Title: Gate-based quantum simulation of Gaussian bosonic circuits on exponentially many modes Show Chinese title

Title: 基于门的量子模拟在指数级多模式上的高斯玻色电路

Abstract: 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. Show Chinese abstract

Abstract: 我们引入了一个框架，用于在 $(n+1)$-量子比特量子计算机上模拟高斯玻色子（GB）电路对 $2^n$模式上的状态的作用。 具体来说，我们将初始玻色子状态在正交算符上的期望值（以及其协方差矩阵）作为输入量子态进行编码。 然后通过一个有效实现由GB门引起的辛传播子的量子电路对其进行演化。 我们发现了一些GB电路和初始状态，使得量子模拟变得高效。 为此，我们引入了一个字典，将GB门和量子比特门进行映射，使得粒子保持（非粒子保持）的GB门在量子比特层面上导致实（虚）时间演化。 对于粒子保持电路的特殊情况，我们提出一个BQP完全的GB决策问题，表明在指数级多模式上的高斯状态的GB演化与通用量子计算机一样强大。 我们还对包含 $\sim8$十亿个模式的干涉仪进行了数值模拟，展示了我们框架的强大功能。