Fast simulation of bosonic qubits via Gaussian functions in phase space

TL;DR

This paper introduces a new formalism for efficiently simulating non-Gaussian bosonic qubits, enabling detailed analysis of their behavior under various quantum operations and measurements, which was previously computationally challenging.

Contribution

The authors develop a novel Gaussian function-based formalism for simulating a broad class of bosonic qubits and their transformations, improving accuracy and computational efficiency over existing methods.

Findings

Simulated GKP, cat, and Fock states using the new formalism.

Analyzed the behavior of bosonic qubits under Gaussian channels and non-Gaussian transformations.

Demonstrated the simulation of fault-tolerant quantum circuits beyond current capabilities.

Abstract

Bosonic qubits are a promising route to building fault-tolerant quantum computers on a variety of physical platforms. Studying the performance of bosonic qubits under realistic gates and measurements is challenging with existing analytical and numerical tools. We present a novel formalism for simulating classes of states that can be represented as linear combinations of Gaussian functions in phase space. This formalism allows us to analyze and simulate a wide class of non-Gaussian states, transformations and measurements. We demonstrate how useful classes of bosonic qubits -- Gottesman-Kitaev-Preskill (GKP), cat, and Fock states -- can be simulated using this formalism, opening the door to investigating the behaviour of bosonic qubits under Gaussian channels and measurements, non-Gaussian transformations such as those achieved via gate teleportation, and important non-Gaussian measurements such as threshold and photon-number detection. Our formalism enables simulating these situations with levels of accuracy that are not feasible with existing methods. Finally, we use a method informed by our formalism to simulate circuits critical to the study of fault-tolerant quantum computing with bosonic qubits but beyond the reach of existing techniques. Specifically, we examine how finite-energy GKP states transform under realistic qubit phase gates; interface with a CV cluster state; and transform under non-Clifford T gate teleportation using magic states. We implement our simulation method as a part of the open-source Strawberry Fields Python library.