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

TL;DR

This paper presents a quantum simulation framework for Gaussian Bosonic circuits on a qubit-based quantum computer, enabling efficient simulation of exponentially many modes and demonstrating the computational power of such circuits.

Contribution

It introduces a novel encoding of Gaussian Bosonic circuits into qubit operations, including a mapping between GB and qubit gates, and establishes the computational complexity of simulating these circuits.

Findings

Efficient simulation of GB circuits on a quantum computer for exponentially many modes.

Identification of a BQP-complete decision problem for particle-preserving GB circuits.

Numerical demonstration of simulating an interferometer on billions of modes.

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.