ASRLD Unit, Gunma University, 1-5-1 Tenjin-cho Kiryu-shi Gunma-ken, 376-0052, Japan.
The Hakubi Center for Advanced Research, Kyoto University, Yoshida-Ushinomiya-cho, Sakyo-ku, Kyoto 606-8302, Japan and Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501, Japan.
Phys Rev Lett. 2014 Apr 4;112(13):130502. doi: 10.1103/PhysRevLett.112.130502. Epub 2014 Apr 2.
Deterministic quantum computation with one quantum bit (DQC1) [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)] is a model of quantum computing where the input is restricted to containing a single qubit in a pure state and has all other qubits in a completely mixed state. Only the single pure qubit is measured at the end of the computation. While it is known that DQC1 can efficiently solve several problems for which no known classical efficient algorithms exist, the question of whether DQC1 is really more powerful than classical computation remains open. In this Letter, we introduce a slightly modified version of DQC1, which we call DQC1(k), where k output qubits are measured, and show that DQC1(k) cannot be classically efficiently simulated for any k≥3 unless the polynomial hierarchy collapses at the third level.
使用一个量子位（DQC1）进行确定性量子计算[E. Knill 和 R. Laflamme，Phys. Rev. Lett. 81, 5672 (1998)]是一种量子计算模型，其中输入限制为仅包含一个处于纯态的量子位，并且所有其他量子位都处于完全混合态。在计算结束时，仅对单个纯量子位进行测量。虽然已知 DQC1 可以有效地解决一些没有已知经典有效算法的问题，但 DQC1 是否真的比经典计算更强大的问题仍然存在争议。在这封信中，我们引入了 DQC1 的一个略有修改的版本，我们称之为 DQC1(k)，其中测量了 k 个输出量子位，并证明除非多项式层次结构在第三级崩溃，否则对于任何 k≥3，DQC1(k)都不能被经典有效地模拟。
