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Paper Abstract and Keywords
Presentation 2014-03-10 10:30
Quantum Commuting Circuits and Complexity of Ising Partition Functions
Keisuke Fujii (Kyoto Univ.), Tomoyuki Morimae (Gunma Univ.) COMP2013-63
Abstract (in Japanese) (See Japanese page) 
(in English) Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal in the sense of standard quantum computation. Nevertheless, it has been shown that if there is a classical algorithm that can simulate IQP efficiently, the polynomial hierarchy (PH) collapses at the third level, which is highly implausible. However, the origin of the classical intractability is still less understood. Here we establish a relationship between IQP and computational complexity of the partition functions of Ising models. We apply the established relationship in two opposite directions. One direction is to find subclasses of IQP that are classically efficiently simulatable in the strong sense, by using exact solvability of certain types of Ising models. Another direction is applying quantum computational complexity of IQP to investigate (im)possibility of efficient classical approximations of Ising models with imaginary coupling constants. Specifically, we show that there is no fully polynomial randomized approximation scheme (FPRAS) for Ising models with almost all imaginary coupling constants even on a planar graph of a bounded degree, unless the PH collapses at the third level. Furthermore, we also show a multiplicative approximation of such a class of Ising partition functions is at least as hard as a multiplicative approximation for the output distribution of an arbitrary quantum circuit.
Keyword (in Japanese) (See Japanese page) 
(in English) quantum computation / Ising model / partition function / / / / /  
Reference Info. IEICE Tech. Rep., vol. 113, no. 488, COMP2013-63, pp. 23-27, March 2014.
Paper # COMP2013-63 
Date of Issue 2014-03-03 (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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Conference Information
Committee COMP  
Conference Date 2014-03-10 - 2014-03-10 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
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Paper Information
Registration To COMP 
Conference Code 2014-03-COMP 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Quantum Commuting Circuits and Complexity of Ising Partition Functions 
Sub Title (in English)  
Keyword(1) quantum computation  
Keyword(2) Ising model  
Keyword(3) partition function  
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1st Author's Name Keisuke Fujii  
1st Author's Affiliation Kyoto University (Kyoto Univ.)
2nd Author's Name Tomoyuki Morimae  
2nd Author's Affiliation Gunma University (Gunma Univ.)
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Speaker Author-1 
Date Time 2014-03-10 10:30:00 
Presentation Time 25 minutes 
Registration for COMP 
Paper # COMP2013-63 
Volume (vol) vol.113 
Number (no) no.488 
Page pp.23-27 
#Pages 5 
Date of Issue 2014-03-03 (COMP) 

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