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Criteria for exact qudit universality

We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 0...

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Published in:	Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2005-05, Vol.71 (5), Article 052318
Main Authors:	Brennen, Gavin, O’Leary, Dianne, Bullock, Stephen
Format:	Article
Language:	English
Subjects:	ALGEBRA ATOMIC AND MOLECULAR PHYSICS COUPLING GROUND STATES HAMILTONIANS HILBERT SPACE IMPLEMENTATION INFORMATION THEORY PULSES QUANTUM COMPUTERS RAMAN EFFECT RUBIDIUM RUBIDIUM 87
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container_title	Physical review. A, Atomic, molecular, and optical physics
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creator	Brennen, Gavin O’Leary, Dianne Bullock, Stephen
description	We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H{sub jk}{sup x}=({Dirac_h}/2{pi}){omega}(vertical bar k>
doi_str_mv	10.1103/PhysRevA.71.052318
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A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. 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A, Atomic, molecular, and optical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Brennen, Gavin</au><au>O’Leary, Dianne</au><au>Bullock, Stephen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Criteria for exact qudit universality</atitle><jtitle>Physical review. A, Atomic, molecular, and optical physics</jtitle><date>2005-05-01</date><risdate>2005</risdate><volume>71</volume><issue>5</issue><artnum>052318</artnum><issn>1050-2947</issn><eissn>1094-1622</eissn><abstract>We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H{sub jk}{sup x}=({Dirac_h}/2{pi}){omega}(vertical bar k><j vertical bar + vertical bar j><k vertical bar) and H{sub jk}{sup y}=({Dirac_h}/2{pi}){omega}(i vertical bar k><j vertical bar -i vertical bar j><k vertical bar). A coupling graph results taking nodes 0, ..., d-1 and edges j{r_reversible}k iff H{sub jk}{sup x,y} are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=({Dirac_h}/2{pi}){omega} vertical bar d-1,d-1><d-1,d-1 vertical bar is also allowed. We discuss implementation in the eight dimensional ground electronic states of {sup 87}Rb and construct an optimal gate sequence using Raman laser pulses.</abstract><cop>United States</cop><doi>10.1103/PhysRevA.71.052318</doi></addata></record>
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subjects	ALGEBRA ATOMIC AND MOLECULAR PHYSICS COUPLING GROUND STATES HAMILTONIANS HILBERT SPACE IMPLEMENTATION INFORMATION THEORY PULSES QUANTUM COMPUTERS RAMAN EFFECT RUBIDIUM RUBIDIUM 87
title	Criteria for exact qudit universality
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