Clifford-deformed Surface Codes

Abstract

Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by applying single-qubit Clifford operators. We first analyze CDSCs on the $3\times 3$ square lattice and find that, depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the effective distance $d^{\prime }$, which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSC families with $50\%$ threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations outperform the thresholds and subthreshold logical error rates, at finite bias, of the best-known translationally invariant codes. We demonstrate the practical relevance of these random CDSC families by constructing a translation-invariant CDSC belonging to a high-performance random CDSC family. We also show that our translation-invariant CDSC outperforms well-known translation-invariant CDSCs such as the XZZX and XY codes.

6+10 pages, 14 figures, v2 changes: added a section on a translation-invariant code belonging to a high-performance random CDSC family to demonstrate the practical relevance of the random CDSCs. The code used for the simulations in the paper is available at https://github.com/dua-arpit/qecsim. See also https://errorcorrectionzoo.org/c/clifford-deformed_surface, v3 changes: PRX Quantum version

References in corpus (11)

• Experimental Quantum Computations on a Topologically Encoded Qubit
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• The XZZX Surface Code
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Fault-tolerant quantum computation against biased noise
• Dynamically Generated Logical Qubits
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Fault-Tolerant Computing With Biased-Noise Superconducting Qubits
• Quantum coding with low-depth random circuits
• Locations of multicritical points for spin glasses on regular lattices
• Multicritical points for the spin glass models on hierarchical lattices

Cited by in corpus (25)

• High-rate quantum LDPC codes for long-range-connected neutral atom registers
• Tensor networks for quantum computing
• Data-driven decoding of quantum error correcting codes using graph neural networks
• Optimizing quantum error correction protocols with erasure qubits
• Fault-tolerant quantum architectures based on erasure qubits
• Designing fault-tolerant circuits using detector error models
• Fault-tolerant hyperbolic Floquet quantum error correcting codes
• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Surface Code Design for Asymmetric Error Channels
• Discovery of Optimal Quantum Error Correcting Codes via Reinforcement Learning
• Surface Code with Imperfect Erasure Checks
• Protecting information via probabilistic cellular automata
• Clifford operations and homological codes for rotors and oscillators
• Snakes and Ladders: Adapting the surface code to defects
• Exact results on finite size corrections for surface codes tailored to biased noise
• The domain wall color code
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code
• Quantum low-density parity-check codes for erasure-biased atomic quantum processors
• Preservation of entanglement in local noisy channels
• Mitigating Temporal Fragility in the XY Surface Code
• Targeted Clifford logical gates for hypergraph product codes
• Error detection without post-selection in adaptive quantum circuits
• Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes
• Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding
• Decoder Dependence in Surface-Code Threshold Estimation under Digitized Hybrid Continuous-Variable and Discrete Noise