2018年5月17日
Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error
Physical Review Letters
- ,
- ,
- ,
- ,
- ,
- 巻
- 120
- 号
- 20
- 開始ページ
- 200502:1
- 終了ページ
- 200502:6
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1103/PhysRevLett.120.200502
- 出版者・発行元
- American Physical Society
The one-clean-qubit model (or the deterministic quantum computation with one quantum bit model) is a restricted model of quantum computing where all but a single input qubits are maximally mixed. It is known that the probability distribution of measurement results on three output qubits of the one-clean-qubit model cannot be classically efficiently sampled within a constant multiplicative error unless the polynomial-time hierarchy collapses to the third level [T. Morimae, K. Fujii, and J. F. Fitzsimons, Phys. Rev. Lett. 112, 130502 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.130502]. It was open whether we can keep the no-go result while reducing the number of output qubits from three to one. Here, we solve the open problem affirmatively. We also show that the third-level collapse of the polynomial-time hierarchy can be strengthened to the second-level one. The strengthening of the collapse level from the third to the second also holds for other subuniversal models such as the instantaneous quantum polynomial model [M. Bremner, R. Jozsa, and D. J. Shepherd, Proc. R. Soc. A 467, 459 (2011)PRLAAZ1364-502110.1098/rspa.2010.0301] and the boson sampling model [S. Aaronson and A. Arkhipov, STOC 2011, p. 333]. We additionally study the classical simulatability of the one-clean-qubit model with further restrictions on the circuit depth or the gate types.
- ID情報
-
- DOI : 10.1103/PhysRevLett.120.200502
- ISSN : 1079-7114
- ISSN : 0031-9007
- SCOPUS ID : 85047381205