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Classical simulation of DQC1$_2$ or DQC2$_1$ implies collapse of the polynomial hierarchy | | Tomoyuki Morimae
; Harumichi Nishimura
; Keisuke Fujii
; Shuhei Tamate
; | | Date: |
24 Sep 2014 | | Abstract: | Deterministic quantum computation with one quantum bit (DQC1) [E. Knill and
R. Laflamme, Phys. Rev. Lett. {f81}, 5672 (1998)] is a restricted model of
quantum computing where the input state is the completely-mixed state except
for a single pure qubit, and a single output qubit is measured at the end of
the computing. We can generalize it to the DQC$k_m$ model where $k$ input
qubits are pure, and $m$ output qubits are measured. It was shown in [T.
Morimae, K. Fujii, and J. F. Fitzsimons, Phys. Rev. Lett. {f112}, 130502
(2014)] that if the output probability distribution of the DQC1$_m$ model for
$mge3$ can be classically efficiently sampled, then the polynomial hierarchy
collapses at the third level. In this paper, we show that the classical
simulability of the DQC$1_2$ model or DQC2$_1$ model also leads to the collapse
of the polynomial hierarchy at the third level. Our idea which solves the
problem of the "shortage of postselected qubits" is to use the complexity class
SBQP instead of postBQP. | | Source: | arXiv, 1409.6777 | | Services: | Forum | Review | PDF | Favorites | |
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