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.

翻译：我们提出了一种在$(n+1)$-量子比特量子计算机上模拟高斯玻色（GB）电路在$2^n$个模式上作用的理论框架。具体而言，我们将初始玻色态在正交算符（及其协方差矩阵）上的期望值编码为输入量子比特态。随后通过一个量子电路演化该态，该电路有效实现了由GB门诱导的辛传播子。我们找到了能够实现高效量子模拟的GB电路族与初始态族。为此，我们建立了一个GB门与量子比特门之间的映射词典，使得粒子数守恒（非守恒）的GB门在量子比特层面分别对应于实（虚）时间演化。针对粒子数守恒电路这一特殊情况，我们提出了一个BQP完全的高斯玻色判定问题，表明在指数级多模式上对高斯态进行GB演化与通用量子计算机具有同等计算能力。我们还对一个涉及约80亿个模式的干涉仪进行了数值模拟，以展示本框架的强大性能。