| 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. |
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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) |
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| Keyword(1) |
DQC1 |
| Keyword(2) |
quantum computing |
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complete problems |
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error reduction |
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| 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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| Speaker |
Author-4 |
| Date Time |
2016-11-25 15:10:00 |
| Presentation Time |
20 minutes |
| Registration for |
QIT |
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