Strong Resilience of Topological Codes to Depolarization

Abstract

The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by mapping the quantum problem onto a classical disordered eight-vertex Ising model. By studying the stability of the related ferromagnetic phase both via large-scale Monte Carlo simulations and via the duality method, we are able to demonstrate an increased error threshold of 18.9(3)% when noise correlations are taken into account. Remarkably, this agrees within error bars with the result for a different class of codes-topological color codes-where the mapping yields interesting new types of interacting eight-vertex models.

10 pages, 6 figures, 1 table - see Physics Viewpoint by D. Gottesman [http://physics.aps.org/articles/v5/50]

References in corpus (8)

• Local stabilizer codes in three dimensions without string logical operators
• Topological Quantum Distillation
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Locations of multicritical points for spin glasses on regular lattices
• Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes
• Incoherent dynamics in the toric code subject to disorder

Cited by in corpus (120)

• Surface codes: Towards practical large-scale quantum computation
• Quantum Error Correction for Quantum Memories
• A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits
• Noise tailoring for scalable quantum computation via randomized compiling
• Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
• Quantum memories at finite temperature
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Single-shot fault-tolerant quantum error correction
• Tailoring surface codes for highly biased noise
• Efficient estimation of Pauli channels
• Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
• High threshold error correction for the surface code
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Decoding color codes by projection onto surface codes
• Triangular color codes on trivalent graphs with flag qubits
• Tensor-Network Simulations of the Surface Code under Realistic Noise
• Efficient Decoders for Qudit Topological Codes
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes
• An efficient Markov chain Monte Carlo algorithm for the surface code
• Advantages of versatile neural-network decoding for topological codes
• Comparing neural network based decoders for the surface code
• Erasure qubits: Overcoming the $T_1$ limit in superconducting circuits
• Intrinsic Mixed-state Topological Order
• Quantum Error Correction with the Semion Code
• Logical blocks for fault-tolerant topological quantum computation
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Errors and pseudo-thresholds for incoherent and coherent noise
• Three-dimensional color code thresholds via statistical-mechanical mapping
• Proof of finite surface code threshold for matching
• Scalable Neural Decoder for Topological Surface Codes
• Kitaev's Z_d-Codes Threshold Estimates
• Combining hard and soft decoders for hypergraph product codes
• Approximate quantum error correction for generalized amplitude damping errors
• 2-D Compass Codes
• Topological code Autotune
• Surface Code Threshold in the Presence of Correlated Errors
• Error Thresholds for Abelian Quantum Double Models: Increasing the bit-flip Stability of Topological Quantum Memory
• A scalable and fast artificial neural network syndrome decoder for surface codes
• Bias-tailored quantum LDPC codes
• Coherent error threshold for surface codes from Majorana delocalization
• Quantum memories and error correction
• Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions
• Deep Q-learning decoder for depolarizing noise on the toric code
• Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits
• Lattice Surgery Translation for Quantum Computation
• Clifford-deformed Surface Codes
• Practical Topological Cluster State Quantum Computing Requires Loss Below 1%
• A polynomial time and space heuristic algorithm for T-count
• Tensor-network codes
• Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
• Logical Error Rate Scaling of the Toric Code
• Numerical and analytical bounds on threshold error rates for hypergraph-product codes
• Coherent errors and readout errors in the surface code
• Breakdown of Surface Code Error Correction Due to Coupling to a Bosonic Bath
• Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
• Tapestry of dualities in decohered quantum error correction codes
• Generating Fault-Tolerant Cluster States from Crystal Structures
• A four-dimensional toric code with non-Clifford transversal gates
• Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code
• A decoding algorithm for CSS codes using the X/Z correlations
• Error threshold estimates for surface code with loss of qubits
• The role of entropy in topological quantum error correction
• Generalized Belief Propagation Algorithms for Decoding of Surface Codes
• On the robustness of topological quantum codes: Ising perturbation
• The Kitaev-Ising model, Transition between topological and ferromagnetic order
• Determination of the Semion Code Threshold using Neural Decoders
• Hierarchical Qubit Maps and Hierarchical Quantum Error Correction
• Duality analysis on random planar lattice
• Dual correspondence between classical spin models and quantum CSS states
• Accurate optimal quantum error correction thresholds from coherent information
• Dependence of a quantum mechanical system on its own initial state and the initial state of the environment it interacts with
• Pseudorandom density matrices
• Fundamental thresholds of realistic quantum error correction circuits from classical spin models
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Fidelity of the surface code in the presence of a bosonic bath
• Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold
• Correcting spanning errors with a fractal code
• Decoding quantum color codes with MaxSAT
• Continuous error correction for Ising anyons
• Ising model formulation for highly accurate topological color codes decoding
• Fault-tolerant logical measurements via homological measurement
• Error-rate-agnostic decoding of topological stabilizer codes
• Comparison of 2D topological codes and their decoding performances
• Coherent information as a mixed-state topological order parameter of fermions
• Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models
• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Stability of topologically-protected quantum computing proposals as seen through spin glasses
• Learning to find order in disorder
• Mixed-state phase transitions in spin-Holstein models
• Decoherence through Ancilla Anyon Reservoirs
• Purification-based metric to measure the distance between quantum states and processes
• Coherent errors in stabilizer codes caused by quasistatic phase damping
• Entanglement Generation by Communication using Phase-Squeezed Light with Photon Loss
• Quantum Codes from Toric Surfaces
• Effect of quantum error correction on detection-induced coherent errors
• Analyticity of the energy in an Ising spin glass with correlated disorder
• The Implications of Ignorance for Quantum Error Correction Thresholds
• Noisy Toric code and random bond Ising model: The error threshold in a dual picture
• Exact results on finite size corrections for surface codes tailored to biased noise
• Optimal correction of independent and correlated errors
• Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
• Fundamental thresholds for computational and erasure errors via the coherent information
• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes
• Numerical evaluation of the fidelity error threshold for the surface code
• Thresholds for post-selected quantum error correction from statistical mechanics
• Lattice surgery-based logical state teleportation via noisy links
• Revisiting Nishimori multicriticality through the lens of information measures
• Memory-corrected quantum repeaters with adaptive syndrome identification
• An extension of estimation of critical points in ground state for random spin systems
• The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
• Thermal stability of two-dimensional Topological Color Code
• Stable quantum memories with limited measurement
• Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds
• Phases of Floquet code under local decoherence
• Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding
• Spectral properties and coding transitions of Haar-random quantum codes
• Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions
• Decoding Quantum Error Correction Codes with Local Variation
• Hardness results for decoding the surface code with Pauli noise