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 behavior 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 continuous-variable 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.
11 More- Received 31 March 2021
- Accepted 7 September 2021
DOI:https://doi.org/10.1103/PRXQuantum.2.040315
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Bosonic qubits refer to encoding a qubit, i.e., a two-dimensional quantum system, into a continuous-variable (CV) quantum system like a pulse of light. Bosonic qubits are a promising path to building a quantum computer: first, they decrease the physical resources required to perform a computation, as qubit preparation, gates, and measurement may correspond to experimentally accessible operations; second, they are capable of correcting the inevitable physical errors that arise during a computation.
Motivated by the quest to build noise-resistant quantum computers that employ bosonic qubits, our paper provides mathematical and numerical tools to simulate bosonic qubits under a wide class of useful gates, measurements, and noise sources. The key to our technique is to represent the state of the CV quantum system as a linear combination of Gaussian functions, with the evolution of the state during a computation corresponding to transformations of the means, covariance matrices, and coefficients of the Gaussian functions. With our technique, we perform novel simulations of a leading type of bosonic qubit known as Gottesman-Kitaev-Preskill states undergoing realistic, noisy gates. We provide our simulator in the user-friendly Strawberry Fields software library.
Our results will be useful for optimizing the construction of device components used to prepare and manipulate bosonic qubits. Moreover, our results will inform more sophisticated models for predicting the behavior of scalable quantum computers employing millions of bosonic qubits.