Quantum Error Correction with the Gottesman-Kitaev-Preskill Code

Abstract

The Gottesman-Kitaev-Preskill (GKP) code was proposed in 2001 by Daniel Gottesman, Alexei Kitaev, and John Preskill as a way to encode a qubit in an oscillator. The GKP codewords are coherent superpositions of periodically displaced squeezed vacuum states. Because of the challenge of merely preparing the codewords, the GKP code was for a long time considered to be impractical. However, the remarkable developments in quantum hardware and control technology in the last two decades has made the GKP code a frontrunner in the race to build practical, fault-tolerant bosonic quantum technology. In this Perspective, we provide an overview of the GKP code with emphasis on its implementation in the circuit-QED architecture and present our outlook on the challenges and opportunities for scaling it up for hardware-efficient, fault-tolerant quantum error correction.

References in corpus (76)

• Topological quantum memory
• Encoding a qubit in an oscillator
• Improved Simulation of Stabilizer Circuits
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Quantum Computing with Very Noisy Devices
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Surface code quantum computing by lattice surgery
• Instantaneous non-local computation of low T-depth quantum circuits
• The Heisenberg Representation of Quantum Computers
• Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Encoding a qubit in a trapped-ion mechanical oscillator
• Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
• Realizing Rapid, High-Fidelity, Single-Shot Dispersive Readout of Superconducting Qubits
• Active stabilisation, quantum computation and quantum state synthesis
• Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
• Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator
• Performance and structure of single-mode bosonic codes
• 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
• Quantum back-action of variable-strength measurement
• Exponential suppression of bit-flips in a qubit encoded in an oscillator
• Perspective: Toward large-scale fault-tolerant universal photonic quantum computing
• 3-Wave Mixing Josephson Dipole Element
• Bosonic Quantum Codes for Amplitude Damping
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Bosonic quantum error correction codes in superconducting quantum circuits
• Bias-preserving gates with stabilized cat qubits
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Fault-tolerant bosonic quantum error correction with the surface-GKP code
• All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
• Repetition Cat Qubits for Fault-Tolerant Quantum Computation
• High-threshold fault-tolerant quantum computation with analog quantum error correction
• Introduction to Quantum-limited Parametric Amplification of Quantum Signals with Josephson Circuits
• Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes
• Fault-tolerant detection of a quantum error
• Quantum computing with rotation-symmetric bosonic codes
• Robust encoding of a qubit in a molecule
• Experimental realization of an intrinsically error-protected superconducting qubit
• Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
• Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
• Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor
• Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
• Quantum information processing with bosonic qubits in circuit QED
• Entangling Bosonic Modes via an Engineered Exchange Interaction
• Quantum Error Correction with the Toric-GKP Code
• Towards Scalable Bosonic Quantum Error Correction
• Schrodinger's catapult: Launching multiphoton quantum states from a microwave cavity memory
• Single-Mode Displacement Sensor
• Gated conditional displacement readout of superconducting qubits
• Realization of a $\Lambda$ system with metastable states of a capacitively-shunted fluxonium
• Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Quantum control of bosonic modes with superconducting circuits
• Error-transparent operations on a logical qubit protected by quantum error correction
• Analog quantum error correction with encoding a qubit into an oscillator
• Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
• Continuous-variable gate teleportation and bosonic-code error correction
• Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes
• Low overhead fault-tolerant quantum error correction with the surface-GKP code
• Achievable rates for the Gaussian quantum channel
• Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits
• Encoding qubits into oscillators with atomic ensembles and squeezed light
• Encoding a qubit in a spin
• Constructing finite dimensional codes with optical continuous variables
• Fault-tolerant preparation of approximate GKP states
• Sequential modular position and momentum measurements of a trapped ion mechanical oscillator
• Fault-Tolerant Quantum Computing in the Pauli or Clifford Frame with Slow Error Diagnostics
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
• Enhanced noise resilience of the surface-GKP code via designed bias
• Quantum computing by color-code lattice surgery
• High-efficiency measurement of an artificial atom embedded in a parametric amplifier
• Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
• Tracking Quantum Error Correction

Cited by in corpus (87)

• Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
• Noisy intermediate-scale quantum computers
• Superconducting cavity qubit with tens of milliseconds single-photon coherence time
• Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences
• Quantum error correction using squeezed Schrödinger cat states
• Dual-rail encoding with superconducting cavities
• Quantum Error Correction of Qudits Beyond Break-even
• Building a large-scale quantum computer with continuous-variable optical technologies
• Creation of Optical Cat and GKP States Using Shaped Free Electrons
• The squeezed Kerr oscillator: spectral kissing and phase-flip robustness
• Encoding qubits in multimode grid states
• High-threshold fault-tolerant quantum computation with the Gottesman-Kitaev-Preskill qubit under noise in an optical setup
• Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound
• Robust and Deterministic Preparation of Bosonic Logical States in a Trapped Ion
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding
• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• Introduction to Quantum Error Correction and Fault Tolerance
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• All-optical quantum computing using cubic phase gates
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements
• Stabilizer subsystem decompositions for single- and multi-mode Gottesman-Kitaev-Preskill codes
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops
• Information processing at the speed of light
• Taming the Rotating Wave Approximation
• Crosstalk-Robust Quantum Control in Multimode Bosonic Systems
• Symplectic geometry and circuit quantization
• Quantum error correction with the color-Gottesman-Kitaev-Preskill code
• Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits
• Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code
• Gottesman-Kitaev-Preskill state preparation using periodic driving
• Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes
• Non-Markovian feedback for optimized quantum error correction
• The $2T$-qutrit, a two-mode bosonic qutrit
• Ground state nature and nonlinear squeezing of Gottesman-Kitaev-Preskill states
• Qubit-oscillator concatenated codes: decoding formalism & code comparison
• Dissipative Quantum Chaos unveiled by Stochastic Quantum Trajectories
• Gaussian conversion protocol for heralded generation of qunaught states
• Bosonic Quantum Error Correction with Neutral Atoms in Optical Dipole Traps
• Neural Network-Based Design of Approximate Gottesman-Kitaev-Preskill Code
• Two-qubit operations for finite-energy Gottesman-Kitaev-Preskill encodings
• Quantum error-correcting codes with a covariant encoding
• Quantum tomography of magnons using Brillouin light scattering
• Analysis of loss correction with the Gottesman-Kitaev-Preskill code
• Seeding Gaussian boson samplers with single photons for enhanced state generation
• Resonant Schrödinger Cat States in Circuit Quantum Electrodynamics
• Dissipative protection of a GKP qubit in a high-impedance superconducting circuit driven by a microwave frequency comb
• Quantum Volume for Photonic Quantum Processors
• Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
• Optimality Condition for the Petz Map
• Characterizing quantum instruments: from non-demolition measurements to quantum error correction
• Designing fast quantum gates using optimal control with a reinforcement-learning ansatz
• Hybrid cat-transmon architecture for scalable, hardware-efficient quantum error correction
• Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator
• Classical simulation and quantum resource theory of non-Gaussian optics
• Gottesman-Kitaev-Preskill encoding in continuous modal variables of single photons
• Clifford operations and homological codes for rotors and oscillators
• Code conversion with the quantum Golay code for a universal transversal gate set
• On Quantum Steering and Wigner Negativity
• Generalized squeezing as a witness
• Incoherent Gaussian equivalence of $m-$mode Gaussian states
• Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion
• Unification of Finite Symmetries in Simulation of Many-body Systems on Quantum Computers
• Generating Gottesman-Kitaev-Preskill qubit using a cross-Kerr interaction between a squeezed light and Fock states in optics
• Quantum Error Correction in the Lowest Landau Level
• Quadrature Coherence Scale of Linear Combinations of Gaussian Functions in Phase Space
• End-to-end switchless architecture for fault-tolerant photonic quantum computing
• Digital Discovery of interferometric Gravitational Wave Detectors
• Improving quantum metrology protocols with programmable photonic circuits
• Cross-resonance control of an oscillator with an auxiliary fluxonium qubit
• Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes
• Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states
• Using a Kerr interaction for GKP magic state preparation
• Bosonic quantum Fourier codes
• Toward a physically motivated notion of Gaussian complexity geometry
• General Approach to Error Detection of Bosonic Codes via Phase Estimation
• Estimating the performance boundary of Gottesman-Kitaev-Preskill codes and number-phase codes
• A method of an on-demand beamsplitter for trapped-ion quantum computers
• Quantum Error Correction with Superpositions of Squeezed Fock States
• Gottesman-Kitaev-Preskill codes: A lattice perspective
• Gate-Based Microwave Quantum Repeater Via Grid-State Encoding
• Autonomous Quantum Error Correction in a Four-Photon Kerr Parametric Oscillator
• Deterministic Gaussian conversion protocols for non-Gaussian single-mode resources
• Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding
• Codeword Stabilized Codes from m-Uniform Graph States
• Environment-Assisted Generation of Non-Gaussian Wavepacket Quantum States
• Cavity cooling using ultrafast electrons
• Quantum steganographic protocols using degenerate and entanglement-assisted quantum codes