Negative Quasi-Probability as a Resource for Quantum Computation
Victor Veitch, Christopher Ferrie, David Gross, Joseph Emerson
备注：
15 pages v4: This is a major revision. In particular, we have added a new section detailing an explicit extension of the Gottesman-Knill simulation protocol to deal with positively represented states and measurement (even when these are non-stabilizer). This paper also includes significant elaboration on the two main results of the previous version
A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection between the potential for quantum speed-up and the onset of negative values in a distinguished quasi-probability representation, a discrete analog of the Wigner function for quantum systems of odd dimension. This connection allows us to resolve an open question on the existence of bound states for magic-state distillation: we prove that there exist mixed states outside the convex hull of stabilizer states that cannot be distilled to non-stabilizer target states using stabilizer operations. We also provide an efficient simulation protocol for Clifford circuits that extends to a large class of mixed states, including bound universal states.
Negative quasiprobability trajectories for Bell-diagonal states under local decoherence
Northwest University（西北大学）；Shaanxi Key Laboratory for Theoretical Physics Frontiers（陕西省理论物理前沿重点实验室）；Peng Huanwu Center for Fundamental Theory（彭桓武理论研究中心）；Fundamental Discipline Research Center for Quantum Science and Technology of Shaanxi Province（陕西省量子科学与技术基础学科研究中心）
Verifier-on-a-Leash: new schemes for verifiable delegated quantum computation, with quasilinear resources
可靠地证明量子设备执行的计算结果的问题正在迅速获得相关性。我们提出了两个协议的经典验证可验证的量子计算委托给两个非通信，但纠缠的量子证明。我们的协议具有接近最优的复杂性，在验证者和诚实证明者所使用的总资源方面，每一方的操作总数，包括诚实证明者所需的纠缠量子比特对的数量，缩放为$O(g\log g)$，用于委托大小为$g$的电路。这与以前的协议相反，以前的协议都需要非常大的多项式开销。我们的第一个协议需要在被委托的电路的深度上线性的回合数，并且是盲的，这意味着两个证明者都不能学习被委托的电路。第二个协议不是盲目的，但只需要恒定数量的交互轮数。我们的主要技术创新是一个有效的刚性定理，它允许验证器测试，两个纠缠的证明者执行测量指定的任意$m$ -量子位张量积的单量子位克利福德观测值在各自的一半的$m$共享EPR对，具有鲁棒性，是独立的$m$。我们的两个证明者经典验证者委托协议是通过将这个刚性定理与Broadbent（Theory of Computing，2018）介绍的用于量子计算的可验证委托的单证明者量子验证者协议相结合而获得的。
