  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.
