Paper Abstract and Keywords |
Presentation |
2008-03-10 10:20
On the Computational Power of Quantum Circuits with Clifford and π/8 Gates Ken Matsumoto, Kazuyuki Amano (Gunma Univ.) COMP2007-57 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
A set of quantum gates (unitary matrix) is universal if any quantum
computation (unitary matrix) is approximated with arbitrary precision.
There have been known several discrete univarsal sets of gates.
However, it seems difficult to give an efficient representation for
a given
unitary matrix with elements of a discrete universal set.
In this paper, we focus on the basis consisting of
Hadamard, $\pi/8$ and CNOT gates, whose universality has been
shown by Boykin et al. [FOCS '99], and analyze the representational power of quantum circuits over this basis.
%But , if a good representation is found, it will be useful for the advancement of research of quantum computing. Then, we paid attention to this problem and researched.
We introduce a normal form of one qubit circuits
that has several nice properties.
Every one qubit circuit can easily be tranformed into a circuit of
such a form. In addition, every two normal circuits
compute same matrix if and only if both circuits are identical.
We also discuss the computational power of circuits consisting
of Hadamard, phase, CNOT gates and a limited number of $\pi/8$ gates. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Representation of Unitary Group / Quantum Circuit / Normal Form / / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 107, no. 537, COMP2007-57, pp. 15-22, March 2008. |
Paper # |
COMP2007-57 |
Date of Issue |
2008-03-03 (COMP) |
ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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COMP2007-57 |
Conference Information |
Committee |
COMP |
Conference Date |
2008-03-10 - 2008-03-10 |
Place (in Japanese) |
(See Japanese page) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2008-03-COMP |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
On the Computational Power of Quantum Circuits with Clifford and π/8 Gates |
Sub Title (in English) |
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Keyword(1) |
Representation of Unitary Group |
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Quantum Circuit |
Keyword(3) |
Normal Form |
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1st Author's Name |
Ken Matsumoto |
1st Author's Affiliation |
Gunma University (Gunma Univ.) |
2nd Author's Name |
Kazuyuki Amano |
2nd Author's Affiliation |
Gunma University (Gunma Univ.) |
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Speaker |
Author-1 |
Date Time |
2008-03-10 10:20:00 |
Presentation Time |
25 minutes |
Registration for |
COMP |
Paper # |
COMP2007-57 |
Volume (vol) |
vol.107 |
Number (no) |
no.537 |
Page |
pp.15-22 |
#Pages |
8 |
Date of Issue |
2008-03-03 (COMP) |
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