Fault-tolerant bosonic quantum error correction with the surface-GKP code
arXiv:1908.03579 · doi:10.1103/PhysRevA.101.012316
Abstract
Bosonic quantum error correction is a viable option for realizing error-corrected quantum information processing in continuous-variable bosonic systems. Various single-mode bosonic quantum error-correcting codes such as cat, binomial, and GKP codes have been implemented experimentally in circuit QED and trapped ion systems. Moreover, there have been many theoretical proposals to scale up such single-mode bosonic codes to realize large-scale fault-tolerant quantum computation. Here, we consider the concatenation of the single-mode GKP code with the surface code, namely, the surface-GKP code. In particular, we thoroughly investigate the performance of the surface-GKP code by assuming realistic GKP states with a finite squeezing and noisy circuit elements due to photon losses. By using a minimum-weight perfect matching decoding algorithm on a 3D space-time graph, we show that fault-tolerant quantum error correction is possible with the surface-GKP code if the squeezing of the GKP states is higher than 11.2dB in the case where the GKP states are the only noisy elements. We also show that the squeezing threshold changes to 18:6dB when both the GKP states and circuit elements are comparably noisy. At this threshold, each circuit component fails with probability 0.69%. Finally, if the GKP states are noiseless, fault-tolerant quantum error correction with the surface-GKP code is possible if each circuit element fails with probability less than 0.81%. We stress that our decoding scheme uses the additional information from GKP-stabilizer measurements and we provide a simple method to compute renormalized edge weights of the matching graphs. Furthermore, our noise model is general as it includes full circuit-level noise.
arXiv comment23 pages, 10 figures, 1 table. Comments welcome!
References in corpus (62)
- Gaussian Quantum Information
- Charge insensitive qubit design derived from the Cooper pair box
- Surface codes: Towards practical large-scale quantum computation
- Quantum Teleportation is a Universal Computational Primitive
- Topological quantum memory
- Measurement-based quantum computation with cluster states
- Encoding a qubit in an oscillator
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Quantum Error Correction for Quantum Memories
- Quantum Computing with Very Noisy Devices
- Quantum computation over continuous variables
- Quantum computation with optical coherent states
- Confining the state of light to a quantum manifold by engineered two-photon loss
- Suppressing Charge Noise Decoherence in Superconducting Charge Qubits
- Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
- New class of quantum error-correcting codes for a bosonic mode
- Efficient Quantum Computation using Coherent States
- Encoding a qubit in a trapped-ion mechanical oscillator
- Quantum codes on a lattice with boundary
- Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
- Quantum computing with nearest neighbor interactions and error rates over 1%
- Performance and structure of single-mode bosonic codes
- Low-distance Surface Codes under Realistic Quantum Noise
- Fault-tolerant linear optical quantum computing with small-amplitude coherent states
- Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
- Symmetrised Characterisation of Noisy Quantum Processes
- 3-Wave Mixing Josephson Dipole Element
- Ultrahigh Error Threshold for Surface Codes with Biased Noise
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- 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
- Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
- Coherent oscillations inside a quantum manifold stabilized by dissipation
- 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
- Effective fault-tolerant quantum computation with slow measurements
- Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors
- Machine learning method for state preparation and gate synthesis on photonic quantum computers
- Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
- Tailoring surface codes for highly biased noise
- Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
- Analog quantum error correction with encoding a qubit into an oscillator
- Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis
- Coping with qubit leakage in topological codes
- Programmable interference between two microwave quantum memories
- Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator
- Encoding qubits into oscillators with atomic ensembles and squeezed light
- Engineering bilinear mode coupling in circuit QED: Theory and experiment
- Constructing finite dimensional codes with optical continuous variables
- Preparing encoded states in an oscillator
- Fault-tolerant preparation of approximate GKP states
- Sequential modular position and momentum measurements of a trapped ion mechanical oscillator
- Modular Bosonic Subsystem Codes
- Equivalence of approximate Gottesman-Kitaev-Preskill codes
- Fault-Tolerant Quantum Computing in the Pauli or Clifford Frame with Slow Error Diagnostics
- Generating continuous variable quantum codewords in the near-field atomic lithography
- Handling Leakage with Subsystem Codes
- Realizing modular quadrature measurements via a tunable photon-pressure coupling in circuit-QED
- Tracking Quantum Error Correction
- Quantum Error Correction with the GKP Code and Concatenation with Stabilizer Codes
Cited by in corpus (122)
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum repeaters: From quantum networks to the quantum internet
- Real-time quantum error correction beyond break-even
- Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
- Bosonic quantum error correction codes in superconducting quantum circuits
- Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes
- Qiskit Pulse: Programming Quantum Computers Through the Cloud with Pulses
- Quantum information processing with bosonic qubits in circuit QED
- Towards Scalable Bosonic Quantum Error Correction
- Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
- Entanglement-Assisted Quantum Networks: Mechanics, Enabling Technologies, Challenges, and Research Directions
- Quantum control of bosonic modes with superconducting circuits
- Fabrication of low-loss quasi-single-mode PPLN waveguide and its application to a modularized broadband high-level squeezer
- A fault-tolerant continuous-variable measurement-based quantum computation architecture
- Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
- Encoding an oscillator into many oscillators
- Low overhead fault-tolerant quantum error correction with the surface-GKP code
- Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits
- Entangled sensor-networks for dark-matter searches
- Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes
- Fault-Tolerant Operation of a Quantum Error-Correction Code
- Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
- Equivalence of approximate Gottesman-Kitaev-Preskill codes
- Quantum-Computing Architecture based on Large-Scale Multi-Dimensional Continuous-Variable Cluster States in a Scalable Photonic Platform
- Building a large-scale quantum computer with continuous-variable optical technologies
- Repetitive quantum non-demolition measurement and soft decoding of a silicon spin qubit
- Measurement-free preparation of grid states
- Cost-Reduced All-Gaussian Universality with the Gottesman-Kitaev-Preskill Code: Resource-Theoretic Approach to Cost Analysis
- Enhanced noise resilience of the surface-GKP code via designed bias
- 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
- Fast simulation of bosonic qubits via Gaussian functions in phase space
- Resource-Efficient Quantum Computing by Breaking Abstractions
- Architecture and noise analysis of continuous-variable quantum gates using two-dimensional cluster states
- Quantum capacity and codes for the bosonic loss-dephasing channel
- Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
- Temporal-mode continuous-variable 3-dimensional cluster state for topologically-protected measurement-based quantum computation
- Introduction to Quantum Error Correction and Fault Tolerance
- Two-photon driven Kerr quantum oscillator with multiple spectral degeneracies
- Efficient backcasting search for optical quantum state synthesis
- Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
- Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
- Cubic phase gates are not suitable for non-Clifford operations on GKP states
- All-optical quantum computing using cubic phase gates
- LDPC-cat codes for low-overhead quantum computing in 2D
- Achieving fault tolerance against amplitude-damping noise
- 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
- All-photonic GKP-qubit repeater using analog-information-assisted multiplexed entanglement ranking
- 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
- Depth analysis of variational quantum algorithms for heat equation
- Subsystem analysis of continuous-variable resource states
- Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons
- Streamlined quantum computing with macronode cluster states
- Quantum spherical codes
- Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits
- Generation of large-scale continuous-variable cluster states multiplexed both in time and frequency domains
- Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
- 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
- Universal quantum computation with optical four-component cat qubits
- Teleportation with a cubic phase gate
- Biased Gottesman-Kitaev-Preskill repetition code
- Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes
- Quantum communication on the bosonic loss-dephasing channel
- Qubit-oscillator concatenated codes: decoding formalism & code comparison
- Teleportation protocols with non-Gaussian operations: conditional photon subtraction versus cubic phase gate
- Characterizing the performance of continuous-variable Gaussian quantum gates
- Memory-assisted decoder for approximate Gottesman-Kitaev-Preskill codes
- Generalized figure of merit for qubit readout
- Hidden qubit cluster states
- Spin squeezed GKP codes for quantum error correction in atomic ensembles
- Improved readout of qubit-coupled Gottesman-Kitaev-Preskill states
- Gaussian conversion protocol for heralded generation of qunaught states
- Analog information decoding of bosonic quantum LDPC codes
- Two-qubit operations for finite-energy Gottesman-Kitaev-Preskill encodings
- Ancilla-free continuous-variable SWAP test
- Improved quantum error correction using soft information
- Dissipative protection of a GKP qubit in a high-impedance superconducting circuit driven by a microwave frequency comb
- Analysis of loss correction with the Gottesman-Kitaev-Preskill code
- Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction
- Weight Reduced Stabilizer Codes with Lower Overhead
- Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
- Optimal encoding of oscillators into more oscillators
- Machine-learning-inspired quantum optimal control of nonadiabatic geometric quantum computation via reverse engineering
- Error of an arbitrary single-mode Gaussian transformation on a weighted cluster state using a cubic phase gate
- Quantum Volume for Photonic Quantum Processors
- Stabilizer codes for Open Quantum Systems
- On noise in swap ASAP repeater chains: exact analytics, distributions and tight approximations
- Bosonic quantum error correction using squeezed Fock states
- Deterministic multi-mode gates on a scalable photonic quantum computing platform
- A complete continuous-variable quantum computation architecture based on the 2D spatiotemporal cluster state
- The resource cost of large scale quantum computing
- Generating Gottesman-Kitaev-Preskill qubit using a cross-Kerr interaction between a squeezed light and Fock states in optics
- End-to-end switchless architecture for fault-tolerant photonic quantum computing
- Cross-resonance control of an oscillator with an auxiliary fluxonium qubit
- Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes
- Practical quantum error correction with the XZZX code and Kerr-cat qubits
- Robust projective measurements through measuring code-inspired observables
- Logical channels in approximate Gottesman-Kitaev-Preskill error correction
- QECV: Quantum Error Correction Verification
- Quantum Computation and Communication in Bosonic Systems
- Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing
- Universal quantum computation and quantum error correction with ultracold atomic mixtures
- Tessellation codes: encoded quantum gates by geometric rotation
- The complexity of Gottesman-Kitaev-Preskill states
- Achievable rates for concatenated square Gottesman-Kitaev-Preskill codes
- Arbitrary high-fidelity binomial codes from multiphoton spin-boson interactions
- Gottesman-Kitaev-Preskill codes: A lattice perspective
- Optical Quantum Computing
- Linear-optical protocols for mitigating and suppressing noise in bosonic systems
- Pinching operators for approximating multiphoton entangled states
- Multimode rotationally symmetric bosonic codes from group-theoretic construction
- Quantum Error Correction with Superpositions of Squeezed Fock States
- Extensible universal photonic quantum computing with nonlinearity
- Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding
- Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding
- Dynamical complexity of non-Gaussian many-body systems with dissipation
- Environment-Assisted Generation of Non-Gaussian Wavepacket Quantum States