Efficient verification of anticoncentrated quantum states

Author:

Bennink Ryan S.

Abstract

AbstractI present a method for estimating the fidelity F(μ, τ) between a preparable quantum state μ and a classically specified pure target state $$\tau =\left|\tau \right\rangle \left\langle \tau \right|$$ τ = τ τ , using simple quantum circuits and on-the-fly classical calculation (or lookup) of selected amplitudes of $$\left|\tau \right\rangle$$ τ . The method is sample efficient for anticoncentrated states (including many states that are hard to simulate classically), with approximate cost 4ϵ−2(1 − F)dpcoll where ϵ is the desired precision of the estimate, d is the dimension of the Hilbert space, and pcoll is the collision probability of the target distribution. This scaling is exponentially better than that of any method based on classical sampling. I also present a more sophisticated version of the method that uses any efficiently preparable and well-characterized quantum state as an importance sampler to further reduce the number of copies of μ needed. Though some challenges remain, this work takes a significant step toward scalable verification of complex states produced by quantum processors.

Funder

DOE Advanced Scientific Computing Research

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,Computer Networks and Communications,Statistical and Nonlinear Physics,Computer Science (miscellaneous)

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Computational advantage of quantum random sampling;Reviews of Modern Physics;2023-07-20

2. QuChain: On the Security and Privacy of Peer-to-Peer System using Blind Quantum Computation;2023 IEEE 23rd International Conference on Nanotechnology (NANO);2023-07-02

3. A probabilistic model of quantum states for classical data security;Frontiers of Physics;2023-05-24

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