title: Hardness of classically simulating the one-clean-qubit model.
abstract: 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.
authors.affiliation: ASRLD Unit, Gunma University, 1-5-1 Tenjin-cho Kiryu-shi Gunma-ken, 376-0052, Japan.
authors.forename: Tomoyuki
authors.initials: T
authors.lastname: Morimae
authors.affiliation: 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.
authors.forename: Keisuke
authors.initials: K
authors.lastname: Fujii
authors.affiliation: Singapore University of Technology and Design, 20 Dover Drive, 138682, Singapore and Center for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, 117543, Singapore.
authors.forename: Joseph F
authors.initials: JF
authors.lastname: Fitzsimons