	3	,	,	PUNCT
ejpam-4824	82	4	xsi	xsi	PROPN
ejpam-4824	82	5	,	,	PUNCT
ejpam-4824	82	6	j	j	PROPN
ejpam-4824	83	1	=	=	NOUN
ejpam-4824	83	2	0	0	NUM
ejpam-4824	83	3	elsewhere	elsewhere	ADV
ejpam-4824	83	4	.	.	PUNCT
ejpam-4824	84	1	4	4	X
ejpam-4824	84	2	.	.	X
ejpam-4824	84	3	xswap	xswap	PROPN
ejpam-4824	84	4	is	be	AUX
ejpam-4824	84	5	a	a	DET
ejpam-4824	84	6	universal	universal	ADJ
ejpam-4824	84	7	quantum	quantum	ADJ
ejpam-4824	84	8	logic	logic	NOUN
ejpam-4824	84	9	gate	gate	NOUN
ejpam-4824	84	10	when	when	SCONJ
ejpam-4824	84	11	x	x	PROPN
ejpam-4824	84	12	̸=	̸=	PROPN
ejpam-4824	84	13	±1	±1	VERB
ejpam-4824	84	14	a	a	DET
ejpam-4824	84	15	quantum	quantum	NOUN
ejpam-4824	84	16	gate	gate	NOUN
ejpam-4824	84	17	must	must	AUX
ejpam-4824	84	18	be	be	AUX
ejpam-4824	84	19	unitary	unitary	ADJ
ejpam-4824	84	20	by	by	ADP
ejpam-4824	84	21	definition	definition	NOUN
ejpam-4824	84	22	.	.	PUNCT
ejpam-4824	85	1	a	a	DET
ejpam-4824	85	2	2	2	NUM
ejpam-4824	85	3	-	-	PUNCT
ejpam-4824	85	4	qudit	qudit	NOUN
ejpam-4824	85	5	gate	gate	NOUN
ejpam-4824	85	6	(	(	PUNCT
ejpam-4824	85	7	i.e.	i.e.	X
ejpam-4824	85	8	a	a	DET
ejpam-4824	85	9	gate	gate	NOUN
ejpam-4824	85	10	operating	operate	VERB
ejpam-4824	85	11	on	on	ADP
ejpam-4824	85	12	two	two	NUM
ejpam-4824	85	13	d	d	ADJ
ejpam-4824	85	14	-	-	PUNCT
ejpam-4824	85	15	level	level	NOUN
ejpam-4824	85	16	qudits	qudit	NOUN
ejpam-4824	85	17	)	)	PUNCT
ejpam-4824	85	18	is	be	AUX
ejpam-4824	85	19	universal	universal	ADJ
ejpam-4824	85	20	if	if	SCONJ
ejpam-4824	85	21	and	and	CCONJ
ejpam-4824	85	22	only	only	ADV
ejpam-4824	85	23	if	if	SCONJ
ejpam-4824	85	24	it	it	PRON
ejpam-4824	85	25	is	be	AUX
ejpam-4824	85	26	entangling	entangle	VERB
ejpam-4824	85	27	[	[	X
ejpam-4824	85	28	3	3	NUM
ejpam-4824	85	29	]	]	PUNCT
ejpam-4824	85	30	.	.	PUNCT
ejpam-4824	86	1	it	it	PRON
ejpam-4824	86	2	is	be	AUX
ejpam-4824	86	3	very	very	ADV
ejpam-4824	86	4	easy	easy	ADJ
ejpam-4824	86	5	to	to	PART
ejpam-4824	86	6	see	see	VERB
ejpam-4824	86	7	a.	a.	NOUN
ejpam-4824	86	8	pourkia	pourkia	NOUN
ejpam-4824	86	9	/	/	SYM
ejpam-4824	86	10	eur	eur	PROPN
ejpam-4824	86	11	.	.	PUNCT
ejpam-4824	87	1	j.	j.	PROPN
ejpam-4824	87	2	pure	pure	PROPN
ejpam-4824	87	3	appl	appl	PROPN
ejpam-4824	87	4	.	.	PROPN
ejpam-4824	87	5	math	math	PROPN
ejpam-4824	87	6	,	,	PUNCT
ejpam-4824	87	7	16	16	NUM
ejpam-4824	87	8	(	(	PUNCT
ejpam-4824	87	9	3	3	NUM
ejpam-4824	87	10	)	)	PUNCT
ejpam-4824	87	11	(	(	PUNCT
ejpam-4824	87	12	2023	2023	NUM
ejpam-4824	87	13	)	)	PUNCT
ejpam-4824	87	14	,	,	PUNCT
ejpam-4824	87	15	1695	1695	NUM
ejpam-4824	87	16	-	-	SYM
ejpam-4824	87	17	1704	1704	NUM
ejpam-4824	87	18	1700	1700	NUM
ejpam-4824	87	19	that	that	PRON
ejpam-4824	87	20	,	,	PUNCT
ejpam-4824	87	21	in	in	ADP
ejpam-4824	87	22	any	any	DET
ejpam-4824	87	23	dimension	dimension	NOUN
ejpam-4824	87	24	d	d	NOUN
ejpam-4824	87	25	and	and	CCONJ
ejpam-4824	87	26	for	for	ADP
ejpam-4824	87	27	any	any	DET
ejpam-4824	87	28	unit	unit	NOUN
ejpam-4824	87	29	complex	complex	ADJ
ejpam-4824	87	30	number	number	NOUN
ejpam-4824	87	31	x	x	NOUN
ejpam-4824	87	32	=	=	SYM
ejpam-4824	87	33	eiφ	eiφ	NOUN
ejpam-4824	87	34	,	,	PUNCT
ejpam-4824	87	35	xswap	xswap	PROPN
ejpam-4824	87	36	is	be	AUX
ejpam-4824	87	37	unitary	unitary	ADJ
ejpam-4824	87	38	.	.	PUNCT
ejpam-4824	88	1	however	however	ADV
ejpam-4824	88	2	,	,	PUNCT
ejpam-4824	88	3	the	the	DET
ejpam-4824	88	4	entangling	entangle	VERB
ejpam-4824	88	5	property	property	NOUN
ejpam-4824	88	6	of	of	ADP
ejpam-4824	88	7	xswap	xswap	PROPN
ejpam-4824	88	8	is	be	AUX
ejpam-4824	88	9	not	not	PART
ejpam-4824	88	10	obvious	obvious	ADJ
ejpam-4824	88	11	for	for	ADP
ejpam-4824	88	12	dimensions	dimension	NOUN
ejpam-4824	88	13	d	d	X
ejpam-4824	88	14	>	>	X
ejpam-4824	88	15	2	2	NUM
ejpam-4824	88	16	(	(	PUNCT
ejpam-4824	88	17	for	for	ADP
ejpam-4824	88	18	d	d	NOUN
ejpam-4824	88	19	=	=	SYM
ejpam-4824	88	20	2	2	NUM
ejpam-4824	88	21	and	and	CCONJ
ejpam-4824	88	22	x	x	PUNCT
ejpam-4824	89	1	=	=	PRON
ejpam-4824	89	2	i	i	PRON
ejpam-4824	89	3	this	this	DET
ejpam-4824	89	4	fact	fact	NOUN
ejpam-4824	89	5	is	be	AUX
ejpam-4824	89	6	well	well	ADV
ejpam-4824	89	7	known	known	ADJ
ejpam-4824	89	8	and	and	CCONJ
ejpam-4824	89	9	easy	easy	ADJ
ejpam-4824	89	10	to	to	PART
ejpam-4824	89	11	prove	prove	VERB
ejpam-4824	89	12	)	)	PUNCT
ejpam-4824	89	13	.	.	PUNCT
ejpam-4824	90	1	in	in	ADP
ejpam-4824	90	2	this	this	DET
ejpam-4824	90	3	section	section	NOUN
ejpam-4824	90	4	we	we	PRON
ejpam-4824	90	5	will	will	AUX
ejpam-4824	90	6	prove	prove	VERB
ejpam-4824	90	7	that	that	SCONJ
ejpam-4824	90	8	xswap	xswap	PROPN
ejpam-4824	90	9	is	be	AUX
ejpam-4824	90	10	a	a	DET
ejpam-4824	90	11	universal	universal	ADJ
ejpam-4824	90	12	quantum	quantum	NOUN
ejpam-4824	90	13	gate	gate	NOUN
ejpam-4824	90	14	when	when	SCONJ
ejpam-4824	90	15	x	x	PROPN
ejpam-4824	90	16	̸=	̸=	PROPN
ejpam-4824	90	17	±1	±1	VERB
ejpam-4824	90	18	.	.	PUNCT
ejpam-4824	91	1	we	we	PRON
ejpam-4824	91	2	use	use	VERB
ejpam-4824	91	3	the	the	DET
ejpam-4824	91	4	non	non	ADJ
ejpam-4824	91	5	-	-	ADJ
ejpam-4824	91	6	entangling	entangle	VERB
ejpam-4824	91	7	criteria	criterion	NOUN
ejpam-4824	91	8	in	in	ADP
ejpam-4824	91	9	[	[	X
ejpam-4824	91	10	1	1	NUM
ejpam-4824	91	11	]	]	PUNCT
ejpam-4824	91	12	.	.	PUNCT
ejpam-4824	92	1	to	to	PART
ejpam-4824	92	2	show	show	VERB
ejpam-4824	92	3	that	that	SCONJ
ejpam-4824	92	4	any	any	DET
ejpam-4824	92	5	operator	operator	NOUN
ejpam-4824	92	6	r	r	NOUN
ejpam-4824	92	7	:	:	PUNCT
ejpam-4824	92	8	h	h	NOUN
ejpam-4824	92	9	⊗h	⊗h	NOUN
ejpam-4824	92	10	→	→	PUNCT
ejpam-4824	92	11	h	h	NOUN
ejpam-4824	92	12	⊗h	⊗h	NOUN
ejpam-4824	92	13	is	be	AUX
ejpam-4824	92	14	entangling	entangle	VERB
ejpam-4824	92	15	,	,	PUNCT
ejpam-4824	92	16	it	it	PRON
ejpam-4824	92	17	is	be	AUX
ejpam-4824	92	18	enough	enough	ADJ
ejpam-4824	92	19	to	to	PART
ejpam-4824	92	20	prove	prove	VERB
ejpam-4824	92	21	neither	neither	CCONJ
ejpam-4824	92	22	r	r	NOUN
ejpam-4824	92	23	nor	nor	CCONJ
ejpam-4824	92	24	rs	rs	NOUN
ejpam-4824	92	25	can	can	AUX
ejpam-4824	92	26	be	be	AUX
ejpam-4824	92	27	factored	factor	VERB
ejpam-4824	92	28	as	as	ADP
ejpam-4824	92	29	x	x	PROPN
ejpam-4824	92	30	⊗	⊗	PROPN
ejpam-4824	92	31	y	y	PROPN
ejpam-4824	92	32	,	,	PUNCT
ejpam-4824	92	33	where	where	SCONJ
ejpam-4824	92	34	x	x	PUNCT
ejpam-4824	92	35	and	and	CCONJ
ejpam-4824	92	36	y	y	PROPN
ejpam-4824	92	37	are	be	AUX
ejpam-4824	92	38	arbitrary	arbitrary	ADJ
ejpam-4824	92	39	operators	operator	NOUN
ejpam-4824	92	40	on	on	ADP
ejpam-4824	92	41	h	h	PROPN
ejpam-4824	92	42	,	,	PUNCT
ejpam-4824	92	43	i.e.	i.e.	X
ejpam-4824	92	44	,	,	PUNCT
ejpam-4824	92	45	x	x	X
ejpam-4824	92	46	,	,	PUNCT
ejpam-4824	92	47	y	y	PROPN
ejpam-4824	92	48	:	:	PUNCT
ejpam-4824	92	49	h	h	PROPN
ejpam-4824	92	50	→	→	SYM
ejpam-4824	92	51	h	h	NOUN
ejpam-4824	92	52	.	.	PUNCT
ejpam-4824	93	1	first	first	ADV
ejpam-4824	93	2	,	,	PUNCT
ejpam-4824	93	3	we	we	PRON
ejpam-4824	93	4	illustrate	illustrate	VERB
ejpam-4824	93	5	this	this	PRON
ejpam-4824	93	6	for	for	ADP
ejpam-4824	93	7	for	for	ADP
ejpam-4824	93	8	d	d	NOUN
ejpam-4824	93	9	=	=	SYM
ejpam-4824	93	10	3	3	NUM
ejpam-4824	93	11	i.e.	i.e.	X
ejpam-4824	93	12	for	for	ADP
ejpam-4824	93	13	xs9	xs9	PROPN
ejpam-4824	93	14	and	and	CCONJ
ejpam-4824	93	15	(	(	PUNCT
ejpam-4824	93	16	xs9)(s9	xs9)(s9	NUM
ejpam-4824	93	17	)	)	PUNCT
ejpam-4824	93	18	.	.	PUNCT
ejpam-4824	94	1	let	let	VERB
ejpam-4824	94	2	xs9	xs9	PUNCT
ejpam-4824	95	1	=	=	PUNCT
ejpam-4824	95	2	x	x	PROPN
ejpam-4824	95	3	⊗	⊗	PROPN
ejpam-4824	95	4	y	y	PROPN
ejpam-4824	95	5	,	,	PUNCT
ejpam-4824	95	6	where	where	SCONJ
ejpam-4824	95	7	x	x	PUNCT
ejpam-4824	95	8	and	and	CCONJ
ejpam-4824	95	9	y	y	PROPN
ejpam-4824	95	10	are	be	AUX
ejpam-4824	95	11	any	any	DET
ejpam-4824	95	12	two	two	NUM
ejpam-4824	95	13	3	3	NUM
ejpam-4824	95	14	by	by	ADP
ejpam-4824	95	15	3	3	NUM
ejpam-4824	95	16	matrices	matrix	NOUN
ejpam-4824	95	17	.	.	PUNCT
ejpam-4824	96	1	this	this	PRON
ejpam-4824	96	2	means	mean	VERB
ejpam-4824	96	3	xs9	xs9	PUNCT
ejpam-4824	96	4	=	=	PUNCT
ejpam-4824	96	5			NOUN
ejpam-4824	96	6	1	1	NUM
ejpam-4824	96	7	0	0	NUM
ejpam-4824	96	8	0	0	NUM
ejpam-4824	96	9	0	0	NUM
ejpam-4824	96	10	0	0	NUM
ejpam-4824	96	11	0	0	NUM
ejpam-4824	96	12	0	0	NUM
ejpam-4824	96	13	0	0	NUM
ejpam-4824	96	14	0	0	NUM
ejpam-4824	96	15	0	0	NUM
ejpam-4824	96	16	0	0	NUM
ejpam-4824	96	17	0	0	NUM
ejpam-4824	96	18	x	x	SYM
ejpam-4824	96	19	0	0	NUM
ejpam-4824	96	20	0	0	NUM
ejpam-4824	96	21	0	0	NUM
ejpam-4824	96	22	0	0	NUM
ejpam-4824	96	23	0	0	NUM
ejpam-4824	96	24	0	0	NUM
ejpam-4824	96	25	0	0	NUM
ejpam-4824	96	26	0	0	NUM
ejpam-4824	96	27	0	0	NUM
ejpam-4824	96	28	0	0	NUM
ejpam-4824	96	29	0	0	NUM
ejpam-4824	97	1	x	x	SYM
ejpam-4824	97	2	0	0	NUM
ejpam-4824	97	3	0	0	NUM
ejpam-4824	97	4	0	0	NUM
ejpam-4824	97	5	x	x	SYM
ejpam-4824	97	6	0	0	NUM
ejpam-4824	97	7	0	0	NUM
ejpam-4824	97	8	0	0	NUM
ejpam-4824	97	9	0	0	NUM
ejpam-4824	97	10	0	0	NUM
ejpam-4824	97	11	0	0	NUM
ejpam-4824	97	12	0	0	NUM
ejpam-4824	97	13	0	0	NUM
ejpam-4824	97	14	0	0	NUM
ejpam-4824	97	15	0	0	NUM
ejpam-4824	97	16	0	0	NUM
ejpam-4824	97	17	1	1	NUM
ejpam-4824	97	18	0	0	NUM
ejpam-4824	97	19	0	0	NUM
ejpam-4824	97	20	0	0	NUM
ejpam-4824	97	21	0	0	NUM
ejpam-4824	97	22	0	0	NUM
ejpam-4824	97	23	0	0	NUM
ejpam-4824	97	24	0	0	NUM
ejpam-4824	97	25	0	0	NUM
ejpam-4824	97	26	0	0	NUM
ejpam-4824	97	27	0	0	NUM
ejpam-4824	97	28	0	0	NUM
ejpam-4824	97	29	x	x	SYM
ejpam-4824	97	30	0	0	NUM
ejpam-4824	97	31	0	0	NUM
ejpam-4824	97	32	0	0	NUM
ejpam-4824	97	33	x	x	SYM
ejpam-4824	97	34	0	0	NUM
ejpam-4824	97	35	0	0	NUM
ejpam-4824	97	36	0	0	NUM
ejpam-4824	97	37	0	0	NUM
ejpam-4824	97	38	0	0	NUM
ejpam-4824	97	39	0	0	NUM
ejpam-4824	97	40	0	0	NUM
ejpam-4824	97	41	0	0	NUM
ejpam-4824	97	42	0	0	NUM
ejpam-4824	97	43	0	0	NUM
ejpam-4824	97	44	0	0	NUM
ejpam-4824	97	45	x	x	SYM
ejpam-4824	97	46	0	0	NUM
ejpam-4824	97	47	0	0	NUM
ejpam-4824	97	48	0	0	NUM
ejpam-4824	97	49	0	0	NUM
ejpam-4824	97	50	0	0	NUM
ejpam-4824	97	51	0	0	NUM
ejpam-4824	97	52	0	0	NUM
ejpam-4824	97	53	0	0	NUM
ejpam-4824	97	54	0	0	NUM
ejpam-4824	97	55	0	0	NUM
ejpam-4824	97	56	0	0	NUM
ejpam-4824	97	57	1	1	NUM
ejpam-4824	97	58			NOUN
ejpam-4824	97	59	=	=	PUNCT
ejpam-4824	98	1			PROPN
ejpam-4824	98	2	x11	x11	NOUN
ejpam-4824	98	3	x12	x12	NUM
ejpam-4824	98	4	x13	x13	PROPN
ejpam-4824	98	5	x21	x21	PROPN
ejpam-4824	98	6	x22	x22	NUM
ejpam-4824	98	7	x23	x23	PROPN
ejpam-4824	98	8	x31	x31	PROPN
ejpam-4824	98	9	x32	x32	PROPN
ejpam-4824	98	10	x33	x33	NUM
ejpam-4824	98	11	⊗	⊗	VERB
ejpam-4824	99	1			PROPN
ejpam-4824	99	2	y11	y11	NOUN
ejpam-4824	99	3	y12	y12	PROPN
ejpam-4824	99	4	y13	y13	PROPN
ejpam-4824	99	5	y21	y21	PROPN
ejpam-4824	99	6	y22	y22	PROPN
ejpam-4824	99	7	y23	y23	NOUN
ejpam-4824	99	8	y31	y31	PROPN
ejpam-4824	99	9	y32	y32	PROPN
ejpam-4824	99	10	y33	y33	NOUN
ejpam-4824	99	11			PROPN
ejpam-4824	99	12	=	=	SYM
ejpam-4824	99	13			NOUN
ejpam-4824	99	14	x11y11	x11y11	PROPN
ejpam-4824	99	15	·	·	PUNCT
ejpam-4824	99	16	·	·	PUNCT
ejpam-4824	99	17	·	·	PUNCT
ejpam-4824	99	18	·	·	PUNCT
ejpam-4824	99	19	·	·	PUNCT
ejpam-4824	99	20	·	·	PUNCT
ejpam-4824	99	21	·	·	PUNCT
ejpam-4824	99	22	·	·	PUNCT
ejpam-4824	99	23	·	·	PUNCT
ejpam-4824	99	24	·	·	PUNCT
ejpam-4824	99	25	·	·	PUNCT
ejpam-4824	99	26	·	·	PUNCT
ejpam-4824	99	27	·	·	PUNCT
ejpam-4824	99	28	·	·	PUNCT
ejpam-4824	99	29	·	·	PUNCT
ejpam-4824	99	30	·	·	PUNCT
ejpam-4824	99	31	·	·	PUNCT
ejpam-4824	99	32	·	·	PUNCT
ejpam-4824	99	33	·	·	PUNCT
ejpam-4824	99	34	x11y33	x11y33	X
ejpam-4824	99	35	·	·	PUNCT
ejpam-4824	99	36	·	·	PUNCT
ejpam-4824	99	37	·	·	PUNCT
ejpam-4824	99	38	·	·	PUNCT
ejpam-4824	99	39	·	·	PUNCT
ejpam-4824	99	40	·	·	PUNCT
ejpam-4824	99	41	·	·	PUNCT
ejpam-4824	99	42	·	·	PUNCT
ejpam-4824	99	43	·	·	PUNCT
ejpam-4824	99	44	·	·	PUNCT
ejpam-4824	99	45	·	·	PUNCT
ejpam-4824	99	46	·	·	PUNCT
ejpam-4824	99	47	·	·	PUNCT
ejpam-4824	99	48	·	·	PUNCT
ejpam-4824	99	49	·	·	PUNCT
ejpam-4824	99	50	·	·	PUNCT
ejpam-4824	99	51	·	·	PUNCT
ejpam-4824	99	52	·	·	PUNCT
ejpam-4824	99	53	·	·	PUNCT
ejpam-4824	99	54	·	·	PUNCT
ejpam-4824	99	55	·	·	PUNCT
ejpam-4824	99	56	·	·	PUNCT
ejpam-4824	99	57	·	·	PUNCT
ejpam-4824	99	58	·	·	PUNCT
ejpam-4824	99	59	·	·	PUNCT
ejpam-4824	99	60	·	·	PUNCT
ejpam-4824	99	61	·	·	PUNCT
ejpam-4824	99	62	·	·	PUNCT
ejpam-4824	99	63	·	·	PUNCT
ejpam-4824	99	64	·	·	PUNCT
ejpam-4824	99	65	·	·	PUNCT
ejpam-4824	99	66	·	·	PUNCT
ejpam-4824	99	67	·	·	PUNCT
ejpam-4824	99	68	·	·	PUNCT
ejpam-4824	99	69	·	·	PUNCT
ejpam-4824	99	70	·	·	PUNCT
ejpam-4824	99	71	·	·	PUNCT
ejpam-4824	99	72	·	·	PUNCT
ejpam-4824	99	73	·	·	PUNCT
ejpam-4824	100	1	x33y11	x33y11	X
ejpam-4824	100	2	·	·	PUNCT
ejpam-4824	100	3	·	·	PUNCT
ejpam-4824	100	4	·	·	PUNCT
ejpam-4824	100	5	·	·	PUNCT
ejpam-4824	100	6	·	·	PUNCT
ejpam-4824	100	7	·	·	PUNCT
ejpam-4824	100	8	·	·	PUNCT
ejpam-4824	100	9	·	·	PUNCT
ejpam-4824	100	10	·	·	PUNCT
ejpam-4824	100	11	·	·	PUNCT
ejpam-4824	100	12	·	·	PUNCT
ejpam-4824	100	13	·	·	PUNCT
ejpam-4824	100	14	·	·	PUNCT
ejpam-4824	100	15	·	·	PUNCT
ejpam-4824	100	16	·	·	PUNCT
ejpam-4824	100	17	·	·	PUNCT
ejpam-4824	100	18	·	·	PUNCT
ejpam-4824	100	19	·	·	PUNCT
ejpam-4824	100	20	·	·	PUNCT
ejpam-4824	100	21	x33y33	x33y33	PROPN
ejpam-4824	100	22			NOUN
ejpam-4824	100	23	then	then	ADV
ejpam-4824	100	24	,	,	PUNCT
ejpam-4824	100	25	comparing	compare	VERB
ejpam-4824	100	26	only	only	ADV
ejpam-4824	100	27	the	the	DET
ejpam-4824	100	28	boxed	box	VERB
ejpam-4824	100	29	diagonal	diagonal	ADJ
ejpam-4824	100	30	entries	entry	NOUN
ejpam-4824	100	31	in	in	ADP
ejpam-4824	100	32	the	the	DET
ejpam-4824	100	33	big	big	ADJ
ejpam-4824	100	34	matrices	matrix	NOUN
ejpam-4824	100	35	above	above	ADP
ejpam-4824	100	36	we	we	PRON
ejpam-4824	100	37	must	must	AUX
ejpam-4824	100	38	have	have	VERB
ejpam-4824	100	39	(	(	PUNCT
ejpam-4824	100	40	x11y11)(x33y33	x11y11)(x33y33	ADJ
ejpam-4824	100	41	)	)	PUNCT
ejpam-4824	100	42	=	=	PRON
ejpam-4824	100	43	(	(	PUNCT
ejpam-4824	100	44	x11y33)(x33y11	x11y33)(x33y11	PROPN
ejpam-4824	100	45	)	)	PUNCT
ejpam-4824	100	46	,	,	PUNCT
ejpam-4824	100	47	which	which	PRON
ejpam-4824	100	48	implies	imply	VERB
ejpam-4824	100	49	the	the	DET
ejpam-4824	100	50	contradictory	contradictory	ADJ
ejpam-4824	100	51	result	result	NOUN
ejpam-4824	100	52	1	1	NUM
ejpam-4824	100	53	=	=	SYM
ejpam-4824	100	54	0	0	NUM
ejpam-4824	100	55	.	.	PUNCT
ejpam-4824	101	1	thus	thus	ADV
ejpam-4824	101	2	,	,	PUNCT
ejpam-4824	101	3	xs9	xs9	PROPN
ejpam-4824	101	4	can	can	AUX
ejpam-4824	101	5	never	never	ADV
ejpam-4824	101	6	be	be	AUX
ejpam-4824	101	7	factored	factor	VERB
ejpam-4824	101	8	as	as	ADP
ejpam-4824	101	9	x	x	PROPN
ejpam-4824	101	10	⊗	⊗	PROPN
ejpam-4824	101	11	y	y	PROPN
ejpam-4824	101	12	.	.	PUNCT
ejpam-4824	102	1	similarly	similarly	ADV
ejpam-4824	102	2	,	,	PUNCT
ejpam-4824	102	3	for	for	ADP
ejpam-4824	102	4	the	the	DET
ejpam-4824	102	5	equality	equality	NOUN
ejpam-4824	102	6	(	(	PUNCT
ejpam-4824	102	7	xs9)(s9	xs9)(s9	NUM
ejpam-4824	102	8	)	)	PUNCT
ejpam-4824	102	9	=	=	PUNCT
ejpam-4824	103	1	x	x	PUNCT
ejpam-4824	103	2	⊗	⊗	PROPN
ejpam-4824	103	3	y	y	PROPN
ejpam-4824	103	4	to	to	PART
ejpam-4824	103	5	happen	happen	VERB
ejpam-4824	103	6	,	,	PUNCT
ejpam-4824	103	7	we	we	PRON
ejpam-4824	103	8	need	need	VERB
ejpam-4824	103	9	to	to	PART
ejpam-4824	103	10	have	have	VERB
ejpam-4824	103	11	:	:	PUNCT
ejpam-4824	103	12	a.	a.	NOUN
ejpam-4824	103	13	pourkia	pourkia	NOUN
ejpam-4824	103	14	/	/	SYM
ejpam-4824	103	15	eur	eur	PROPN
ejpam-4824	103	16	.	.	PUNCT
ejpam-4824	104	1	j.	j.	PROPN
ejpam-4824	104	2	pure	pure	PROPN
ejpam-4824	104	3	appl	appl	PROPN
ejpam-4824	104	4	.	.	PROPN
ejpam-4824	104	5	math	math	PROPN
ejpam-4824	104	6	,	,	PUNCT
ejpam-4824	104	7	16	16	NUM
ejpam-4824	104	8	(	(	PUNCT
ejpam-4824	104	9	3	3	NUM
ejpam-4824	104	10	)	)	PUNCT
ejpam-4824	104	11	(	(	PUNCT
ejpam-4824	104	12	2023	2023	NUM
ejpam-4824	104	13	)	)	PUNCT
ejpam-4824	104	14	,	,	PUNCT
ejpam-4824	104	15	1695	1695	NUM
ejpam-4824	104	16	-	-	SYM
ejpam-4824	104	17	1704	1704	NUM
ejpam-4824	104	18	1701	1701	NUM
ejpam-4824	104	19	(	(	PUNCT
ejpam-4824	104	20	xs9)(s9	xs9)(s9	NUM
ejpam-4824	104	21	)	)	PUNCT
ejpam-4824	104	22	=	=	SYM
ejpam-4824	104	23			NOUN
ejpam-4824	104	24	1	1	NUM
ejpam-4824	104	25	0	0	NUM
ejpam-4824	104	26	0	0	NUM
ejpam-4824	104	27	0	0	NUM
ejpam-4824	104	28	0	0	NUM
ejpam-4824	104	29	0	0	NUM
ejpam-4824	104	30	0	0	NUM
ejpam-4824	104	31	0	0	NUM
ejpam-4824	104	32	0	0	NUM
ejpam-4824	104	33	0	0	NUM
ejpam-4824	105	1	x	x	SYM
ejpam-4824	105	2	0	0	NUM
ejpam-4824	105	3	0	0	NUM
ejpam-4824	105	4	0	0	NUM
ejpam-4824	105	5	0	0	NUM
ejpam-4824	105	6	0	0	NUM
ejpam-4824	105	7	0	0	NUM
ejpam-4824	105	8	0	0	NUM
ejpam-4824	105	9	0	0	NUM
ejpam-4824	105	10	0	0	NUM
ejpam-4824	105	11	x	x	SYM
ejpam-4824	105	12	0	0	NUM
ejpam-4824	105	13	0	0	NUM
ejpam-4824	105	14	0	0	NUM
ejpam-4824	105	15	0	0	NUM
ejpam-4824	105	16	0	0	NUM
ejpam-4824	105	17	0	0	NUM
ejpam-4824	105	18	0	0	NUM
ejpam-4824	105	19	0	0	NUM
ejpam-4824	105	20	0	0	NUM
ejpam-4824	105	21	x	x	SYM
ejpam-4824	105	22	0	0	NUM
ejpam-4824	105	23	0	0	NUM
ejpam-4824	105	24	0	0	NUM
ejpam-4824	105	25	0	0	NUM
ejpam-4824	105	26	0	0	NUM
ejpam-4824	105	27	0	0	NUM
ejpam-4824	105	28	0	0	NUM
ejpam-4824	105	29	0	0	NUM
ejpam-4824	105	30	0	0	NUM
ejpam-4824	105	31	1	1	NUM
ejpam-4824	105	32	0	0	NUM
ejpam-4824	105	33	0	0	NUM
ejpam-4824	105	34	0	0	NUM
ejpam-4824	105	35	0	0	NUM
ejpam-4824	105	36	0	0	NUM
ejpam-4824	105	37	0	0	NUM
ejpam-4824	105	38	0	0	NUM
ejpam-4824	105	39	0	0	NUM
ejpam-4824	105	40	0	0	NUM
ejpam-4824	105	41	x	x	SYM
ejpam-4824	105	42	0	0	NUM
ejpam-4824	105	43	0	0	NUM
ejpam-4824	105	44	0	0	NUM
ejpam-4824	105	45	0	0	NUM
ejpam-4824	105	46	0	0	NUM
ejpam-4824	105	47	0	0	NUM
ejpam-4824	105	48	0	0	NUM
ejpam-4824	105	49	0	0	NUM
ejpam-4824	105	50	0	0	NUM
ejpam-4824	105	51	x	x	SYM
ejpam-4824	105	52	0	0	NUM
ejpam-4824	105	53	0	0	NUM
ejpam-4824	105	54	0	0	NUM
ejpam-4824	105	55	0	0	NUM
ejpam-4824	105	56	0	0	NUM
ejpam-4824	105	57	0	0	NUM
ejpam-4824	105	58	0	0	NUM
ejpam-4824	105	59	0	0	NUM
ejpam-4824	105	60	0	0	NUM
ejpam-4824	105	61	x	x	SYM
ejpam-4824	105	62	0	0	NUM
ejpam-4824	105	63	0	0	NUM
ejpam-4824	105	64	0	0	NUM
ejpam-4824	105	65	0	0	NUM
ejpam-4824	105	66	0	0	NUM
ejpam-4824	105	67	0	0	NUM
ejpam-4824	105	68	0	0	NUM
ejpam-4824	105	69	0	0	NUM
ejpam-4824	105	70	0	0	NUM
ejpam-4824	105	71	1	1	NUM
ejpam-4824	105	72			NOUN
ejpam-4824	105	73	=	=	PUNCT
ejpam-4824	106	1			PROPN
ejpam-4824	106	2	x11	x11	NOUN
ejpam-4824	106	3	x12	x12	NUM
ejpam-4824	106	4	x13	x13	PROPN
ejpam-4824	106	5	x21	x21	PROPN
ejpam-4824	106	6	x22	x22	NUM
ejpam-4824	106	7	x23	x23	PROPN
ejpam-4824	106	8	x31	x31	PROPN
ejpam-4824	106	9	x32	x32	PROPN
ejpam-4824	106	10	x33	x33	NUM
ejpam-4824	106	11	⊗	⊗	VERB
ejpam-4824	107	1			PROPN
ejpam-4824	107	2	y11	y11	NOUN
ejpam-4824	107	3	y12	y12	PROPN
ejpam-4824	107	4	y13	y13	PROPN
ejpam-4824	107	5	y21	y21	PROPN
ejpam-4824	107	6	y22	y22	PROPN
ejpam-4824	107	7	y23	y23	NOUN
ejpam-4824	107	8	y31	y31	PROPN
ejpam-4824	107	9	y32	y32	PROPN
ejpam-4824	107	10	y33	y33	NOUN
ejpam-4824	107	11			PROPN
ejpam-4824	107	12	=	=	SYM
ejpam-4824	107	13			NOUN
ejpam-4824	107	14	x11y11	x11y11	PROPN
ejpam-4824	107	15	·	·	PUNCT
ejpam-4824	107	16	·	·	PUNCT
ejpam-4824	107	17	·	·	PUNCT
ejpam-4824	107	18	·	·	PUNCT
ejpam-4824	107	19	·	·	PUNCT
ejpam-4824	107	20	·	·	PUNCT
ejpam-4824	107	21	·	·	PUNCT
ejpam-4824	107	22	·	·	PUNCT
ejpam-4824	107	23	·	·	PUNCT
ejpam-4824	107	24	·	·	PUNCT
ejpam-4824	107	25	·	·	PUNCT
ejpam-4824	107	26	·	·	PUNCT
ejpam-4824	107	27	·	·	PUNCT
ejpam-4824	107	28	·	·	PUNCT
ejpam-4824	107	29	·	·	PUNCT
ejpam-4824	107	30	·	·	PUNCT
ejpam-4824	107	31	·	·	PUNCT
ejpam-4824	107	32	·	·	PUNCT
ejpam-4824	107	33	·	·	PUNCT
ejpam-4824	107	34	x11y33	x11y33	X
ejpam-4824	107	35	·	·	PUNCT
ejpam-4824	107	36	·	·	PUNCT
ejpam-4824	107	37	·	·	PUNCT
ejpam-4824	107	38	·	·	PUNCT
ejpam-4824	107	39	·	·	PUNCT
ejpam-4824	107	40	·	·	PUNCT
ejpam-4824	107	41	·	·	PUNCT
ejpam-4824	107	42	·	·	PUNCT
ejpam-4824	107	43	·	·	PUNCT
ejpam-4824	107	44	·	·	PUNCT
ejpam-4824	107	45	·	·	PUNCT
ejpam-4824	107	46	·	·	PUNCT
ejpam-4824	107	47	·	·	PUNCT
ejpam-4824	107	48	·	·	PUNCT
ejpam-4824	107	49	·	·	PUNCT
ejpam-4824	107	50	·	·	PUNCT
ejpam-4824	107	51	·	·	PUNCT
ejpam-4824	107	52	·	·	PUNCT
ejpam-4824	107	53	·	·	PUNCT
ejpam-4824	107	54	·	·	PUNCT
ejpam-4824	107	55	·	·	PUNCT
ejpam-4824	107	56	·	·	PUNCT
ejpam-4824	107	57	·	·	PUNCT
ejpam-4824	107	58	·	·	PUNCT
ejpam-4824	107	59	·	·	PUNCT
ejpam-4824	107	60	·	·	PUNCT
ejpam-4824	107	61	·	·	PUNCT
ejpam-4824	107	62	·	·	PUNCT
ejpam-4824	107	63	·	·	PUNCT
ejpam-4824	107	64	·	·	PUNCT
ejpam-4824	107	65	·	·	PUNCT
ejpam-4824	107	66	·	·	PUNCT
ejpam-4824	107	67	·	·	PUNCT
ejpam-4824	107	68	·	·	PUNCT
ejpam-4824	107	69	·	·	PUNCT
ejpam-4824	107	70	·	·	PUNCT
ejpam-4824	107	71	·	·	PUNCT
ejpam-4824	107	72	·	·	PUNCT
ejpam-4824	107	73	·	·	PUNCT
ejpam-4824	108	1	x33y11	x33y11	X
ejpam-4824	108	2	·	·	PUNCT
ejpam-4824	108	3	·	·	PUNCT
ejpam-4824	108	4	·	·	PUNCT
ejpam-4824	108	5	·	·	PUNCT
ejpam-4824	108	6	·	·	PUNCT
ejpam-4824	108	7	·	·	PUNCT
ejpam-4824	108	8	·	·	PUNCT
ejpam-4824	108	9	·	·	PUNCT
ejpam-4824	108	10	·	·	PUNCT
ejpam-4824	108	11	·	·	PUNCT
ejpam-4824	108	12	·	·	PUNCT
ejpam-4824	108	13	·	·	PUNCT
ejpam-4824	108	14	·	·	PUNCT
ejpam-4824	108	15	·	·	PUNCT
ejpam-4824	108	16	·	·	PUNCT
ejpam-4824	108	17	·	·	PUNCT
ejpam-4824	108	18	·	·	PUNCT
ejpam-4824	108	19	·	·	PUNCT
ejpam-4824	108	20	·	·	PUNCT
ejpam-4824	108	21	x33y33	x33y33	PROPN
ejpam-4824	108	22			NOUN
ejpam-4824	108	23	again	again	ADV
ejpam-4824	108	24	,	,	PUNCT
ejpam-4824	108	25	comparing	compare	VERB
ejpam-4824	108	26	only	only	ADV
ejpam-4824	108	27	the	the	DET
ejpam-4824	108	28	boxed	box	VERB
ejpam-4824	108	29	diagonal	diagonal	ADJ
ejpam-4824	108	30	entries	entry	NOUN
ejpam-4824	108	31	in	in	ADP
ejpam-4824	108	32	the	the	DET
ejpam-4824	108	33	big	big	ADJ
ejpam-4824	108	34	matrices	matrix	NOUN
ejpam-4824	108	35	above	above	ADP
ejpam-4824	108	36	we	we	PRON
ejpam-4824	108	37	must	must	AUX
ejpam-4824	108	38	have	have	VERB
ejpam-4824	108	39	(	(	PUNCT
ejpam-4824	108	40	x11y11)(x33y33	x11y11)(x33y33	ADJ
ejpam-4824	108	41	)	)	PUNCT
ejpam-4824	108	42	=	=	PRON
ejpam-4824	108	43	(	(	PUNCT
ejpam-4824	108	44	x11y33)(x33y11	x11y33)(x33y11	PROPN
ejpam-4824	108	45	)	)	PUNCT
ejpam-4824	108	46	,	,	PUNCT
ejpam-4824	108	47	which	which	PRON
ejpam-4824	108	48	implies	imply	VERB
ejpam-4824	108	49	1	1	NUM
ejpam-4824	108	50	=	=	SYM
ejpam-4824	108	51	x2	x2	PROPN
ejpam-4824	108	52	.	.	PUNCT
ejpam-4824	109	1	therefore	therefore	ADV
ejpam-4824	109	2	,	,	PUNCT
ejpam-4824	109	3	for	for	SCONJ
ejpam-4824	109	4	x	x	SYM
ejpam-4824	109	5	̸=	̸=	PROPN
ejpam-4824	109	6	±1	±1	VERB
ejpam-4824	109	7	,	,	PUNCT
ejpam-4824	109	8	(	(	PUNCT
ejpam-4824	109	9	xs9)(s9	xs9)(s9	NUM
ejpam-4824	109	10	)	)	PUNCT
ejpam-4824	109	11	can	can	AUX
ejpam-4824	109	12	not	not	PART
ejpam-4824	109	13	be	be	AUX
ejpam-4824	109	14	factored	factor	VERB
ejpam-4824	109	15	as	as	ADP
ejpam-4824	109	16	x	x	PROPN
ejpam-4824	109	17	⊗	⊗	PROPN
ejpam-4824	109	18	y	y	PROPN
ejpam-4824	109	19	.	.	PUNCT
ejpam-4824	110	1	the	the	DET
ejpam-4824	110	2	general	general	ADJ
ejpam-4824	110	3	result	result	NOUN
ejpam-4824	110	4	and	and	CCONJ
ejpam-4824	110	5	its	its	PRON
ejpam-4824	110	6	proof	proof	NOUN
ejpam-4824	110	7	is	be	AUX
ejpam-4824	110	8	presented	present	VERB
ejpam-4824	110	9	in	in	ADP
ejpam-4824	110	10	the	the	DET
ejpam-4824	110	11	following	follow	VERB
ejpam-4824	110	12	theorem	theorem	PROPN
ejpam-4824	110	13	.	.	PUNCT
ejpam-4824	110	14	theorem	theorem	NOUN
ejpam-4824	110	15	1	1	NUM
ejpam-4824	110	16	.	.	X
ejpam-4824	111	1	for	for	ADP
ejpam-4824	111	2	any	any	DET
ejpam-4824	111	3	d	d	PROPN
ejpam-4824	111	4	≥	≥	NUM
ejpam-4824	111	5	2	2	NUM
ejpam-4824	111	6	and	and	CCONJ
ejpam-4824	111	7	for	for	ADP
ejpam-4824	111	8	any	any	DET
ejpam-4824	111	9	x	x	NOUN
ejpam-4824	111	10	=	=	PRON
ejpam-4824	111	11	eiφ	eiφ	NOUN
ejpam-4824	111	12	in	in	ADP
ejpam-4824	111	13	which	which	PRON
ejpam-4824	111	14	φ	φ	PROPN
ejpam-4824	111	15	is	be	AUX
ejpam-4824	111	16	a	a	DET
ejpam-4824	111	17	real	real	ADJ
ejpam-4824	111	18	number	number	NOUN
ejpam-4824	111	19	,	,	PUNCT
ejpam-4824	111	20	the	the	DET
ejpam-4824	111	21	xswap	xswap	NOUN
ejpam-4824	111	22	from	from	ADP
ejpam-4824	111	23	definition	definition	NOUN
ejpam-4824	111	24	1	1	NUM
ejpam-4824	111	25	is	be	AUX
ejpam-4824	111	26	unitary	unitary	ADJ
ejpam-4824	111	27	and	and	CCONJ
ejpam-4824	111	28	it	it	PRON
ejpam-4824	111	29	is	be	AUX
ejpam-4824	111	30	entangling	entangle	VERB
ejpam-4824	111	31	when	when	SCONJ
ejpam-4824	111	32	x	x	PROPN
ejpam-4824	111	33	̸=	̸=	PROPN
ejpam-4824	111	34	±1	±1	VERB
ejpam-4824	111	35	.	.	PUNCT
ejpam-4824	112	1	hence	hence	ADV
ejpam-4824	112	2	,	,	PUNCT
ejpam-4824	112	3	for	for	SCONJ
ejpam-4824	112	4	x	x	SYM
ejpam-4824	112	5	̸=	̸=	PROPN
ejpam-4824	112	6	±1	±1	VERB
ejpam-4824	112	7	,	,	PUNCT
ejpam-4824	112	8	xswap	xswap	PROPN
ejpam-4824	112	9	is	be	AUX
ejpam-4824	112	10	a	a	DET
ejpam-4824	112	11	universal	universal	ADJ
ejpam-4824	112	12	quantum	quantum	NOUN
ejpam-4824	112	13	gate	gate	NOUN
ejpam-4824	112	14	for	for	ADP
ejpam-4824	112	15	d	d	NOUN
ejpam-4824	112	16	-	-	PUNCT
ejpam-4824	112	17	level	level	NOUN
ejpam-4824	112	18	qudit	qudit	NOUN
ejpam-4824	112	19	systems	system	NOUN
ejpam-4824	112	20	.	.	PUNCT
ejpam-4824	113	1	proof	proof	NOUN
ejpam-4824	113	2	.	.	PUNCT
ejpam-4824	114	1	the	the	DET
ejpam-4824	114	2	unitarity	unitarity	NOUN
ejpam-4824	114	3	of	of	ADP
ejpam-4824	114	4	xswap	xswap	PROPN
ejpam-4824	114	5	is	be	AUX
ejpam-4824	114	6	obvious	obvious	ADJ
ejpam-4824	114	7	because	because	SCONJ
ejpam-4824	114	8	of	of	ADP
ejpam-4824	114	9	the	the	DET
ejpam-4824	114	10	choice	choice	NOUN
ejpam-4824	114	11	x	x	NOUN
ejpam-4824	114	12	=	=	SYM
ejpam-4824	114	13	eiφ	eiφ	NOUN
ejpam-4824	114	14	.	.	PUNCT
ejpam-4824	115	1	as	as	ADP
ejpam-4824	115	2	for	for	ADP
ejpam-4824	115	3	the	the	DET
ejpam-4824	115	4	entangling	entangle	VERB
ejpam-4824	115	5	property	property	NOUN
ejpam-4824	115	6	,	,	PUNCT
ejpam-4824	115	7	we	we	PRON
ejpam-4824	115	8	need	need	VERB
ejpam-4824	115	9	to	to	PART
ejpam-4824	115	10	show	show	VERB
ejpam-4824	115	11	that	that	SCONJ
ejpam-4824	115	12	for	for	SCONJ
ejpam-4824	115	13	x	x	SYM
ejpam-4824	115	14	̸=	̸=	PROPN
ejpam-4824	115	15	±1	±1	VERB
ejpam-4824	115	16	none	none	NOUN
ejpam-4824	115	17	of	of	ADP
ejpam-4824	115	18	xs	xs	PROPN
ejpam-4824	115	19	and	and	CCONJ
ejpam-4824	115	20	(	(	PUNCT
ejpam-4824	115	21	xs)(s	xs)(s	PRON
ejpam-4824	115	22	)	)	PUNCT
ejpam-4824	115	23	can	can	AUX
ejpam-4824	115	24	factor	factor	VERB
ejpam-4824	115	25	as	as	ADP
ejpam-4824	115	26	x	x	PROPN
ejpam-4824	115	27	⊗	⊗	PROPN
ejpam-4824	115	28	y	y	PROPN
ejpam-4824	115	29	,	,	PUNCT
ejpam-4824	115	30	where	where	SCONJ
ejpam-4824	115	31	x	x	PUNCT
ejpam-4824	115	32	and	and	CCONJ
ejpam-4824	115	33	y	y	PROPN
ejpam-4824	115	34	are	be	AUX
ejpam-4824	115	35	d	d	X
ejpam-4824	115	36	by	by	ADP
ejpam-4824	115	37	d	d	NOUN
ejpam-4824	115	38	matrices	matrix	NOUN
ejpam-4824	115	39	[	[	X
ejpam-4824	115	40	1	1	NUM
ejpam-4824	115	41	]	]	PUNCT
ejpam-4824	115	42	.	.	PUNCT
ejpam-4824	116	1	for	for	ADP
ejpam-4824	116	2	both	both	DET
ejpam-4824	116	3	cases	case	NOUN
ejpam-4824	116	4	,	,	PUNCT
ejpam-4824	116	5	we	we	PRON
ejpam-4824	116	6	assume	assume	VERB
ejpam-4824	116	7	the	the	DET
ejpam-4824	116	8	opposite	opposite	ADJ
ejpam-4824	116	9	,	,	PUNCT
ejpam-4824	116	10	i.e.	i.e.	X
ejpam-4824	116	11	,	,	PUNCT
ejpam-4824	116	12	we	we	PRON
ejpam-4824	116	13	assume	assume	VERB
ejpam-4824	116	14	xs	xs	X
ejpam-4824	117	1	=	=	PUNCT
ejpam-4824	118	1	x	x	PROPN
ejpam-4824	119	1	⊗	⊗	PROPN
ejpam-4824	119	2	y	y	PROPN
ejpam-4824	119	3	or	or	CCONJ
ejpam-4824	119	4	(	(	PUNCT
ejpam-4824	119	5	xs)(s	xs)(s	PUNCT
ejpam-4824	119	6	)	)	PUNCT
ejpam-4824	120	1	=	=	PUNCT
ejpam-4824	121	1	x	x	PUNCT
ejpam-4824	121	2	⊗	⊗	NUM
ejpam-4824	121	3	y	y	PROPN
ejpam-4824	121	4	.	.	PUNCT
ejpam-4824	122	1	then	then	ADV
ejpam-4824	122	2	,	,	PUNCT
ejpam-4824	122	3	using	use	VERB
ejpam-4824	122	4	definition	definition	NOUN
ejpam-4824	122	5	1	1	NUM
ejpam-4824	122	6	,	,	PUNCT
ejpam-4824	122	7	we	we	PRON
ejpam-4824	122	8	compare	compare	VERB
ejpam-4824	122	9	the	the	DET
ejpam-4824	122	10	following	following	ADJ
ejpam-4824	122	11	equality	equality	NOUN
ejpam-4824	122	12	,	,	PUNCT
ejpam-4824	122	13	(	(	PUNCT
ejpam-4824	122	14	x11y11)(xddydd	x11y11)(xddydd	X
ejpam-4824	122	15	)	)	PUNCT
ejpam-4824	122	16	=	=	SYM
ejpam-4824	122	17	(	(	PUNCT
ejpam-4824	122	18	x11ydd)(xddy11	x11ydd)(xddy11	NUM
ejpam-4824	122	19	)	)	PUNCT
ejpam-4824	122	20	(	(	PUNCT
ejpam-4824	122	21	6	6	X
ejpam-4824	122	22	)	)	PUNCT
ejpam-4824	122	23	a.	a.	NOUN
ejpam-4824	122	24	pourkia	pourkia	NOUN
ejpam-4824	122	25	/	/	SYM
ejpam-4824	122	26	eur	eur	PROPN
ejpam-4824	122	27	.	.	PUNCT
ejpam-4824	123	1	j.	j.	PROPN
ejpam-4824	123	2	pure	pure	PROPN
ejpam-4824	123	3	appl	appl	PROPN
ejpam-4824	123	4	.	.	PROPN
ejpam-4824	123	5	math	math	PROPN
ejpam-4824	123	6	,	,	PUNCT
ejpam-4824	123	7	16	16	NUM
ejpam-4824	123	8	(	(	PUNCT
ejpam-4824	123	9	3	3	NUM
ejpam-4824	123	10	)	)	PUNCT
ejpam-4824	123	11	(	(	PUNCT
ejpam-4824	123	12	2023	2023	NUM
ejpam-4824	123	13	)	)	PUNCT
ejpam-4824	123	14	,	,	PUNCT
ejpam-4824	123	15	1695	1695	NUM
ejpam-4824	123	16	-	-	SYM
ejpam-4824	123	17	1704	1704	NUM
ejpam-4824	123	18	1702	1702	NUM
ejpam-4824	123	19	which	which	PRON
ejpam-4824	123	20	involves	involve	VERB
ejpam-4824	123	21	certain	certain	ADJ
ejpam-4824	123	22	diagonal	diagonal	ADJ
ejpam-4824	123	23	entries	entry	NOUN
ejpam-4824	123	24	from	from	ADP
ejpam-4824	123	25	the	the	DET
ejpam-4824	123	26	tensor	tensor	NOUN
ejpam-4824	123	27	product	product	NOUN
ejpam-4824	123	28	matrix	matrix	NOUN
ejpam-4824	123	29	x	x	PUNCT
ejpam-4824	123	30	⊗	⊗	PROPN
ejpam-4824	123	31	y	y	PROPN
ejpam-4824	123	32	with	with	ADP
ejpam-4824	123	33	the	the	DET
ejpam-4824	123	34	same	same	ADJ
ejpam-4824	123	35	equality	equality	NOUN
ejpam-4824	123	36	involving	involve	VERB
ejpam-4824	123	37	the	the	DET
ejpam-4824	123	38	same	same	ADJ
ejpam-4824	123	39	entries	entry	NOUN
ejpam-4824	123	40	from	from	ADP
ejpam-4824	123	41	the	the	DET
ejpam-4824	123	42	matrix	matrix	NOUN
ejpam-4824	123	43	s	s	PART
ejpam-4824	123	44	or	or	CCONJ
ejpam-4824	123	45	(	(	PUNCT
ejpam-4824	123	46	xs)(s	xs)(s	PROPN
ejpam-4824	123	47	)	)	PUNCT
ejpam-4824	123	48	)	)	PUNCT
ejpam-4824	123	49	.	.	PUNCT
ejpam-4824	124	1	the	the	DET
ejpam-4824	124	2	above	above	ADJ
ejpam-4824	124	3	mentioned	mention	VERB
ejpam-4824	124	4	comparison	comparison	NOUN
ejpam-4824	124	5	for	for	ADP
ejpam-4824	124	6	the	the	DET
ejpam-4824	124	7	case	case	NOUN
ejpam-4824	124	8	of	of	ADP
ejpam-4824	124	9	xs	xs	PROPN
ejpam-4824	124	10	=	=	PUNCT
ejpam-4824	125	1	x	x	SYM
ejpam-4824	125	2	⊗	⊗	PROPN
ejpam-4824	125	3	y	y	PROPN
ejpam-4824	125	4	implies	imply	VERB
ejpam-4824	125	5	1	1	NUM
ejpam-4824	125	6	=	=	SYM
ejpam-4824	125	7	0	0	NUM
ejpam-4824	125	8	,	,	PUNCT
ejpam-4824	125	9	which	which	PRON
ejpam-4824	125	10	is	be	AUX
ejpam-4824	125	11	impossible	impossible	ADJ
ejpam-4824	125	12	regardless	regardless	ADV
ejpam-4824	125	13	of	of	ADP
ejpam-4824	125	14	the	the	DET
ejpam-4824	125	15	value	value	NOUN
ejpam-4824	125	16	of	of	ADP
ejpam-4824	125	17	x.	x.	NOUN
ejpam-4824	125	18	also	also	ADV
ejpam-4824	125	19	for	for	ADP
ejpam-4824	125	20	the	the	DET
ejpam-4824	125	21	case	case	NOUN
ejpam-4824	125	22	of	of	ADP
ejpam-4824	125	23	(	(	PUNCT
ejpam-4824	125	24	xs)(s	xs)(s	PUNCT
ejpam-4824	125	25	)	)	PUNCT
ejpam-4824	126	1	=	=	PUNCT
ejpam-4824	127	1	x	x	X
ejpam-4824	127	2	⊗	⊗	PROPN
ejpam-4824	127	3	y	y	PROPN
ejpam-4824	127	4	it	it	PRON
ejpam-4824	127	5	implies	imply	VERB
ejpam-4824	127	6	x2	x2	PROPN
ejpam-4824	127	7	=	=	NOUN
ejpam-4824	127	8	1	1	X
ejpam-4824	127	9	.	.	PUNCT
ejpam-4824	128	1	this	this	PRON
ejpam-4824	128	2	finishes	finish	VERB
ejpam-4824	128	3	the	the	DET
ejpam-4824	128	4	proof	proof	NOUN
ejpam-4824	128	5	.	.	PUNCT
ejpam-4824	129	1	remark	remark	NOUN
ejpam-4824	129	2	1	1	NUM
ejpam-4824	129	3	.	.	PUNCT
ejpam-4824	129	4	to	to	PART
ejpam-4824	129	5	directly	directly	ADV
ejpam-4824	129	6	prove	prove	VERB
ejpam-4824	129	7	a	a	DET
ejpam-4824	129	8	2	2	NUM
ejpam-4824	129	9	-	-	PUNCT
ejpam-4824	129	10	qudit	qudit	NOUN
ejpam-4824	129	11	gate	gate	NOUN
ejpam-4824	129	12	g	g	PROPN
ejpam-4824	129	13	is	be	AUX
ejpam-4824	129	14	universal	universal	ADJ
ejpam-4824	129	15	one	one	NUM
ejpam-4824	129	16	needs	need	VERB
ejpam-4824	129	17	to	to	PART
ejpam-4824	129	18	show	show	VERB
ejpam-4824	129	19	that	that	SCONJ
ejpam-4824	129	20	the	the	DET
ejpam-4824	129	21	set	set	NOUN
ejpam-4824	129	22	containing	contain	VERB
ejpam-4824	129	23	g	g	NOUN
ejpam-4824	129	24	and	and	CCONJ
ejpam-4824	129	25	all	all	DET
ejpam-4824	129	26	1	1	NUM
ejpam-4824	129	27	-	-	PUNCT
ejpam-4824	129	28	qudit	qudit	NOUN
ejpam-4824	129	29	gates	gate	NOUN
ejpam-4824	129	30	is	be	AUX
ejpam-4824	129	31	enough	enough	ADJ
ejpam-4824	129	32	to	to	PART
ejpam-4824	129	33	produce	produce	VERB
ejpam-4824	129	34	other	other	ADJ
ejpam-4824	129	35	qudit	qudit	NOUN
ejpam-4824	129	36	gates	gate	NOUN
ejpam-4824	129	37	.	.	PUNCT
ejpam-4824	130	1	showing	show	VERB
ejpam-4824	130	2	this	this	PRON
ejpam-4824	130	3	directly	directly	ADV
ejpam-4824	130	4	is	be	AUX
ejpam-4824	130	5	not	not	PART
ejpam-4824	130	6	always	always	ADV
ejpam-4824	130	7	easy	easy	ADJ
ejpam-4824	130	8	even	even	ADV
ejpam-4824	130	9	in	in	ADP
ejpam-4824	130	10	dimension	dimension	NOUN
ejpam-4824	130	11	d	d	NOUN
ejpam-4824	130	12	=	=	SYM
ejpam-4824	130	13	2	2	X
ejpam-4824	130	14	.	.	PUNCT
ejpam-4824	131	1	this	this	PRON
ejpam-4824	131	2	is	be	AUX
ejpam-4824	131	3	why	why	SCONJ
ejpam-4824	131	4	we	we	PRON
ejpam-4824	131	5	have	have	AUX
ejpam-4824	131	6	instead	instead	ADV
ejpam-4824	131	7	used	use	VERB
ejpam-4824	131	8	the	the	DET
ejpam-4824	131	9	powerful	powerful	ADJ
ejpam-4824	131	10	brylinskis	brylinski	NOUN
ejpam-4824	131	11	’	'	PUNCT
ejpam-4824	131	12	criterion	criterion	NOUN
ejpam-4824	132	1	[	[	X
ejpam-4824	132	2	3	3	NUM
ejpam-4824	132	3	]	]	PUNCT
ejpam-4824	132	4	and	and	CCONJ
ejpam-4824	132	5	the	the	DET
ejpam-4824	132	6	the	the	DET
ejpam-4824	132	7	non	non	ADJ
ejpam-4824	132	8	-	-	ADJ
ejpam-4824	132	9	entangling	entangle	VERB
ejpam-4824	132	10	criteria	criterion	NOUN
ejpam-4824	132	11	from	from	ADP
ejpam-4824	132	12	[	[	X
ejpam-4824	132	13	1	1	NUM
ejpam-4824	132	14	]	]	PUNCT
ejpam-4824	132	15	.	.	PUNCT
ejpam-4824	133	1	5	5	X
ejpam-4824	133	2	.	.	X
ejpam-4824	133	3	concluding	conclude	VERB
ejpam-4824	133	4	remarks	remark	NOUN
ejpam-4824	133	5	in	in	ADP
ejpam-4824	133	6	the	the	DET
ejpam-4824	133	7	recent	recent	ADJ
ejpam-4824	133	8	decades	decade	NOUN
ejpam-4824	133	9	,	,	PUNCT
ejpam-4824	133	10	there	there	PRON
ejpam-4824	133	11	has	have	AUX
ejpam-4824	133	12	been	be	AUX
ejpam-4824	133	13	an	an	DET
ejpam-4824	133	14	ever	ever	ADV
ejpam-4824	133	15	increasing	increase	VERB
ejpam-4824	133	16	interest	interest	NOUN
ejpam-4824	133	17	in	in	ADP
ejpam-4824	133	18	applications	application	NOUN
ejpam-4824	133	19	of	of	ADP
ejpam-4824	133	20	d	d	NOUN
ejpam-4824	133	21	-	-	PUNCT
ejpam-4824	133	22	level	level	NOUN
ejpam-4824	133	23	qudits	qudit	NOUN
ejpam-4824	133	24	,	,	PUNCT
ejpam-4824	133	25	for	for	ADP
ejpam-4824	133	26	d	d	PROPN
ejpam-4824	133	27	≥	≥	NUM
ejpam-4824	133	28	3	3	NUM
ejpam-4824	133	29	,	,	PUNCT
ejpam-4824	133	30	in	in	ADP
ejpam-4824	133	31	quantum	quantum	NOUN
ejpam-4824	133	32	computing	computing	NOUN
ejpam-4824	133	33	and	and	CCONJ
ejpam-4824	133	34	quantum	quantum	NOUN
ejpam-4824	133	35	information	information	NOUN
ejpam-4824	133	36	.	.	PUNCT
ejpam-4824	134	1	this	this	PRON
ejpam-4824	134	2	is	be	AUX
ejpam-4824	134	3	due	due	ADJ
ejpam-4824	134	4	to	to	ADP
ejpam-4824	134	5	their	their	PRON
ejpam-4824	134	6	advantages	advantage	NOUN
ejpam-4824	134	7	over	over	ADP
ejpam-4824	134	8	the	the	DET
ejpam-4824	134	9	conventional	conventional	ADJ
ejpam-4824	134	10	qubits	qubit	NOUN
ejpam-4824	134	11	(	(	PUNCT
ejpam-4824	134	12	i.e.	i.e.	X
ejpam-4824	134	13	,	,	PUNCT
ejpam-4824	134	14	d	d	NOUN
ejpam-4824	134	15	=	=	SYM
ejpam-4824	134	16	2	2	NUM
ejpam-4824	134	17	)	)	PUNCT
ejpam-4824	134	18	.	.	PUNCT
ejpam-4824	135	1	these	these	DET
ejpam-4824	135	2	advantages	advantage	NOUN
ejpam-4824	135	3	include	include	VERB
ejpam-4824	135	4	larger	large	ADJ
ejpam-4824	135	5	storing	storing	NOUN
ejpam-4824	135	6	and	and	CCONJ
ejpam-4824	135	7	processing	processing	NOUN
ejpam-4824	135	8	space	space	NOUN
ejpam-4824	135	9	for	for	ADP
ejpam-4824	135	10	information	information	NOUN
ejpam-4824	135	11	,	,	PUNCT
ejpam-4824	135	12	smaller	small	ADJ
ejpam-4824	135	13	number	number	NOUN
ejpam-4824	135	14	of	of	ADP
ejpam-4824	135	15	qudits	qudit	NOUN
ejpam-4824	135	16	required	require	VERB
ejpam-4824	135	17	to	to	PART
ejpam-4824	135	18	span	span	VERB
ejpam-4824	135	19	the	the	DET
ejpam-4824	135	20	state	state	NOUN
ejpam-4824	135	21	space	space	NOUN
ejpam-4824	135	22	,	,	PUNCT
ejpam-4824	135	23	better	well	ADJ
ejpam-4824	135	24	noise	noise	NOUN
ejpam-4824	135	25	-	-	PUNCT
ejpam-4824	135	26	resistant	resistant	ADJ
ejpam-4824	135	27	,	,	PUNCT
ejpam-4824	135	28	simplifying	simplify	VERB
ejpam-4824	135	29	quantum	quantum	ADJ
ejpam-4824	135	30	logic	logic	NOUN
ejpam-4824	135	31	,	,	PUNCT
ejpam-4824	135	32	and	and	CCONJ
ejpam-4824	135	33	more	more	ADJ
ejpam-4824	135	34	.	.	PUNCT
ejpam-4824	136	1	moreover	moreover	ADV
ejpam-4824	136	2	,	,	PUNCT
ejpam-4824	136	3	there	there	PRON
ejpam-4824	136	4	has	have	AUX
ejpam-4824	136	5	been	be	AUX
ejpam-4824	136	6	very	very	ADV
ejpam-4824	136	7	interesting	interesting	ADJ
ejpam-4824	136	8	developments	development	NOUN
ejpam-4824	136	9	regarding	regard	VERB
ejpam-4824	136	10	the	the	DET
ejpam-4824	136	11	physical	physical	ADJ
ejpam-4824	136	12	implementation	implementation	NOUN
ejpam-4824	136	13	of	of	ADP
ejpam-4824	136	14	qudit	qudit	NOUN
ejpam-4824	136	15	-	-	PUNCT
ejpam-4824	136	16	based	base	VERB
ejpam-4824	136	17	quantum	quantum	NOUN
ejpam-4824	136	18	computing	computing	NOUN
ejpam-4824	136	19	systems	system	NOUN
ejpam-4824	137	1	[	[	X
ejpam-4824	137	2	7–9	7–9	NUM
ejpam-4824	137	3	,	,	PUNCT
ejpam-4824	137	4	11–13	11–13	NUM
ejpam-4824	137	5	,	,	PUNCT
ejpam-4824	137	6	17	17	NUM
ejpam-4824	137	7	]	]	PUNCT
ejpam-4824	137	8	.	.	PUNCT
ejpam-4824	138	1	naturally	naturally	ADV
ejpam-4824	138	2	,	,	PUNCT
ejpam-4824	138	3	to	to	PART
ejpam-4824	138	4	make	make	VERB
ejpam-4824	138	5	it	it	PRON
ejpam-4824	138	6	possible	possible	ADJ
ejpam-4824	138	7	to	to	PART
ejpam-4824	138	8	work	work	VERB
ejpam-4824	138	9	with	with	ADP
ejpam-4824	138	10	d	d	ADJ
ejpam-4824	138	11	-	-	PUNCT
ejpam-4824	138	12	level	level	NOUN
ejpam-4824	138	13	qudits	qudit	VERB
ejpam-4824	138	14	one	one	NUM
ejpam-4824	138	15	needs	need	NOUN
ejpam-4824	138	16	to	to	PART
ejpam-4824	138	17	have	have	VERB
ejpam-4824	138	18	quantum	quantum	ADJ
ejpam-4824	138	19	logic	logic	NOUN
ejpam-4824	138	20	gates	gate	NOUN
ejpam-4824	138	21	that	that	PRON
ejpam-4824	138	22	could	could	AUX
ejpam-4824	138	23	operate	operate	VERB
ejpam-4824	138	24	on	on	ADP
ejpam-4824	138	25	them	they	PRON
ejpam-4824	138	26	.	.	PUNCT
ejpam-4824	139	1	in	in	ADP
ejpam-4824	139	2	the	the	DET
ejpam-4824	139	3	present	present	ADJ
ejpam-4824	139	4	paper	paper	NOUN
ejpam-4824	139	5	we	we	PRON
ejpam-4824	139	6	have	have	AUX
ejpam-4824	139	7	generalized	generalize	VERB
ejpam-4824	139	8	the	the	DET
ejpam-4824	139	9	swap	swap	NOUN
ejpam-4824	139	10	gate	gate	NOUN
ejpam-4824	139	11	and	and	CCONJ
ejpam-4824	139	12	the	the	DET
ejpam-4824	139	13	iswap	iswap	PROPN
ejpam-4824	139	14	gate	gate	NOUN
ejpam-4824	139	15	to	to	ADP
ejpam-4824	139	16	any	any	DET
ejpam-4824	139	17	dimension	dimension	NOUN
ejpam-4824	139	18	d	d	X
ejpam-4824	139	19	≥	≥	NUM
ejpam-4824	139	20	2	2	NUM
ejpam-4824	139	21	,	,	PUNCT
ejpam-4824	139	22	in	in	ADP
ejpam-4824	139	23	terms	term	NOUN
ejpam-4824	139	24	of	of	ADP
ejpam-4824	139	25	permutation	permutation	NOUN
ejpam-4824	139	26	matrices	matrix	NOUN
ejpam-4824	139	27	.	.	PUNCT
ejpam-4824	140	1	we	we	PRON
ejpam-4824	140	2	have	have	AUX
ejpam-4824	140	3	unified	unify	VERB
ejpam-4824	140	4	these	these	DET
ejpam-4824	140	5	gates	gate	NOUN
ejpam-4824	140	6	by	by	ADP
ejpam-4824	140	7	introducing	introduce	VERB
ejpam-4824	140	8	a	a	DET
ejpam-4824	140	9	more	more	ADV
ejpam-4824	140	10	general	general	ADJ
ejpam-4824	140	11	gate	gate	NOUN
ejpam-4824	140	12	xswap	xswap	PROPN
ejpam-4824	140	13	for	for	ADP
ejpam-4824	140	14	x	x	SYM
ejpam-4824	140	15	=	=	PUNCT
ejpam-4824	140	16	eiφ	eiφ	NOUN
ejpam-4824	140	17	where	where	SCONJ
ejpam-4824	140	18	φ	φ	PROPN
ejpam-4824	140	19	is	be	AUX
ejpam-4824	140	20	a	a	DET
ejpam-4824	140	21	real	real	ADJ
ejpam-4824	140	22	number	number	NOUN
ejpam-4824	140	23	.	.	PUNCT
ejpam-4824	141	1	moreover	moreover	ADV
ejpam-4824	141	2	,	,	PUNCT
ejpam-4824	141	3	we	we	PRON
ejpam-4824	141	4	have	have	AUX
ejpam-4824	141	5	shown	show	VERB
ejpam-4824	141	6	that	that	SCONJ
ejpam-4824	141	7	xswap	xswap	PROPN
ejpam-4824	141	8	is	be	AUX
ejpam-4824	141	9	universal	universal	ADJ
ejpam-4824	141	10	for	for	ADP
ejpam-4824	141	11	quantum	quantum	NOUN
ejpam-4824	141	12	computing	computing	NOUN
ejpam-4824	141	13	when	when	SCONJ
ejpam-4824	141	14	x	x	PROPN
ejpam-4824	141	15	̸=	̸=	PROPN
ejpam-4824	141	16	±1	±1	VERB
ejpam-4824	141	17	.	.	PUNCT
ejpam-4824	142	1	these	these	DET
ejpam-4824	142	2	higher	high	ADJ
ejpam-4824	142	3	dimensional	dimensional	ADJ
ejpam-4824	142	4	gates	gate	NOUN
ejpam-4824	142	5	can	can	AUX
ejpam-4824	142	6	serve	serve	VERB
ejpam-4824	142	7	as	as	ADP
ejpam-4824	142	8	quantum	quantum	NOUN
ejpam-4824	142	9	logic	logic	NOUN
ejpam-4824	142	10	gates	gate	NOUN
ejpam-4824	142	11	acting	act	VERB
ejpam-4824	142	12	on	on	ADP
ejpam-4824	142	13	two	two	NUM
ejpam-4824	142	14	d	d	ADJ
ejpam-4824	142	15	-	-	PUNCT
ejpam-4824	142	16	level	level	NOUN
ejpam-4824	142	17	qudits	qudit	NOUN
ejpam-4824	142	18	.	.	PUNCT
ejpam-4824	143	1	let	let	VERB
ejpam-4824	143	2	us	we	PRON
ejpam-4824	143	3	conclude	conclude	VERB
ejpam-4824	143	4	by	by	ADP
ejpam-4824	143	5	mentioning	mention	VERB
ejpam-4824	143	6	some	some	DET
ejpam-4824	143	7	future	future	ADJ
ejpam-4824	143	8	research	research	NOUN
ejpam-4824	143	9	directions	direction	NOUN
ejpam-4824	143	10	related	relate	VERB
ejpam-4824	143	11	to	to	ADP
ejpam-4824	143	12	the	the	DET
ejpam-4824	143	13	present	present	ADJ
ejpam-4824	143	14	work	work	NOUN
ejpam-4824	143	15	.	.	PUNCT
ejpam-4824	144	1	it	it	PRON
ejpam-4824	144	2	would	would	AUX
ejpam-4824	144	3	be	be	AUX
ejpam-4824	144	4	interesting	interesting	ADJ
ejpam-4824	144	5	to	to	PART
ejpam-4824	144	6	generalize	generalize	VERB
ejpam-4824	144	7	the	the	DET
ejpam-4824	144	8	xswap	xswap	NOUN
ejpam-4824	144	9	further	far	ADV
ejpam-4824	144	10	by	by	ADP
ejpam-4824	144	11	using	use	VERB
ejpam-4824	144	12	different	different	ADJ
ejpam-4824	144	13	variables	variable	NOUN
ejpam-4824	144	14	x1	x1	PROPN
ejpam-4824	144	15	,	,	PUNCT
ejpam-4824	144	16	x2	x2	PROPN
ejpam-4824	144	17	,	,	PUNCT
ejpam-4824	144	18	x3	x3	ADJ
ejpam-4824	144	19	,	,	PUNCT
ejpam-4824	144	20	etc	etc	X
ejpam-4824	144	21	.	.	X
ejpam-4824	144	22	,	,	PUNCT
ejpam-4824	144	23	instead	instead	ADV
ejpam-4824	144	24	of	of	ADP
ejpam-4824	144	25	only	only	ADV
ejpam-4824	144	26	one	one	NUM
ejpam-4824	144	27	variable	variable	ADJ
ejpam-4824	144	28	x.	x.	NOUN
ejpam-4824	144	29	using	use	VERB
ejpam-4824	144	30	the	the	DET
ejpam-4824	144	31	definition	definition	NOUN
ejpam-4824	144	32	to	to	PART
ejpam-4824	144	33	prove	prove	VERB
ejpam-4824	144	34	the	the	DET
ejpam-4824	144	35	universality	universality	NOUN
ejpam-4824	144	36	is	be	AUX
ejpam-4824	144	37	usually	usually	ADV
ejpam-4824	144	38	not	not	PART
ejpam-4824	144	39	very	very	ADV
ejpam-4824	144	40	easy	easy	ADJ
ejpam-4824	144	41	even	even	ADV
ejpam-4824	144	42	in	in	ADP
ejpam-4824	144	43	dimension	dimension	NOUN
ejpam-4824	144	44	d	d	NOUN
ejpam-4824	144	45	=	=	SYM
ejpam-4824	144	46	2	2	NUM
ejpam-4824	144	47	(	(	PUNCT
ejpam-4824	144	48	refer	refer	VERB
ejpam-4824	144	49	to	to	PART
ejpam-4824	144	50	remark	remark	VERB
ejpam-4824	144	51	1	1	NUM
ejpam-4824	144	52	)	)	PUNCT
ejpam-4824	144	53	.	.	PUNCT
ejpam-4824	145	1	however	however	ADV
ejpam-4824	145	2	,	,	PUNCT
ejpam-4824	145	3	it	it	PRON
ejpam-4824	145	4	would	would	AUX
ejpam-4824	145	5	be	be	AUX
ejpam-4824	145	6	still	still	ADV
ejpam-4824	145	7	interesting	interesting	ADJ
ejpam-4824	145	8	and	and	CCONJ
ejpam-4824	145	9	useful	useful	ADJ
ejpam-4824	145	10	to	to	PART
ejpam-4824	145	11	find	find	VERB
ejpam-4824	145	12	such	such	DET
ejpam-4824	145	13	a	a	DET
ejpam-4824	145	14	direct	direct	ADJ
ejpam-4824	145	15	proof	proof	NOUN
ejpam-4824	145	16	based	base	VERB
ejpam-4824	145	17	on	on	ADP
ejpam-4824	145	18	the	the	DET
ejpam-4824	145	19	definition	definition	NOUN
ejpam-4824	145	20	.	.	PUNCT
ejpam-4824	146	1	these	these	DET
ejpam-4824	146	2	research	research	NOUN
ejpam-4824	146	3	directions	direction	NOUN
ejpam-4824	146	4	will	will	AUX
ejpam-4824	146	5	be	be	AUX
ejpam-4824	146	6	pursued	pursue	VERB
ejpam-4824	146	7	in	in	ADP
ejpam-4824	146	8	a	a	DET
ejpam-4824	146	9	sequel	sequel	NOUN
ejpam-4824	146	10	to	to	ADP
ejpam-4824	146	11	this	this	DET
ejpam-4824	146	12	paper	paper	NOUN
ejpam-4824	146	13	.	.	PUNCT
ejpam-4824	147	1	acknowledgement	acknowledgement	NOUN
ejpam-4824	147	2	the	the	DET
ejpam-4824	147	3	author	author	NOUN
ejpam-4824	147	4	would	would	AUX
ejpam-4824	147	5	like	like	VERB
ejpam-4824	147	6	to	to	PART
ejpam-4824	147	7	thank	thank	VERB
ejpam-4824	147	8	referees	referee	NOUN
ejpam-4824	147	9	for	for	ADP
ejpam-4824	147	10	their	their	PRON
ejpam-4824	147	11	invaluable	invaluable	ADJ
ejpam-4824	147	12	feedback	feedback	NOUN
ejpam-4824	147	13	which	which	PRON
ejpam-4824	147	14	helped	help	VERB
ejpam-4824	147	15	to	to	PART
ejpam-4824	147	16	greatly	greatly	ADV
ejpam-4824	147	17	increase	increase	VERB
ejpam-4824	147	18	the	the	DET
ejpam-4824	147	19	quality	quality	NOUN
ejpam-4824	147	20	and	and	CCONJ
ejpam-4824	147	21	the	the	DET
ejpam-4824	147	22	presentation	presentation	NOUN
ejpam-4824	147	23	of	of	ADP
ejpam-4824	147	24	this	this	DET
ejpam-4824	147	25	work	work	NOUN
ejpam-4824	147	26	.	.	PUNCT
ejpam-4824	148	1	i	i	PRON
ejpam-4824	148	2	would	would	AUX
ejpam-4824	148	3	also	also	ADV
ejpam-4824	148	4	like	like	VERB
ejpam-4824	148	5	to	to	PART
ejpam-4824	148	6	thank	thank	VERB
ejpam-4824	148	7	dr	dr	PROPN
ejpam-4824	148	8	.	.	PROPN
ejpam-4824	148	9	sinan	sinan	PROPN
ejpam-4824	148	10	kapçak	kapçak	PROPN
ejpam-4824	148	11	for	for	ADP
ejpam-4824	148	12	introducing	introduce	VERB
ejpam-4824	148	13	me	i	PRON
ejpam-4824	148	14	to	to	ADP
ejpam-4824	148	15	the	the	DET
ejpam-4824	148	16	computer	computer	NOUN
ejpam-4824	148	17	algebra	algebra	NOUN
ejpam-4824	148	18	system	system	NOUN
ejpam-4824	148	19	sagemath	sagemath	NOUN
ejpam-4824	148	20	which	which	PRON
ejpam-4824	148	21	was	be	AUX
ejpam-4824	148	22	useful	useful	ADJ
ejpam-4824	148	23	in	in	ADP
ejpam-4824	148	24	testing	test	VERB
ejpam-4824	148	25	the	the	DET
ejpam-4824	148	26	validity	validity	NOUN
ejpam-4824	148	27	of	of	ADP
ejpam-4824	148	28	some	some	DET
ejpam-4824	148	29	formulas	formula	NOUN
ejpam-4824	148	30	before	before	ADP
ejpam-4824	148	31	finding	find	VERB
ejpam-4824	148	32	the	the	DET
ejpam-4824	148	33	general	general	ADJ
ejpam-4824	148	34	proof	proof	NOUN
ejpam-4824	148	35	for	for	ADP
ejpam-4824	148	36	references	reference	NOUN
ejpam-4824	148	37	1703	1703	NUM
ejpam-4824	148	38	them	they	PRON
ejpam-4824	148	39	.	.	PUNCT
ejpam-4824	149	1	last	last	ADJ
ejpam-4824	149	2	but	but	CCONJ
ejpam-4824	149	3	not	not	PART
ejpam-4824	149	4	least	least	ADJ
ejpam-4824	149	5	,	,	PUNCT
ejpam-4824	149	6	i	i	PRON
ejpam-4824	149	7	would	would	AUX
ejpam-4824	149	8	like	like	VERB
ejpam-4824	149	9	to	to	PART
ejpam-4824	149	10	thank	thank	VERB
ejpam-4824	149	11	mrs	mrs	PROPN
ejpam-4824	149	12	.	.	PROPN
ejpam-4824	149	13	elena	elena	PROPN
ejpam-4824	149	14	ryzhova	ryzhova	PROPN
ejpam-4824	149	15	for	for	ADP
ejpam-4824	149	16	helping	help	VERB
ejpam-4824	149	17	with	with	ADP
ejpam-4824	149	18	the	the	DET
ejpam-4824	149	19	proofreading	proofreading	NOUN
ejpam-4824	149	20	of	of	ADP
ejpam-4824	149	21	this	this	DET
ejpam-4824	149	22	paper	paper	NOUN
ejpam-4824	149	23	and	and	CCONJ
ejpam-4824	149	24	for	for	ADP
ejpam-4824	149	25	fruitful	fruitful	ADJ
ejpam-4824	149	26	conversations	conversation	NOUN
ejpam-4824	149	27	.	.	PUNCT
ejpam-4824	150	1	references	reference	NOUN
ejpam-4824	150	2	[	[	X
ejpam-4824	150	3	1	1	NUM
ejpam-4824	150	4	]	]	PUNCT
ejpam-4824	150	5	gorjan	gorjan	NOUN
ejpam-4824	150	6	alagic	alagic	NOUN
ejpam-4824	150	7	,	,	PUNCT
ejpam-4824	150	8	michael	michael	PROPN
ejpam-4824	150	9	jarret	jarret	PROPN
ejpam-4824	150	10	,	,	PUNCT
ejpam-4824	150	11	and	and	CCONJ
ejpam-4824	150	12	stephen	stephen	PROPN
ejpam-4824	150	13	p.	p.	PROPN
ejpam-4824	150	14	jordan	jordan	PROPN
ejpam-4824	150	15	.	.	PUNCT
ejpam-4824	151	1	yang	yang	PROPN
ejpam-4824	151	2	-	-	PUNCT
ejpam-4824	151	3	baxter	baxter	PROPN
ejpam-4824	151	4	operators	operator	NOUN
ejpam-4824	151	5	need	need	VERB
ejpam-4824	151	6	quantum	quantum	ADJ
ejpam-4824	151	7	entanglement	entanglement	NOUN
ejpam-4824	151	8	to	to	PART
ejpam-4824	151	9	distinguish	distinguish	VERB
ejpam-4824	151	10	knots	knot	NOUN
ejpam-4824	151	11	.	.	PUNCT
ejpam-4824	152	1	journal	journal	PROPN
ejpam-4824	152	2	of	of	ADP
ejpam-4824	152	3	physics	physics	PROPN
ejpam-4824	152	4	a	a	PRON
ejpam-4824	152	5	:	:	PUNCT
ejpam-4824	152	6	mathematical	mathematical	ADJ
ejpam-4824	152	7	and	and	CCONJ
ejpam-4824	152	8	theoretical	theoretical	ADJ
ejpam-4824	152	9	,	,	PUNCT
ejpam-4824	152	10	49(7	49(7	NUM
ejpam-4824	152	11	)	)	PUNCT
ejpam-4824	152	12	,	,	PUNCT
ejpam-4824	152	13	2016	2016	NUM
ejpam-4824	152	14	.	.	PUNCT
ejpam-4824	153	1	[	[	X
ejpam-4824	153	2	2	2	NUM
ejpam-4824	153	3	]	]	X
ejpam-4824	153	4	monika	monika	PROPN
ejpam-4824	153	5	bartkowiak	bartkowiak	PROPN
ejpam-4824	153	6	and	and	CCONJ
ejpam-4824	153	7	adam	adam	PROPN
ejpam-4824	153	8	miranowicz	miranowicz	PROPN
ejpam-4824	153	9	.	.	PUNCT
ejpam-4824	154	1	linear	linear	ADJ
ejpam-4824	154	2	-	-	PUNCT
ejpam-4824	154	3	optical	optical	ADJ
ejpam-4824	154	4	implementations	implementation	NOUN
ejpam-4824	154	5	of	of	ADP
ejpam-4824	154	6	the	the	DET
ejpam-4824	154	7	iswap	iswap	NOUN
ejpam-4824	154	8	and	and	CCONJ
ejpam-4824	154	9	controlled	control	VERB
ejpam-4824	154	10	not	not	PART
ejpam-4824	154	11	gates	gate	NOUN
ejpam-4824	154	12	based	base	VERB
ejpam-4824	154	13	on	on	ADP
ejpam-4824	154	14	conventional	conventional	ADJ
ejpam-4824	154	15	detectors	detector	NOUN
ejpam-4824	154	16	.	.	PUNCT
ejpam-4824	155	1	j.	j.	PROPN
ejpam-4824	155	2	opt	opt	PROPN
ejpam-4824	155	3	.	.	PUNCT
ejpam-4824	156	1	soc	soc	PROPN
ejpam-4824	156	2	.	.	PUNCT
ejpam-4824	157	1	am	be	AUX
ejpam-4824	157	2	.	.	PUNCT
ejpam-4824	158	1	b	b	X
ejpam-4824	158	2	,	,	PUNCT
ejpam-4824	158	3	27:2369–2377	27:2369–2377	NUM
ejpam-4824	158	4	,	,	PUNCT
ejpam-4824	158	5	2010	2010	NUM
ejpam-4824	158	6	.	.	PUNCT
ejpam-4824	159	1	[	[	X
ejpam-4824	159	2	3	3	X
ejpam-4824	159	3	]	]	X
ejpam-4824	159	4	jl	jl	PROPN
ejpam-4824	159	5	brylinski	brylinski	PROPN
ejpam-4824	159	6	and	and	CCONJ
ejpam-4824	159	7	r	r	PROPN
ejpam-4824	159	8	brylinski	brylinski	NOUN
ejpam-4824	159	9	.	.	PUNCT
ejpam-4824	160	1	universal	universal	ADJ
ejpam-4824	160	2	quantum	quantum	ADJ
ejpam-4824	160	3	gates	gate	NOUN
ejpam-4824	160	4	.	.	PUNCT
ejpam-4824	161	1	mathematics	mathematic	NOUN
ejpam-4824	161	2	of	of	ADP
ejpam-4824	161	3	quantum	quantum	ADJ
ejpam-4824	161	4	computation	computation	NOUN
ejpam-4824	161	5	.	.	PUNCT
ejpam-4824	162	1	chapman	chapman	NOUN
ejpam-4824	162	2	and	and	CCONJ
ejpam-4824	162	3	hall	hall	PROPN
ejpam-4824	162	4	/	/	SYM
ejpam-4824	162	5	crc	crc	PROPN
ejpam-4824	162	6	,	,	PUNCT
ejpam-4824	162	7	first	first	ADJ
ejpam-4824	162	8	edition	edition	NOUN
ejpam-4824	162	9	,	,	PUNCT
ejpam-4824	162	10	2002	2002	NUM
ejpam-4824	162	11	.	.	PUNCT
ejpam-4824	163	1	[	[	X
ejpam-4824	163	2	4	4	NUM
ejpam-4824	163	3	]	]	X
ejpam-4824	163	4	garcia	garcia	PROPN
ejpam-4824	163	5	-	-	PUNCT
ejpam-4824	163	6	escartin	escartin	PROPN
ejpam-4824	163	7	j.	j.	PROPN
ejpam-4824	163	8	c.	c.	PROPN
ejpam-4824	163	9	and	and	CCONJ
ejpam-4824	163	10	chamorro	chamorro	PROPN
ejpam-4824	163	11	-	-	PUNCT
ejpam-4824	163	12	posada	posada	PROPN
ejpam-4824	163	13	p.	p.	PROPN
ejpam-4824	163	14	a	a	DET
ejpam-4824	163	15	swap	swap	NOUN
ejpam-4824	163	16	gate	gate	NOUN
ejpam-4824	163	17	for	for	ADP
ejpam-4824	163	18	qudits	qudit	NOUN
ejpam-4824	163	19	.	.	PUNCT
ejpam-4824	163	20	quantum	quantum	PROPN
ejpam-4824	163	21	inf	inf	NOUN
ejpam-4824	163	22	process	process	NOUN
ejpam-4824	163	23	,	,	PUNCT
ejpam-4824	163	24	12:3625–3631	12:3625–3631	NUM
ejpam-4824	163	25	,	,	PUNCT
ejpam-4824	163	26	2013	2013	NUM
ejpam-4824	163	27	.	.	PUNCT
ejpam-4824	164	1	[	[	X
ejpam-4824	164	2	5	5	X
ejpam-4824	164	3	]	]	X
ejpam-4824	164	4	peng	peng	PROPN
ejpam-4824	164	5	xu	xu	PROPN
ejpam-4824	164	6	.	.	PUNCT
ejpam-4824	165	1	et	et	PROPN
ejpam-4824	165	2	al	al	PROPN
ejpam-4824	165	3	.	.	PUNCT
ejpam-4824	166	1	realization	realization	NOUN
ejpam-4824	166	2	of	of	ADP
ejpam-4824	166	3	the	the	DET
ejpam-4824	166	4	iswap	iswap	NOUN
ejpam-4824	166	5	-	-	PUNCT
ejpam-4824	166	6	like	like	ADJ
ejpam-4824	166	7	gate	gate	NOUN
ejpam-4824	166	8	among	among	ADP
ejpam-4824	166	9	the	the	DET
ejpam-4824	166	10	superconducting	superconducte	VERB
ejpam-4824	166	11	qutrits	qutrit	NOUN
ejpam-4824	166	12	.	.	PUNCT
ejpam-4824	167	1	chinese	chinese	ADJ
ejpam-4824	167	2	phys	phy	NOUN
ejpam-4824	167	3	.	.	PUNCT
ejpam-4824	168	1	b	b	X
ejpam-4824	168	2	,	,	PUNCT
ejpam-4824	168	3	32(020306	32(020306	NUM
ejpam-4824	168	4	)	)	PUNCT
ejpam-4824	168	5	,	,	PUNCT
ejpam-4824	168	6	2023	2023	NUM
ejpam-4824	168	7	.	.	PUNCT
ejpam-4824	169	1	[	[	X
ejpam-4824	169	2	6	6	NUM
ejpam-4824	169	3	]	]	PUNCT
ejpam-4824	169	4	adriano	adriano	PROPN
ejpam-4824	169	5	barenco	barenco	PROPN
ejpam-4824	169	6	et	et	PROPN
ejpam-4824	169	7	al	al	PROPN
ejpam-4824	169	8	.	.	PROPN
ejpam-4824	169	9	elementary	elementary	PROPN
ejpam-4824	169	10	gates	gate	NOUN
ejpam-4824	169	11	for	for	ADP
ejpam-4824	169	12	quantum	quantum	ADJ
ejpam-4824	169	13	computation	computation	NOUN
ejpam-4824	169	14	.	.	PUNCT
ejpam-4824	170	1	phys	phy	NOUN
ejpam-4824	170	2	.	.	PUNCT
ejpam-4824	171	1	rev	rev	PROPN
ejpam-4824	171	2	.	.	PROPN
ejpam-4824	172	1	a	a	PRON
ejpam-4824	172	2	,	,	PUNCT
ejpam-4824	172	3	52	52	NUM
ejpam-4824	172	4	,	,	PUNCT
ejpam-4824	172	5	1995	1995	NUM
ejpam-4824	172	6	.	.	PUNCT
ejpam-4824	173	1	[	[	X
ejpam-4824	173	2	7	7	NUM
ejpam-4824	173	3	]	]	X
ejpam-4824	173	4	kaszlikowski	kaszlikowski	PROPN
ejpam-4824	173	5	d.	d.	PROPN
ejpam-4824	173	6	et	et	PROPN
ejpam-4824	173	7	al	al	PROPN
ejpam-4824	173	8	.	.	PUNCT
ejpam-4824	173	9	quantum	quantum	PROPN
ejpam-4824	173	10	cryptography	cryptography	NOUN
ejpam-4824	173	11	based	base	VERB
ejpam-4824	173	12	on	on	ADP
ejpam-4824	173	13	qutrit	qutrit	PROPN
ejpam-4824	173	14	bell	bell	PROPN
ejpam-4824	173	15	inequalities	inequality	NOUN
ejpam-4824	173	16	.	.	PUNCT
ejpam-4824	174	1	phys	phy	NOUN
ejpam-4824	174	2	.	.	PUNCT
ejpam-4824	175	1	rev	rev	PROPN
ejpam-4824	175	2	.	.	PROPN
ejpam-4824	176	1	a	a	DET
ejpam-4824	176	2	,	,	PUNCT
ejpam-4824	176	3	67:656	67:656	NUM
ejpam-4824	176	4	,	,	PUNCT
ejpam-4824	176	5	2003	2003	NUM
ejpam-4824	176	6	.	.	PUNCT
ejpam-4824	177	1	[	[	X
ejpam-4824	177	2	8	8	NUM
ejpam-4824	177	3	]	]	X
ejpam-4824	177	4	kues	kue	NOUN
ejpam-4824	177	5	m.	m.	NOUN
ejpam-4824	177	6	et	et	PROPN
ejpam-4824	177	7	al	al	PROPN
ejpam-4824	177	8	.	.	PROPN
ejpam-4824	178	1	on	on	ADP
ejpam-4824	178	2	-	-	PUNCT
ejpam-4824	178	3	chip	chip	NOUN
ejpam-4824	178	4	generation	generation	NOUN
ejpam-4824	178	5	of	of	ADP
ejpam-4824	178	6	high	high	ADJ
ejpam-4824	178	7	-	-	PUNCT
ejpam-4824	178	8	dimensional	dimensional	ADJ
ejpam-4824	178	9	entangled	entangled	ADJ
ejpam-4824	178	10	quantum	quantum	NOUN
ejpam-4824	178	11	states	state	NOUN
ejpam-4824	178	12	and	and	CCONJ
ejpam-4824	178	13	their	their	PRON
ejpam-4824	178	14	coherent	coherent	ADJ
ejpam-4824	178	15	control	control	NOUN
ejpam-4824	178	16	.	.	PUNCT
ejpam-4824	179	1	nature	nature	NOUN
ejpam-4824	179	2	,	,	PUNCT
ejpam-4824	179	3	546:622–626	546:622–626	NUM
ejpam-4824	179	4	,	,	PUNCT
ejpam-4824	179	5	2017	2017	NUM
ejpam-4824	179	6	.	.	PUNCT
ejpam-4824	180	1	[	[	X
ejpam-4824	180	2	9	9	NUM
ejpam-4824	180	3	]	]	X
ejpam-4824	180	4	lanyon	lanyon	NOUN
ejpam-4824	180	5	b.	b.	PROPN
ejpam-4824	181	1	p.	p.	NOUN
ejpam-4824	181	2	et	et	PROPN
ejpam-4824	182	1	al	al	PROPN
ejpam-4824	182	2	.	.	PUNCT
ejpam-4824	182	3	simplifying	simplify	VERB
ejpam-4824	182	4	quantum	quantum	ADJ
ejpam-4824	182	5	logic	logic	NOUN
ejpam-4824	182	6	using	use	VERB
ejpam-4824	182	7	higher	higher	ADV
ejpam-4824	182	8	-	-	PUNCT
ejpam-4824	182	9	dimensional	dimensional	ADJ
ejpam-4824	182	10	hilbert	hilbert	NOUN
ejpam-4824	182	11	spaces	space	NOUN
ejpam-4824	182	12	.	.	PUNCT
ejpam-4824	183	1	nat	nat	NOUN
ejpam-4824	183	2	.	.	PUNCT
ejpam-4824	184	1	phys	phy	NOUN
ejpam-4824	184	2	.	.	PUNCT
ejpam-4824	184	3	,	,	PUNCT
ejpam-4824	184	4	5:134–140	5:134–140	NUM
ejpam-4824	184	5	,	,	PUNCT
ejpam-4824	184	6	2008	2008	NUM
ejpam-4824	184	7	.	.	PUNCT
ejpam-4824	185	1	[	[	X
ejpam-4824	185	2	10	10	NUM
ejpam-4824	185	3	]	]	X
ejpam-4824	185	4	marco	marco	PROPN
ejpam-4824	186	1	fiorentino	fiorentino	PROPN
ejpam-4824	186	2	et	et	PROPN
ejpam-4824	186	3	al	al	PROPN
ejpam-4824	186	4	.	.	PUNCT
ejpam-4824	187	1	single	single	ADJ
ejpam-4824	187	2	-	-	PUNCT
ejpam-4824	187	3	photon	photon	NOUN
ejpam-4824	187	4	two	two	NUM
ejpam-4824	187	5	-	-	PUNCT
ejpam-4824	187	6	qubit	qubit	NOUN
ejpam-4824	187	7	swap	swap	NOUN
ejpam-4824	187	8	gate	gate	NOUN
ejpam-4824	187	9	for	for	ADP
ejpam-4824	187	10	entanglement	entanglement	NOUN
ejpam-4824	187	11	manipulation	manipulation	NOUN
ejpam-4824	187	12	.	.	PUNCT
ejpam-4824	188	1	phys	phy	NOUN
ejpam-4824	188	2	.	.	PUNCT
ejpam-4824	189	1	rev	rev	PROPN
ejpam-4824	189	2	.	.	PROPN
ejpam-4824	190	1	a	a	DET
ejpam-4824	190	2	,	,	PUNCT
ejpam-4824	190	3	72	72	NUM
ejpam-4824	190	4	,	,	PUNCT
ejpam-4824	190	5	2005	2005	NUM
ejpam-4824	190	6	.	.	PUNCT
ejpam-4824	191	1	[	[	X
ejpam-4824	191	2	11	11	NUM
ejpam-4824	191	3	]	]	X
ejpam-4824	191	4	neeley	neeley	PROPN
ejpam-4824	191	5	m.	m.	PROPN
ejpam-4824	191	6	et	et	PROPN
ejpam-4824	191	7	al	al	PROPN
ejpam-4824	191	8	.	.	PUNCT
ejpam-4824	192	1	emulation	emulation	NOUN
ejpam-4824	192	2	of	of	ADP
ejpam-4824	192	3	a	a	DET
ejpam-4824	192	4	quantum	quantum	NOUN
ejpam-4824	192	5	spin	spin	NOUN
ejpam-4824	192	6	with	with	ADP
ejpam-4824	192	7	a	a	DET
ejpam-4824	192	8	superconducting	superconducte	VERB
ejpam-4824	192	9	phase	phase	NOUN
ejpam-4824	192	10	qudit	qudit	NOUN
ejpam-4824	192	11	.	.	PUNCT
ejpam-4824	193	1	science	science	NOUN
ejpam-4824	193	2	,	,	PUNCT
ejpam-4824	193	3	325:722–725	325:722–725	NUM
ejpam-4824	193	4	,	,	PUNCT
ejpam-4824	193	5	2009	2009	NUM
ejpam-4824	193	6	.	.	PUNCT
ejpam-4824	194	1	[	[	X
ejpam-4824	194	2	12	12	NUM
ejpam-4824	194	3	]	]	X
ejpam-4824	194	4	shlyakhov	shlyakhov	PROPN
ejpam-4824	194	5	a.	a.	PROPN
ejpam-4824	194	6	r.	r.	PROPN
ejpam-4824	194	7	et	et	PROPN
ejpam-4824	194	8	al	al	PROPN
ejpam-4824	194	9	.	.	PUNCT
ejpam-4824	194	10	quantum	quantum	PROPN
ejpam-4824	194	11	metrology	metrology	NOUN
ejpam-4824	194	12	with	with	ADP
ejpam-4824	194	13	a	a	DET
ejpam-4824	194	14	transmon	transmon	NOUN
ejpam-4824	194	15	qutrit	qutrit	NOUN
ejpam-4824	194	16	.	.	PUNCT
ejpam-4824	195	1	phys	phy	NOUN
ejpam-4824	195	2	.	.	PUNCT
ejpam-4824	196	1	rev	rev	PROPN
ejpam-4824	196	2	.	.	PROPN
ejpam-4824	197	1	a	a	DET
ejpam-4824	197	2	,	,	PUNCT
ejpam-4824	197	3	97(2	97(2	NUM
ejpam-4824	197	4	)	)	PUNCT
ejpam-4824	197	5	,	,	PUNCT
ejpam-4824	197	6	2018	2018	NUM
ejpam-4824	197	7	.	.	PUNCT
ejpam-4824	198	1	[	[	X
ejpam-4824	198	2	13	13	NUM
ejpam-4824	198	3	]	]	SYM
ejpam-4824	198	4	soltamov	soltamov	PROPN
ejpam-4824	198	5	v.a	v.a	PROPN
ejpam-4824	198	6	.	.	PROPN
ejpam-4824	198	7	et	et	PROPN
ejpam-4824	198	8	al	al	PROPN
ejpam-4824	198	9	.	.	PROPN
ejpam-4824	198	10	excitation	excitation	NOUN
ejpam-4824	198	11	and	and	CCONJ
ejpam-4824	198	12	coherent	coherent	ADJ
ejpam-4824	198	13	control	control	NOUN
ejpam-4824	198	14	of	of	ADP
ejpam-4824	198	15	spin	spin	NOUN
ejpam-4824	198	16	qudit	qudit	NOUN
ejpam-4824	198	17	modes	mode	NOUN
ejpam-4824	198	18	in	in	ADP
ejpam-4824	198	19	silicon	silicon	NOUN
ejpam-4824	198	20	carbide	carbide	NOUN
ejpam-4824	198	21	at	at	ADP
ejpam-4824	198	22	room	room	NOUN
ejpam-4824	198	23	temperature	temperature	NOUN
ejpam-4824	198	24	.	.	PUNCT
ejpam-4824	199	1	nature	nature	NOUN
ejpam-4824	199	2	communications	communication	NOUN
ejpam-4824	199	3	,	,	PUNCT
ejpam-4824	199	4	10	10	NUM
ejpam-4824	199	5	,	,	PUNCT
ejpam-4824	199	6	2019	2019	NUM
ejpam-4824	199	7	.	.	PUNCT
ejpam-4824	200	1	[	[	X
ejpam-4824	200	2	14	14	NUM
ejpam-4824	200	3	]	]	X
ejpam-4824	200	4	yan	yan	PROPN
ejpam-4824	200	5	guo	guo	PROPN
ejpam-4824	200	6	-	-	PUNCT
ejpam-4824	200	7	an	an	PROPN
ejpam-4824	200	8	,	,	PUNCT
ejpam-4824	200	9	qiao	qiao	PROPN
ejpam-4824	200	10	hao	hao	PROPN
ejpam-4824	200	11	-	-	PROPN
ejpam-4824	200	12	xue	xue	PROPN
ejpam-4824	200	13	,	,	PUNCT
ejpam-4824	200	14	and	and	CCONJ
ejpam-4824	200	15	lu	lu	PROPN
ejpam-4824	200	16	hua	hua	PROPN
ejpam-4824	200	17	.	.	PUNCT
ejpam-4824	200	18	quantum	quantum	PROPN
ejpam-4824	200	19	iswap	iswap	PROPN
ejpam-4824	200	20	gate	gate	NOUN
ejpam-4824	200	21	in	in	ADP
ejpam-4824	200	22	optical	optical	ADJ
ejpam-4824	200	23	cavities	cavity	NOUN
ejpam-4824	200	24	with	with	ADP
ejpam-4824	200	25	a	a	DET
ejpam-4824	200	26	cyclic	cyclic	ADJ
ejpam-4824	200	27	three	three	NUM
ejpam-4824	200	28	-	-	PUNCT
ejpam-4824	200	29	level	level	NOUN
ejpam-4824	200	30	system	system	NOUN
ejpam-4824	200	31	.	.	PUNCT
ejpam-4824	201	1	quantum	quantum	PROPN
ejpam-4824	201	2	inf	inf	NOUN
ejpam-4824	201	3	process	process	NOUN
ejpam-4824	201	4	,	,	PUNCT
ejpam-4824	201	5	17(71	17(71	NUM
ejpam-4824	201	6	)	)	PUNCT
ejpam-4824	201	7	,	,	PUNCT
ejpam-4824	201	8	2018	2018	NUM
ejpam-4824	201	9	.	.	PUNCT
ejpam-4824	202	1	references	reference	NOUN
ejpam-4824	202	2	1704	1704	NUM
ejpam-4824	202	3	[	[	X
ejpam-4824	202	4	15	15	NUM
ejpam-4824	202	5	]	]	X
ejpam-4824	202	6	nielsen	nielsen	PROPN
ejpam-4824	202	7	m.	m.	PROPN
ejpam-4824	202	8	and	and	CCONJ
ejpam-4824	202	9	chuang	chuang	PROPN
ejpam-4824	202	10	i.	i.	PROPN
ejpam-4824	202	11	quantum	quantum	PROPN
ejpam-4824	202	12	computation	computation	NOUN
ejpam-4824	202	13	and	and	CCONJ
ejpam-4824	202	14	quantum	quantum	NOUN
ejpam-4824	202	15	information	information	NOUN
ejpam-4824	202	16	.	.	PUNCT
ejpam-4824	203	1	cambridge	cambridge	PROPN
ejpam-4824	203	2	university	university	PROPN
ejpam-4824	203	3	press	press	PROPN
ejpam-4824	203	4	,	,	PUNCT
ejpam-4824	203	5	10th	10th	ADJ
ejpam-4824	203	6	anniversary	anniversary	NOUN
ejpam-4824	203	7	edition	edition	NOUN
ejpam-4824	203	8	,	,	PUNCT
ejpam-4824	203	9	2010	2010	NUM
ejpam-4824	203	10	.	.	PUNCT
ejpam-4824	204	1	[	[	X
ejpam-4824	204	2	16	16	NUM
ejpam-4824	204	3	]	]	X
ejpam-4824	204	4	colin	colin	PROPN
ejpam-4824	204	5	m.	m.	PROPN
ejpam-4824	204	6	wilmott	wilmott	PROPN
ejpam-4824	204	7	and	and	CCONJ
ejpam-4824	204	8	peter	peter	PROPN
ejpam-4824	204	9	r.	r.	PROPN
ejpam-4824	204	10	wild	wild	PROPN
ejpam-4824	204	11	.	.	PUNCT
ejpam-4824	205	1	on	on	ADP
ejpam-4824	205	2	a	a	DET
ejpam-4824	205	3	generalized	generalized	ADJ
ejpam-4824	205	4	quantum	quantum	NOUN
ejpam-4824	205	5	swap	swap	NOUN
ejpam-4824	205	6	gate	gate	NOUN
ejpam-4824	205	7	.	.	PUNCT
ejpam-4824	206	1	international	international	ADJ
ejpam-4824	206	2	journal	journal	NOUN
ejpam-4824	206	3	of	of	ADP
ejpam-4824	206	4	quantum	quantum	ADJ
ejpam-4824	206	5	information	information	NOUN
ejpam-4824	206	6	,	,	PUNCT
ejpam-4824	206	7	10(3	10(3	NUM
ejpam-4824	206	8	)	)	PUNCT
ejpam-4824	206	9	,	,	PUNCT
ejpam-4824	206	10	2012	2012	NUM
ejpam-4824	206	11	.	.	PUNCT
ejpam-4824	207	1	[	[	X
ejpam-4824	207	2	17	17	NUM
ejpam-4824	207	3	]	]	X
ejpam-4824	207	4	wang	wang	PROPN
ejpam-4824	207	5	y	y	PROPN
ejpam-4824	207	6	,	,	PUNCT
ejpam-4824	207	7	hu	hu	PROPN
ejpam-4824	208	1	z	z	PROPN
ejpam-4824	208	2	,	,	PUNCT
ejpam-4824	208	3	sanders	sanders	PROPN
ejpam-4824	208	4	b.c	b.c	PROPN
ejpam-4824	208	5	.	.	PROPN
ejpam-4824	208	6	,	,	PUNCT
ejpam-4824	208	7	and	and	CCONJ
ejpam-4824	208	8	kais	kais	PROPN
ejpam-4824	208	9	s.	s.	PROPN
ejpam-4824	208	10	qudits	qudits	PROPN
ejpam-4824	208	11	and	and	CCONJ
ejpam-4824	208	12	high	high	ADJ
ejpam-4824	208	13	-	-	PUNCT
ejpam-4824	208	14	dimensional	dimensional	ADJ
ejpam-4824	208	15	quantum	quantum	ADJ
ejpam-4824	208	16	computing	computing	NOUN
ejpam-4824	208	17	.	.	PUNCT
ejpam-4824	209	1	front	front	NOUN
ejpam-4824	209	2	.	.	PUNCT
ejpam-4824	210	1	phys	phy	NOUN
ejpam-4824	210	2	.	.	PUNCT
ejpam-4824	210	3	,	,	PUNCT
ejpam-4824	210	4	8	8	NUM
ejpam-4824	210	5	,	,	PUNCT
ejpam-4824	210	6	2020	2020	NUM
ejpam-4824	210	7	.	.	PUNCT