The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
arXiv:2412.21055 · doi:10.1103/psf5-b6j2
Abstract
We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely coherent information and quantum relative entropy. Using numerical simulations and developing a phenomenological field theory, focusing on the most general single-qubit X-error channel, we show that, for any nonzero incoherent noise component, the coherence of the logical noise is exponentially suppressed with the code distance. We also find that the information-theoretic measures require this suppression to detect optimal thresholds for Pauli recovery; for this they thus require increasingly large distances for increasing error coherence and ultimately break down for fully coherent errors. To obtain our results, we develop a statistical mechanics mapping and a corresponding matrix-product-state algorithm for approximate syndrome sampling. These methods enable the large scale simulation of these non-Pauli errors, including their maximum-likelihood thresholds, away from the limits captured by previous approaches.
17 pages, 6 figures; v2: new title and revised manuscript; v3: accepted manuscript
References in corpus (75)
- Quantum Computing in the NISQ era and beyond
- Non-Abelian Anyons and Topological Quantum Computation
- Entanglement Entropy and Quantum Field Theory
- Surface codes: Towards practical large-scale quantum computation
- Entanglement entropy and conformal field theory
- Suppressing quantum errors by scaling a surface code logical qubit
- Logical quantum processor based on reconfigurable atom arrays
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Quantum error correction below the surface code threshold
- Surface code quantum computing by lattice surgery
- Noise tailoring for scalable quantum computation via randomized compiling
- Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
- Dynamical purification phase transitions induced by quantum measurements
- Condensate induced transitions between topologically ordered phases
- Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
- Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
- Topological Defects on the Lattice I: The Ising model
- Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
- Heralded magnetism in non-Hermitian atomic systems
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Anyon condensation and its applications
- Exponential Decay of Correlations Implies Area Law
- Quantum criticality under decoherence or weak measurement
- Computational advantage of quantum random sampling
- Strong Resilience of Topological Codes to Depolarization
- An area law for entanglement from exponential decay of correlations
- Correcting coherent errors with surface codes
- Entanglement negativity and topological order
- Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition
- Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
- Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
- High threshold error correction for the surface code
- Diagnostics of mixed-state topological order and breakdown of quantum memory
- Statistical mechanical models for quantum codes with correlated noise
- Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
- Symmetry as a shadow of topological order and a derivation of topological holographic principle
- Performance of quantum error correction with coherent errors
- Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
- Dualities in one-dimensional quantum lattice models: topological sectors
- Modeling coherent errors in quantum error correction
- Bulk Anyons as Edge Symmetries: Boundary Phase Diagrams of Topologically Ordered States
- Cluster state as a non-invertible symmetry protected topological phase
- Anyon condensation and the color code
- Coherence in logical quantum channels
- A Noisy Approach to Intrinsically Mixed-State Topological Order
- Errors and pseudo-thresholds for incoherent and coherent noise
- Towards a classification of mixed-state topological orders in two dimensions
- Separability transitions in topological states induced by local decoherence
- Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
- Coherent error threshold for surface codes from Majorana delocalization
- Hidden Inverses: Coherent Error Cancellation at the Circuit Level
- Stability of mixed-state quantum phases via finite Markov length
- Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits
- Non-invertible symmetries act locally by quantum operations
- Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
- Surface codes, quantum circuits, and entanglement phases
- Non-invertible symmetry-protected topological order in a group-based cluster state
- Tapestry of dualities in decohered quantum error correction codes
- Robust teleportation of a surface code and cascade of topological quantum phase transitions
- Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations
- Accurate optimal quantum error correction thresholds from coherent information
- Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes
- Disentangling transitions in topological order induced by boundary decoherence
- Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
- Characterizing Coherent Errors using Matrix-Element Amplification
- Experimental Demonstration of Break-Even for the Compact Fermionic Encoding
- Coherent information as a mixed-state topological order parameter of fermions
- Non-Pauli errors can be efficiently sampled in qudit surface codes
- Global Symmetries, Code Ensembles, and Sums Over Geometries
- Decoherence through Ancilla Anyon Reservoirs
- Topology and Spectrum in Measurement-Induced Phase Transitions
- Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
- Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
- Mixed-State Topological Order under Coherent Noise
- Fundamental thresholds for computational and erasure errors via the coherent information