Correcting coherent errors with surface codes

Abstract

We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on the 2D surface code in the presence of coherent errors. The algorithm has runtime $O(n^2)$, where $n$ is the number of physical qubits. It allows us to simulate systems with more than one thousand qubits and obtain the first error threshold estimates for several toy models of coherent noise. Numerical results are reported for storage of logical states subject to $Z$-rotation errors and for logical state preparation with general $SU(2)$ errors. We observe that for large code distances the effective logical-level noise is well-approximated by random Pauli errors even though the physical-level noise is coherent. Our algorithm works by mapping the surface code to a system of Majorana fermions.

arXiv comment18 pages, 14 figures

References in corpus (39)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Topological quantum memory
• State preservation by repetitive error detection in a superconducting quantum circuit
• Fault-tolerant quantum computation with high threshold in two dimensions
• Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• High threshold universal quantum computation on the surface code
• Quantum orders in an exact soluble model
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Classical simulation of noninteracting-fermion quantum circuits
• Low-distance Surface Codes under Realistic Quantum Noise
• Symmetrised Characterisation of Noisy Quantum Processes
• Towards practical classical processing for the surface code
• Demonstration of weight-four parity measurements in the surface code architecture
• Estimating the Coherence of Noise
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Comparing Experiments to the Fault-Tolerance Threshold
• Bounding quantum gate error rate based on reported average fidelity
• Tensor-Network Simulations of the Surface Code under Realistic Noise
• From Majorana Fermions to Topological Order
• Bringing order through disorder: Localization of errors in topological quantum memories
• Modeling coherent errors in quantum error correction
• Experimentally scalable protocol for identification of correctable codes
• Exact Performance of Concatenated Quantum Codes
• Modeling quantum noise for efficient testing of fault-tolerant circuits
• Proof of finite surface code threshold for matching
• Approximation of real error channels by Clifford channels and Pauli measurements
• Localization of Toric Code Defects
• Disorder-assisted error correction in Majorana chains
• Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models
• Fault Tolerance with Bare Ancillae for a [[7,1,3]] Code
• Linear-time general decoding algorithm for the surface code
• Hard decoding algorithm for optimizing thresholds under general Markovian noise
• Quantum error correction failure distributions: comparison of coherent and stochastic error models
• Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
• Efficient simulation of quantum error correction under coherent error based on non-unitary free-fermionic formalism
• Generalized Performance of Concatenated Quantum Codes -- A Dynamical Systems Approach

Cited by in corpus (84)

• Logical quantum processor based on reconfigurable atom arrays
• Simulating quantum many-body dynamics on a current digital quantum computer
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Performance of quantum error correction with coherent errors
• Benchmarking Coherent Errors in Controlled-Phase Gates due to Spectator Qubits
• Phase transition in magic with random quantum circuits
• Dynamical Magic Transitions in Monitored Clifford+T Circuits
• Mitigating Coherent Noise Using Pauli Conjugation
• Analysing correlated noise on the surface code using adaptive decoding algorithms
• Decoding algorithms for surface codes
• Boundaries of quantum supremacy via random circuit sampling
• Training Saturation in Layerwise Quantum Approximate Optimisation
• Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking
• Coherent error threshold for surface codes from Majorana delocalization
• Error statistics and scalability of quantum error mitigation formulas
• Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits
• Stabilizer Slicing: Coherent Error Cancellations in LDPC Codes
• Dynamically corrected gates suppress spatio-temporal error correlations as measured by randomized benchmarking
• How to simulate quantum measurement without computing marginals
• Surface codes, quantum circuits, and entanglement phases
• Tailoring quantum error correction to spin qubits
• Coherent errors and readout errors in the surface code
• Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
• Conservation laws and quantum error correction: towards a generalised matching decoder
• Suppressing Coherent Two-Qubit Errors via Dynamical Decoupling
• Robust teleportation of a surface code and cascade of topological quantum phase transitions
• Classical simulation of non-Gaussian fermionic circuits
• Tailoring three-dimensional topological codes for biased noise
• Towards early fault tolerance on a 2$\times$N array of qubits equipped with shuttling
• Robustness of quantum algorithms against coherent control errors
• Efficient Quantum Simulation of Open Quantum System Dynamics on Noisy Quantum Computers
• Improved quantum error correction with randomized compiling
• Accurate optimal quantum error correction thresholds from coherent information
• Optimizing Stabilizer Parities for Improved Logical Qubit Memories
• Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code
• Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes
• Designing the Quantum Channels Induced by Diagonal Gates
• Benchmarking quantum logic operations relative to thresholds for fault tolerance
• Benchmarking universal quantum gates via channel spectrum
• Benchmarking quantum gates and circuits
• Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory
• Non-Pauli errors can be efficiently sampled in qudit surface codes
• Coherent information as a mixed-state topological order parameter of fermions
• Efficient diagnostics for quantum error correction
• Modeling error correction with Lindblad dynamics and approximate channels
• Simulation of the five-qubit quantum error correction code on superconducting qubits
• Quantum computer error structure probed by quantum error correction syndrome measurements
• Quantum codes do not fix isotropic errors
• Coherent errors in stabilizer codes caused by quasistatic phase damping
• Segmented Composite Design of Robust Single-Qubit Quantum Gates
• Shor-Laflamme distributions of graph states and noise robustness of entanglement
• A rapidly mixing Markov chain from any gapped quantum many-body system
• Low-overhead quantum error correction codes with a cyclic topology
• Effect of quantum error correction on detection-induced coherent errors
• Non-Pauli Errors in the Three-Dimensional Surface Code
• A graph-based formalism for surface codes and twists
• Error mitigation and circuit division for early fault-tolerant quantum phase estimation
• Estimating the bias of CX gates via character randomized benchmarking
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Characterization of coherent errors in gate layers with robustness to Pauli noise
• Compiling the surface code to crossbar spin qubit architectures
• Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
• Vulnerability of fault-tolerant topological quantum error correction to quantum deviations in code space
• High-Rate Amplitude-Damping Shor Codes with Immunity to Collective Coherent Errors
• Enhancing Quantum Memory Lifetime with Measurement-Free Local Error Correction and Reinforcement Learning
• Quantum noise modeling through Reinforcement Learning
• Logical Error Rates for the Surface Code Under a Mixed Coherent and Stochastic Circuit-Level Noise Model Inspired by Trapped Ions
• Mixed-State Topological Order under Coherent Noise
• Generalizing the matching decoder for the Chamon code
• Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat
• The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
• Noise resilience in adaptive and symmetric monitored quantum circuits
• Optimal number of stabilizer measurement rounds in an idling surface code patch
• Sampling-based quasiprobability simulation for fault-tolerant quantum error correction on the surface codes under coherent noise
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Taming Rydberg Decay with Measurement-based Quantum Computation
• Overhead in Quantum Circuits with Time-Multiplexed Qubit Control
• Leakage Mobility in Superconducting Qubits as a Leakage Reduction Unit
• Resilience-Runtime Tradeoff Relations for Quantum Algorithms
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Quantum dual extended Hamming code immune to collective coherent errors
• Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction
• Unbiased observable estimation with approximate channels in fault-tolerant quantum computation