Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
arXiv:2308.02913 · doi:10.1016/j.pquantelec.2023.100496
Abstract
Encoding quantum information into a set of harmonic oscillators is considered a hardware efficient approach to mitigate noise for reliable quantum information processing. Various codes have been proposed to encode a qubit into an oscillator -- including cat codes, binomial codes and Gottesman-Kitaev-Preskill (GKP) codes -- and are among the first to reach a break-even point for quantum error correction. Though GKP codes are widely recognized for their promise in quantum computation, they also facilitate near-optimal quantum communication rates in bosonic channels and offer the ability to safeguard arbitrary quantum states of oscillators. This review focuses on the basic working mechanism, performance characterization, and the many applications of GKP codes -- emphasizing recent experimental progress in superconducting circuit architectures and theoretical advancements in multimode GKP qubit codes and oscillators-to-oscillators (O2O) codes. We begin with a preliminary continuous-variable formalism needed for bosonic codes. We then proceed to the quantum engineering involved to physically realize GKP states. We take a deep dive into GKP stabilization and preparation in superconducting architectures and examine proposals for realizing GKP states in the optical domain (along with a concise review of GKP realization in trapped-ion platforms). Finally, we present multimode GKP qubits and GKP-O2O codes, examine code performance and discuss applications of GKP codes in quantum information processing tasks such as computing, communication, and sensing.
77+7 pages, 31 figures. close to final published version. references updated compared to last version
References in corpus (206)
- Quantum Cryptography
- Fault-tolerant quantum computation by anyons
- The Quantum Internet
- Quantum cryptography: Public key distribution and coin tossing
- Quantum sensing
- Advances in Quantum Metrology
- Gaussian Quantum Information
- Charge insensitive qubit design derived from the Cooper pair box
- Surface codes: Towards practical large-scale quantum computation
- Circuit Quantum Electrodynamics
- A Quantum Engineer's Guide to Superconducting Qubits
- Advances in Quantum Cryptography
- Topological quantum memory
- Secure quantum key distribution with realistic devices
- Encoding a qubit in an oscillator
- Integrated photonics on thin-film lithium niobate
- Superconducting Qubits: Current State of Play
- General Benchmarks for Quantum Repeaters
- Coupling Superconducting Qubits via a Cavity Bus
- Fundamental Limits of Repeaterless Quantum Communications
- Quantum Error Correction for Quantum Memories
- Trapped-Ion Quantum Computing: Progress and Challenges
- Quantum computation over continuous variables
- Suppressing quantum errors by scaling a surface code logical qubit
- Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Advances in Photonic Quantum Sensing
- Fluxonium: single Cooper pair circuit free of charge offsets
- The capacity of the noisy quantum channel
- A quantum network of clocks
- A simple formula for the average gate fidelity of a quantum dynamical operation
- Dynamically protected cat-qubits: a new paradigm for universal quantum computation
- On the impossibility of distilling Gaussian states with Gaussian operations
- Superadditivity of communication capacity using entangled inputs
- The characterization of Gaussian operations and Distillation of Gaussian States
- Confining the state of light to a quantum manifold by engineered two-photon loss
- New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds
- Quantum repeaters: From quantum networks to the quantum internet
- Squeezing as an irreducible resource
- Quantum transduction of optical photons from a superconducting qubit
- Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
- The Kerr-Cat Qubit: Stabilization, Readout, and Gates
- Positive Wigner functions render classical simulation of quantum computation efficient
- Longer-Baseline Telescopes Using Quantum Repeaters
- Efficient Classical Simulation of Continuous Variable Quantum Information Processes
- Real-time quantum error correction beyond break-even
- Gaussian transformations and distillation of entangled Gaussian states
- A quantum-enhanced search for dark matter axions
- Development of Quantum InterConnects for Next-Generation Information Technologies
- Encoding a qubit in a trapped-ion mechanical oscillator
- Negative Quasi-Probability as a Resource for Quantum Computation
- A quantum memory with near-millisecond coherence in circuit QED
- Coherent coupling between radio frequency, optical, and acoustic waves in piezo-optomechanical circuits
- Quantum Communication With Zero-Capacity Channels
- A No-Go Theorem for Gaussian Quantum Error Correction
- A Survey on Quantum Channel Capacities
- Extremality of Gaussian quantum states
- Introduction to Quantum Electromagnetic Circuits
- 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
- Perspectives on quantum transduction
- Performance and structure of single-mode bosonic codes
- Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
- Non-Gaussian Quantum States and Where to Find Them
- The sphere packing problem in dimension 24
- Coherent quantum phase slip
- Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
- Microwave-to-optics conversion using a mechanical oscillator in its quantum groundstate
- Achieving the Heisenberg limit in quantum metrology using quantum error correction
- Resource theory of quantum non-Gaussianity and Wigner negativity
- Microwave-to-optical conversion using lithium niobate thin-film acoustic resonators
- Bosonic Quantum Codes for Amplitude Damping
- Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays
- Towards 1% single photon nonlinearity with periodically-poled lithium niobate microring resonators
- Error correction for continuous quantum variables
- Protected gates for superconducting qubits
- Superconducting Nanocircuits for Topologically Protected Qubits
- Quantum Capacities of Bosonic Channels
- Phase-slip flux qubits
- Convex resource theory of non-Gaussianity
- Searching for Dark Matter with a Superconducting Qubit
- Beating the break-even point with a discrete-variable-encoded logical qubit
- 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
- Analog quantum error correction
- Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes
- Fault-tolerant detection of a quantum error
- Demonstration of a Reconfigurable Entangled Radiofrequency-Photonic Sensor Network
- Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
- Experimental realization of an intrinsically error-protected superconducting qubit
- 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
- Erasure conversion in a high-fidelity Rydberg quantum simulator
- 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
- Single-Mode Displacement Sensor
- Model-Free Quantum Control with Reinforcement Learning
- Unitarily localizable entanglement of Gaussian states
- Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
- Cavity piezo-mechanics for superconducting-nanophotonic quantum interface
- Entanglement-Enhanced Optomechanical Sensing
- Quantum control of bosonic modes with superconducting circuits
- Analog quantum error correction with encoding a qubit into an oscillator
- Moving beyond the transmon: Noise-protected superconducting quantum circuits
- Stellar representation of non-Gaussian quantum states
- Mode-Wise Entanglement of Gaussian States
- Optomechanical quantum teleportation
- Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis
- A fault-tolerant continuous-variable measurement-based quantum computation architecture
- On-Chip Microwave Quantum Hall Circulator
- Surface code implementation of block code state distillation
- Superconducting circuit protected by two-Cooper-pair tunneling
- Heralded Generation and Detection of Entangled Microwave--Optical Photon Pairs
- Deterministic implementation of weak quantum cubic nonlinearity
- Non-Gaussian states for continuous variable quantum computation via Gaussian maps
- The superconducting quasicharge qubit
- Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
- Encoding an oscillator into many oscillators
- Coherence properties of the 0- qubit
- A coaxial line architecture for integrating and scaling 3D cQED systems
- Continuous-variable gate teleportation and bosonic-code error correction
- Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
- Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences
- Achievable rates for the Gaussian quantum channel
- Low overhead fault-tolerant quantum error correction with the surface-GKP code
- Resource theory of non-Gaussian operations
- High-fidelity measurement of qubits encoded in multilevel superconducting circuits
- All-Optical Long-Distance Quantum Communication with Gottesman-Kitaev-Preskill qubits
- Hall Effect Gyrators and Circulators
- Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits
- Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion
- Simulating realistic non-Gaussian state preparation
- Dual-rail encoding with superconducting cavities
- Fault-tolerant quantum computation with static linear optics
- Distributed quantum sensing enhanced by continuous-variable error correction
- How to decompose arbitrary continuous-variable quantum operations
- Fault-tolerant preparation of approximate GKP states
- Fundamental building block for all-optical scalable quantum networks
- Sequential modular position and momentum measurements of a trapped ion mechanical oscillator
- Resources for bosonic quantum computational advantage
- Entangled sensor-networks for dark-matter searches
- Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes
- Production of photonic universal quantum gates enhanced by machine learning
- Narrow Bounds for the Quantum Capacity of Thermal Attenuators
- Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
- Modular Bosonic Subsystem Codes
- Certification of non-Gaussian states with operational measurements
- Energy-constrained private and quantum capacities of quantum channels
- Quantum-Computing Architecture based on Large-Scale Multi-Dimensional Continuous-Variable Cluster States in a Scalable Photonic Platform
- The upside of noise: engineered dissipation as a resource in superconducting circuits
- Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
- Creation of Optical Cat and GKP States Using Shaped Free Electrons
- Generation of optical Gottesman-Kitaev-Preskill states with cavity QED
- Path-Independent Quantum Gates with Noisy Ancilla
- ON states as resource units for universal quantum computation with photonic architectures
- Universal fault-tolerant measurement-based quantum computation
- Enhanced noise resilience of the surface-GKP code via designed bias
- Quantum nondemolition measurements with optical parametric amplifiers for ultrafast universal quantum information processing
- Encoding qubits in multimode grid states
- Quantum information processing in phase space: A modular variables approach
- Floquet Many-body Engineering: Topological and Many-body Physics in Phase Space Lattices
- Witnessing Wigner Negativity
- Breaking Lorentz reciprocity with frequency conversion and delay
- Control and Coherence Time Enhancement of the 0- Qubit
- Quantum capacity and codes for the bosonic loss-dephasing channel
- Measurement-based generation and preservation of cat and grid states within a continuous-variable cluster state
- Quantum non-Gaussianity of light and atoms
- Ultimate precision limit of noise sensing and dark matter search
- Engineering Purely Nonlinear Coupling with the Quarton
- Temporal trapping: a route to strong coupling and deterministic optical quantum computation
- Exact solution for the quantum and private capacities of bosonic dephasing channels
- Gaussian quantum channels
- Efficient simulatability of continuous-variable circuits with large Wigner negativity
- Multiparametric Amplification and Qubit Measurement with a Kerr-free Josephson Ring Modulator
- Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
- Superadditivity of the Classical Capacity with Limited Entanglement Assistance
- Magnifying quantum phase fluctuations with Cooper-pair pairing
- Self impedance matched Hall-effect gyrators and circulators
- Continuous-variable error correction for general Gaussian noises
- Free-electron interactions with photonic GKP states: universal control and quantum error correction
- Quantum error correction with higher Gottesman-Kitaev-Preskill codes: minimal measurements and linear optics
- Phase-space methods for representing, manipulating, and correcting Gottesman-Kitaev-Preskill qubits
- Subsystem analysis of continuous-variable resource states
- Formalism for the solution of quadratic Hamiltonians with large cosine terms
- Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits
- Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code
- Biased Gottesman-Kitaev-Preskill repetition code
- Non-reciprocal quantum Hall devices with driven edge magnetoplasmons in 2-dimensional materials
- Qubit-oscillator concatenated codes: decoding formalism & code comparison
- Phase Space Crystal Vibrations: Chiral Edge States with Preserved Time-reversal Symmetry
- The vacuum provides quantum advantage to otherwise simulatable architectures
- Improved readout of qubit-coupled Gottesman-Kitaev-Preskill states
- Two-qubit operations for finite-energy Gottesman-Kitaev-Preskill encodings
- Engineering Arbitrary Hamiltonians in Phase Space
- Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
- Optimal encoding of oscillators into more oscillators
- Enhancing distributed sensing with imperfect error correction
- Stability and decoherence rates of a GKP qubit protected by dissipation
- Resource distillation in convex Gaussian resource theories
- Error-corrected quantum repeaters with GKP qudits
- Robust suppression of noise propagation in GKP error-correction
Cited by in corpus (19)
- Non-Markovian feedback for optimized quantum error correction
- Bosonic Quantum Error Correction with Neutral Atoms in Optical Dipole Traps
- Stochastic waveform estimation at the fundamental quantum limit
- Strategies for implementing quantum error correction in molecular rotation
- Single-shot Quantum Signal Processing Interferometry
- Passive environment-assisted quantum communication with GKP states
- Engineering Bosonic Codes with Quantum Lattice Gates
- Quantum-enhanced dark matter detection with in-cavity control: mitigating the Rayleigh curse
- Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code
- Complexity of quantum tomography from genuine non-Gaussian entanglement
- Adaptive Non-Gaussian Quantum State Engineering
- Monte Carlo approach for finding optimally controlled quantum gates with differential geometry
- Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing
- Quantum-enhanced learning with a controllable bosonic variational sensor network
- Error-mitigated Geometric Quantum Control over an Oscillator
- The complexity of Gottesman-Kitaev-Preskill states
- Arbitrary high-fidelity binomial codes from multiphoton spin-boson interactions
- Estimating the performance boundary of Gottesman-Kitaev-Preskill codes and number-phase codes
- Linear-optical protocols for mitigating and suppressing noise in bosonic systems