Fast simulation of bosonic qubits via Gaussian functions in phase space

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.

Code available at: https://github.com/XanaduAI/strawberryfields. Documentation available at: https://strawberryfields.readthedocs.io/en/latest/. Tutorials available at: https://strawberryfields.ai/photonics/demonstrations.html

References in corpus (69)

• Array Programming with NumPy
• Gaussian Quantum Information
• Encoding a qubit in an oscillator
• Negativity of the Wigner function as an indicator of nonclassicality
• Quantum computation with optical coherent states
• Quantum circuits with many photons on a programmable nanophotonic chip
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Positive Wigner functions render classical simulation of quantum computation efficient
• Quantum error correction of a qubit encoded in grid states of an oscillator
• A Simple Quantum Computer
• The Real Symplectic Groups in Quantum Mechanics and Optics
• Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
• Strawberry Fields: A Software Platform for Photonic Quantum Computing
• Performance and structure of single-mode bosonic codes
• Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
• Bias-preserving gates with stabilized cat qubits
• Fault-tolerant bosonic quantum error correction with the surface-GKP code
• All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
• High-threshold fault-tolerant quantum computation with analog quantum error correction
• Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes
• Quantum computing with rotation-symmetric bosonic codes
• Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• All-optical generation of states for "Encoding a qubit in an oscillator"
• Quantum Error Correction with the Toric-GKP Code
• Generating Grid States From Schrödinger Cat States without Post-Selection
• Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors
• Single-Mode Displacement Sensor
• Gaussian Boson Sampling using threshold detectors
• Implementation of a quantum cubic gate by adaptive non-Gaussian measurement
• Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions
• Operator-sum Representation for Bosonic Gaussian Channels
• Applications of Near-Term Photonic Quantum Computers: Software and Algorithms
• Stellar representation of non-Gaussian quantum states
• A Hybrid Long-Distance Entanglement Distribution Protocol
• Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis
• Non-Gaussian states for continuous variable quantum computation via Gaussian maps
• Quantum repeaters with entangled coherent states
• Error Analysis For Encoding A Qubit In An Oscillator
• Continuous-variable gate teleportation and bosonic-code error correction
• Repeat-until-success cubic phase gate for universal continuous-variable quantum computation
• Precision measurements with photon-subtracted or photon-added Gaussian states
• Majorization theory approach to the Gaussian channel minimum entropy conjecture
• Simulating realistic non-Gaussian state preparation
• Distributed quantum sensing enhanced by continuous-variable error correction
• Scalable squeezed light source for continuous variable quantum sampling
• Production of photonic universal quantum gates enhanced by machine learning
• Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments
• Equivalence of approximate Gottesman-Kitaev-Preskill codes
• Modular Bosonic Subsystem Codes
• Exact simulation of Gaussian Boson Sampling in polynomial space and exponential time
• Point Processes with Gaussian Boson Sampling
• Cost-Reduced All-Gaussian Universality with the Gottesman-Kitaev-Preskill Code: Resource-Theoretic Approach to Cost Analysis
• Polynomial approximation of non-Gaussian unitaries by counting one photon at a time
• Conditional non-Gaussian quantum state preparation
• Efficient representation of Gaussian states for multi-mode non-Gaussian quantum state engineering via subtraction of arbitrary number of photons
• Classical simulation of Gaussian quantum circuits with non-Gaussian input states
• Temporal-mode continuous-variable 3-dimensional cluster state for topologically-protected measurement-based quantum computation
• Efficient simulatability of continuous-variable circuits with large Wigner negativity
• Coherent State Topological Cluster State Production
• A measurement-induced optical Kerr interaction
• Exact and approximate continuous-variable gate decompositions
• Degenerate Squeezing in Waveguides: A Unified Theoretical Approach
• Classical benchmarking of Gaussian Boson Sampling on the Titan supercomputer
• Thermal-difference states of light: quantum states of heralded photons
• Fast optimization of parametrized quantum optical circuits
• Squeezed comb states
• Memory-assisted decoder for approximate Gottesman-Kitaev-Preskill codes
• Hybrid Quantum Repeater Protocol With Fast Local Processing

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• Fault-tolerant quantum computation with static linear optics
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• Stabilizer subsystem decompositions for single- and multi-mode Gottesman-Kitaev-Preskill codes
• Classical models may be a better explanation of the Jiuzhang 1.0 Gaussian Boson Sampler than its targeted squeezed light model
• Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits
• Threshold detection statistics of bosonic states
• Riemannian optimization of photonic quantum circuits in phase and Fock space
• Noiseless Linear Amplification and Loss-Tolerant Quantum Relay using Coherent State Superpositions
• Natural Gradient Optimization for Optical Quantum Circuits
• Accelerated Magnonic Motional Cooling with Deep Reinforcement Learning
• Analysis of loss correction with the Gottesman-Kitaev-Preskill code
• A learning theory for quantum photonic processors and beyond