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.
Highlights
Photonics and superconducting cavities are the leading platforms for building a scalable fault-tolerant quantum computer [1,2,3,4,5,6,7,8,9,10]
II B we provide an overview of Strawberry Fields, the programming library in which we implement the formalism and methods developed in the rest of the paper
One advantage of the GKP encoding is that Clifford gates and measurements correspond to Gaussian transformations [11], which are experimentally accessible in the photonics context, as we review in Appendix √H Pauli X and Z gates correspond to displacements by π along the q and p quadratures, respectively
Summary
Photonics and superconducting cavities are the leading platforms for building a scalable fault-tolerant quantum computer [1,2,3,4,5,6,7,8,9,10]. Motivated as a tool to facilitate the design of quantum computing architectures, our framework can model important sources of decoherence (such as optical loss in photonics or dissipation in superconducting cavities) as well as transformations and measurements that are readily implementable in photonics, such as linear optics, squeezing operations, homodyne, and photoncounting detection We accomplish this by leveraging the most convenient aspects of the Gaussian CV formalism—namely, the ability to regard the transformation of a state as a transformation of means vectors and covariance matrices—while providing the capability to simulate nonGaussian systems, which is necessary to the construction of a quantum computer [27]. For a more hands-on introduction to the simulations that are enabled by our formalism, we invite the reader to consult the open-source code available in Strawberry Fields [28,33] and an accompanying set of tutorials available online [34,35,36]
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