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Paper Abstract and Keywords
Presentation 2016-11-25 15:10
Power of Quantum Computation with Few Clean Qubits
Keisuke Fujii (Univ. Tokyo), Hirotada Kobayashi (NII), Tomoyuki Morimae (Gunma Univ.), Harumichi Nishimura (Nagoya Univ.), Shuhei Tamate (NII), Seiichiro Tani (NTT)
Abstract (in Japanese) (See Japanese page) 
(in English) This paper investigates the power of polynomial-time quantum computation in which only a very limited number of qubits are initially clean in the |0> state, and all the remaining qubits are initially in the totally mixed state. No initializations of qubits are allowed during the computation, nor are intermediate measurements. The main contribution of this paper is to develop unexpectedly strong error-reduction methods for such quantum computations that simultaneously reduce the number of necessary clean qubits. It is proved that any problem solvable by a polynomial-time quantum computation with one-sided bounded error that uses logarithmically many clean qubits is also solvable with exponentially small one-sided error using just two clean qubits, and with polynomially small one-sided error using just one clean qubit. It is further proved in the two-sided-error case that any problem solvable by such a computation with a constant gap between completeness and soundness using logarithmically many clean qubits is also solvable with exponentially small two-sided error using just two clean qubits. If only one clean qubit is available,
the problem is again still solvable with exponentially small error in one of the completeness and soundness and with polynomially small error in the other. An immediate consequence is that the Trace Estimation problem defined with fixed constant threshold parameters is complete for the classes of problems solvable by polynomial-time quantum computations with completeness 2/3 and soundness 1/3 using just one and logarithmically many clean qubits, respectively. The techniques used for proving the error-reduction results may be of independent interest in themselves, and one of the technical tools can also be used to show the hardness of weak classical simulations of one-clean-qubit computations (i.e., DQC1 computations).
Keyword (in Japanese) (See Japanese page) 
(in English) DQC1 / quantum computing / complete problems / error reduction / / / /  
Reference Info. IEICE Tech. Rep.
Paper #  
Date of Issue  
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
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Conference Information
Committee QIT  
Conference Date 2016-11-24 - 2016-11-25 
Place (in Japanese) (See Japanese page) 
Place (in English) KEK Kobayashi-hall 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Quantum Information 
Paper Information
Registration To QIT 
Conference Code 2016-11-QIT 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Power of Quantum Computation with Few Clean Qubits 
Sub Title (in English)  
Keyword(1) DQC1  
Keyword(2) quantum computing  
Keyword(3) complete problems  
Keyword(4) error reduction  
1st Author's Name Keisuke Fujii  
1st Author's Affiliation The University of Tokyo (Univ. Tokyo)
2nd Author's Name Hirotada Kobayashi  
2nd Author's Affiliation National Institute of Informatics (NII)
3rd Author's Name Tomoyuki Morimae  
3rd Author's Affiliation Gunma University (Gunma Univ.)
4th Author's Name Harumichi Nishimura  
4th Author's Affiliation Nagoya University (Nagoya Univ.)
5th Author's Name Shuhei Tamate  
5th Author's Affiliation National Institute of Informatics (NII)
6th Author's Name Seiichiro Tani  
6th Author's Affiliation NTT Corporation (NTT)
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Date Time 2016-11-25 15:10:00 
Presentation Time 20 
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