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arXiv 2407.06290quant-phcs.CC
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基于门的指数多模高斯玻色线路量子模拟

Gate-based quantum simulation of Gaussian bosonic circuits on exponentially many modes

Alice Barthe, M. Cerezo, Andrew T. Sornborger, Martin Larocca, Diego García-Martín

AI总结:

本研究提出一种量子模拟框架,可在(n+1)量子比特计算机上模拟指数多模高斯玻色线路的演化,证明其计算能力等价于通用量子计算机,并通过大规模数值模拟验证了框架有效性。

摘要:

我们提出一种框架,可在(n+1)量子比特的量子计算机上,模拟高斯玻色(GB)线路对2^n个模式上量子态的作用。具体而言,我们将初始玻色态在正交算符上的期望值(及其协方差矩阵)编码为输入量子比特态,随后由量子线路演化,该线路有效实现GB门诱导的辛传播子。我们找到了可实现高效量子模拟的GB线路族与初始态族。为此,我们提出一种在GB门与量子比特门之间映射的对应规则,使得粒子守恒(非粒子守恒)的GB门对应量子比特层面的实(虚)时间演化。对于粒子守恒线路的特殊情况,我们提出一个BQP完全的GB判定问题,表明指数多模高斯态的GB演化与通用量子计算机的计算能力相当。我们还对约80亿个模式的干涉仪进行了数值模拟,验证了本框架的能力。

英文摘要:

We introduce a framework for simulating, on an $(n+1)$-qubit quantum computer, the action of a Gaussian Bosonic (GB) circuit on a state over $2^n$ modes. Specifically, we encode the initial bosonic state's expectation values over quadrature operators (and their covariance matrix) as an input qubit-state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real (imaginary) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a BQP-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on $\sim8$ billion modes, illustrating the power of our framework.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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