Performance and structure of single-mode bosonic codes

Abstract

The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce new codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat/binomial/GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multi-qubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a new multi-qudit code.

34 pages, 11 figures, 4 tables. v3: published version. See related talk at https://absuploads.aps.org/presentation.cfm?pid=13511

References in corpus (22)

• Quantum Computing in the NISQ era and beyond
• High-sensitivity diamond magnetometer with nanoscale resolution
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Fault-tolerant linear optical quantum computing with small-amplitude coherent states
• Direct and Reverse Secret-Key Capacities of a Quantum Channel
• Quantum Capacities of Bosonic Channels
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Generating Grid States From Schrödinger Cat States without Post-Selection
• Optimum Quantum Error Recovery using Semidefinite Programming
• Quantum Capacities of Channels with small Environment
• Sequential modular position and momentum measurements of a trapped ion mechanical oscillator
• Narrow Bounds for the Quantum Capacity of Thermal Attenuators
• Protecting an optical qubit against photon loss
• Experimentally feasible quantum erasure-correcting code for continuous variables
• Quantum Error Correction via Convex Optimization
• Information trade-offs for optical quantum communication
• Continuous variable encoding by ponderomotive interaction
• Hardware-Efficient Bosonic Quantum Error-Correcting Codes Based on Symmetry Operators
• SU(1,1) symmetry of multimode squeezed states
• Noisy propagation of coherent states in a lossy Kerr medium
• Nonadditive quantum error correcting codes adapted to the ampltitude damping channel
• Channel-Adapted Quantum Error Correction

Cited by in corpus (211)

• Advances in Quantum Cryptography
• Microwave photonics with superconducting quantum circuits
• Quantum repeaters: From quantum networks to the quantum internet
• Quantum error correction of a qubit encoded in grid states of an oscillator
• Encoding a qubit in a trapped-ion mechanical oscillator
• Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
• Building a fault-tolerant quantum computer using concatenated cat codes
• Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
• Harnessing electro-optic correlations in an efficient mechanical converter
• Perspective: Toward large-scale fault-tolerant universal photonic quantum computing
• Bosonic quantum error correction codes in superconducting quantum circuits
• Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
• Fault-tolerant bosonic quantum error correction with the surface-GKP code
• All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
• Hardware-efficient quantum random access memory with hybrid quantum acoustic systems
• Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes
• Quantum computing with rotation-symmetric bosonic codes
• Robust encoding of a qubit in a molecule
• Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
• Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
• Entangling Bosonic Modes via an Engineered Exchange Interaction
• Quantum information processing with bosonic qubits in circuit QED
• Quantum Error Correction with the Toric-GKP Code
• Towards Scalable Bosonic Quantum Error Correction
• Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
• Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors
• Quantum control of bosonic modes with superconducting circuits
• Coherent spin-spin coupling mediated by virtual microwave photons
• Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis
• A fault-tolerant continuous-variable measurement-based quantum computation architecture
• Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
• Encoding an oscillator into many oscillators
• Quantum bits with Josephson junctions
• Continuous-variable gate teleportation and bosonic-code error correction
• Continuous symmetries and approximate quantum error correction
• Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences
• Pair-cat codes: autonomous error-correction with low-order nonlinearity
• Low overhead fault-tolerant quantum error correction with the surface-GKP code
• High-fidelity measurement of qubits encoded in multilevel superconducting circuits
• Nonadiabatic geometric quantum computation with cat qubits via invariant-based reverse engineering
• All-Optical Long-Distance Quantum Communication with Gottesman-Kitaev-Preskill qubits
• Quantum error correction using squeezed Schrödinger cat states
• Simulating realistic non-Gaussian state preparation
• Distributed quantum sensing enhanced by continuous-variable error correction
• A critical Schrödinger cat qubit
• Fault-tolerant preparation of approximate GKP states
• Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes
• Production of photonic universal quantum gates enhanced by machine learning
• Engineering a Kerr-based Deterministic Cubic Phase Gate via Gaussian Operations
• Experimental demonstration of remotely creating Wigner negativity via quantum steering
• Equivalence of approximate Gottesman-Kitaev-Preskill codes
• Modular Bosonic Subsystem Codes
• Spatial noise filtering through error correction for quantum sensing
• Building a large-scale quantum computer with continuous-variable optical technologies
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
• Generation of optical Gottesman-Kitaev-Preskill states with cavity QED
• Creation of Optical Cat and GKP States Using Shaped Free Electrons
• Measurement-free preparation of grid states
• Superposition of two-mode squeezed states for quantum information processing and quantum sensing
• Room-Temperature Photonic Logical Qubits via Second-Order Nonlinearities
• Generation of time-frequency grid state with integrated biphoton frequency combs
• Fast binomial-code holonomic quantum computation with ultrastrong light-matter coupling
• Engineering Schrödinger cat states with a photonic even-parity detector
• Encoding qubits in multimode grid states
• High-threshold fault-tolerant quantum computation with the Gottesman-Kitaev-Preskill qubit under noise in an optical setup
• Fast simulation of bosonic qubits via Gaussian functions in phase space
• Quantum error correction with dissipatively stabilized squeezed cat qubits
• Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound
• Quantum capacity and codes for the bosonic loss-dephasing channel
• Architecture and noise analysis of continuous-variable quantum gates using two-dimensional cluster states
• Optimal approximate quantum error correction for quantum metrology
• Resource-Efficient Quantum Computing by Breaking Abstractions
• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• Resource reduction for distributed quantum information processing using quantum multiplexed photons
• Generation of Schrödinger cat states with Wigner negativity using continuous-wave low-loss waveguide optical parametric amplifier
• Heralded-Multiplexed High-Efficiency Cascaded Source of Dual-Rail Polarization-Entangled Photon Pairs using Spontaneous Parametric Down Conversion
• Deterministic generation of a four-component optical cat state
• Flexible learning of quantum states with generative query neural networks
• Time-frequency as quantum continuous variables
• Introduction to Quantum Error Correction and Fault Tolerance
• High-fidelity bosonic quantum state transfer using imperfect transducers and interference
• Efficient simulatability of continuous-variable circuits with large Wigner negativity
• Generation of Flying Logical Qubits using Generalized Photon Subtraction with Adaptive Gaussian Operations
• Efficient backcasting search for optical quantum state synthesis
• Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
• Realizing modular quadrature measurements via a tunable photon-pressure coupling in circuit-QED
• Canonical forms for single-qutrit Clifford+T operators
• Towards long-distance quantum networks with superconducting processors and optical links
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Quantum computation with cat qubits
• Cubic phase gates are not suitable for non-Clifford operations on GKP states
• All-optical quantum computing using cubic phase gates
• Degenerate Squeezing in Waveguides: A Unified Theoretical Approach
• Multispin Clifford codes for angular momentum errors in spin systems
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements
• Information processing at the speed of light
• Topological zero modes and edge symmetries of metastable Markovian bosonic systems
• Stabilizer subsystem decompositions for single- and multi-mode Gottesman-Kitaev-Preskill codes
• All-photonic GKP-qubit repeater using analog-information-assisted multiplexed entanglement ranking
• Distributed Private Randomness Distillation
• Phase-space methods for representing, manipulating, and correcting Gottesman-Kitaev-Preskill qubits
• Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons
• Subsystem analysis of continuous-variable resource states
• Drive-induced nonlinearities of cavity modes coupled to a transmon ancilla
• Continuous-variable quantum communication
• Quantum spherical codes
• The Near-optimal Performance of Quantum Error Correction Codes
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Quantum error correction with the color-Gottesman-Kitaev-Preskill code
• Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code
• Gottesman-Kitaev-Preskill state preparation using periodic driving
• Æ codes
• Universal quantum computation with optical four-component cat qubits
• Biased Gottesman-Kitaev-Preskill repetition code
• Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes
• The $2T$-qutrit, a two-mode bosonic qutrit
• Non-Markovian feedback for optimized quantum error correction
• Quantum communication on the bosonic loss-dephasing channel
• Memory-assisted decoder for approximate Gottesman-Kitaev-Preskill codes
• Error Correction Using Squeezed Fock States
• Qubit-oscillator concatenated codes: decoding formalism & code comparison
• Characterizing the performance of continuous-variable Gaussian quantum gates
• Designing good bosonic quantum codes via creating destructive interference
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Squeezed comb states
• Photon-Number-Dependent Hamiltonian Engineering for Cavities
• Hidden qubit cluster states
• Gaussian conversion protocol for heralded generation of qunaught states
• Spin squeezed GKP codes for quantum error correction in atomic ensembles
• Classification and reconstruction of optical quantum states with deep neural networks
• Bosonic Quantum Error Correction with Neutral Atoms in Optical Dipole Traps
• Improved readout of qubit-coupled Gottesman-Kitaev-Preskill states
• Neural Network-Based Design of Approximate Gottesman-Kitaev-Preskill Code
• Continuous-variable quantum state designs: theory and applications
• Two-qubit operations for finite-energy Gottesman-Kitaev-Preskill encodings
• Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits
• Classical simulation of non-Gaussian bosonic circuits
• Adaptive variational low-rank dynamics for open quantum systems
• Engineering Arbitrary Hamiltonians in Phase Space
• Universal quantum computing with thermal state bosonic systems
• Probing the Jaynes-Cummings Ladder with Spin Circuit Quantum Electrodynamics
• The Zak transform: a framework for quantum computation with the Gottesman-Kitaev-Preskill code
• Quantum error-correcting codes with a covariant encoding
• Quantum error correction under numerically exact open-quantum-system dynamics
• Analysis of loss correction with the Gottesman-Kitaev-Preskill code
• Performance of Rotation-Symmetric Bosonic Codes in a Quantum Repeater Network
• Quantum Volume for Photonic Quantum Processors
• Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
• Efficient Concatenated Bosonic Code for Additive Gaussian Noise
• Optimality Condition for the Petz Map
• Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian
• Trade-offs on number and phase shift resilience in bosonic quantum codes
• Non-commutative graphs based on finite-infinite system couplings: quantum error correction for a qubit coupled to a coherent field
• Passive environment-assisted quantum communication with GKP states
• Simultaneous preparation of two optical cat states based on a nondegenerate optical parametric amplifier
• Gottesman-Kitaev-Preskill encoding in continuous modal variables of single photons
• On noise in swap ASAP repeater chains: exact analytics, distributions and tight approximations
• Clifford operations and homological codes for rotors and oscillators
• Encoding qubits into harmonic-oscillator modes via quantum walks in phase space
• Non-adiabatic holonomic quantum operations in continuous variable systems
• Bosonic quantum error correction using squeezed Fock states
• Robustness-optimized quantum error correction
• Explicit error-correction scheme and code distance for bosonic codes with rotational symmetry
• Information transmission with continuous variable quantum erasure channels
• A Computational Framework for Simulations of Dissipative Non-Adiabatic Dynamics on Hybrid Oscillator-Qubit Quantum Devices
• Error suppression in multicomponent cat codes with photon subtraction and teleamplification
• Effect of Decoherence for Gate Operations on a Superconducting Bosonic Qubit
• Wigner distribution on a double cylinder phase space for studying quantum error correction protocol
• Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion
• Generalized Number-Phase Lattice Encoding of a Bosonic Mode for Quantum Error Correction
• Quantum Error Correction in the Lowest Landau Level
• Interfacing Gottesman-Kitaev-Preskill Qubits to Quantum Memories
• Mixed-State Topological Order under Coherent Noise
• Generating Gottesman-Kitaev-Preskill qubit using a cross-Kerr interaction between a squeezed light and Fock states in optics
• Unification of Finite Symmetries in Simulation of Many-body Systems on Quantum Computers
• Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning
• Improving Continuous-variable Quantum Channels with Unitary Averaging
• Hybrid Rabi interaction with traveling states of light
• Continuous-variable designs and design-based shadow tomography from random lattices
• High-rate extended binomial codes for multiqubit encoding
• Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code
• Detecting Quantum Capacities of Continuous-Variable Quantum Channels
• General Approach to Error Detection of Bosonic Codes via Phase Estimation
• Generalized Parity Measurements and Efficient Large Multi-component Cat State Preparation with Quantum Signal Processing
• Using a Kerr interaction for GKP magic state preparation
• Error-mitigated Geometric Quantum Control over an Oscillator
• Relative-belief inference in quantum information theory
• Logical channels in approximate Gottesman-Kitaev-Preskill error correction
• Quantum error correction beyond $SU(2)$: spin, bosonic, and permutation-invariant codes from convex geometry
• Linear-optical approach to encoding qubits into harmonic-oscillator modes via quantum walks
• Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing
• A Mathematical Structure for Amplitude-Mixing Error-Transparent Gates for Binomial Codes
• Quantum Computation and Communication in Bosonic Systems
• Topological stabilizer models on continuous variables
• Photonic Hybrid Quantum Computing
• Protected phase gate for the $0$-$\pi$ qubit using its internal modes
• Linear optical quantum computing with a hybrid squeezed cat code
• Arbitrary high-fidelity binomial codes from multiphoton spin-boson interactions
• Constructing Qudits from Infinite Dimensional Oscillators by Coupling to Qubits
• Unitary-transformed projective squeezing: applications for circuit-knitting and state-preparation of non-Gaussian states
• Nonperturbative leakage elimination for a logical qubit encoded in a mechanical oscillator
• Environment-Assisted Generation of Non-Gaussian Wavepacket Quantum States
• Linear-optical protocols for mitigating and suppressing noise in bosonic systems
• Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding
• Quantum Error Correction with Superpositions of Squeezed Fock States
• Deterministic Gaussian conversion protocols for non-Gaussian single-mode resources
• Fault-Tolerant Non-Clifford GKP Gates using Polynomial Phase Gates and On-Demand Noise Biasing
• Estimating the performance boundary of Gottesman-Kitaev-Preskill codes and number-phase codes
• Entangling Quantum Memories at Channel Capacity
• Circuit-level fault tolerance of cat codes
• Detecting the event of a single photon loss on quantum signals