@article{oai:nagoya.repo.nii.ac.jp:00026544,
author = {Fujii, Keisuke and Kobayashi, Hirotada and Morimae, Tomoyuki and Nishimura, Harumichi and Tamate, Shuhei and Tani, Seiichiro},
issue = {20},
journal = {Physical Review Letters},
month = {May},
note = {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)]. 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)] 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.},
title = {Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error},
volume = {120},
year = {2018}
}