Error- and Loss-Tolerances of Surface Codes with General Lattice Structures

Abstract

We propose a family of surface codes with general lattice structures, where the error-tolerances against bit and phase errors can be controlled asymmetrically by changing the underlying lattice geometries. The surface codes on various lattices are found to be efficient in the sense that their threshold values universally approach the quantum Gilbert-Varshamov bound. We find that the error-tolerance of surface codes depends on the connectivity of underlying lattices; the error chains on a lattice of lower connectivity are easier to correct. On the other hand, the loss-tolerance of surface codes exhibits an opposite behavior; the logical information on a lattice of higher connectivity has more robustness against qubit loss. As a result, we come upon a fundamental trade-off between error- and loss-tolerances in the family of the surface codes with different lattice geometries.

5pages, 3 figures

References in corpus (10)

• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Topological Computation without Braiding
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Fault-Tolerant Computing With Biased-Noise Superconducting Qubits
• Locations of multicritical points for spin glasses on regular lattices
• Incoherent dynamics in the toric code subject to disorder
• Error threshold estimates for surface code with loss of qubits
• Error tolerance and tradeoffs in loss- and failure-tolerant quantum computing schemes

Cited by in corpus (25)

• High-threshold fault-tolerant quantum computation with analog quantum error correction
• Optimizing Quantum Error Correction Codes with Reinforcement Learning
• Efficient Decoders for Qudit Topological Codes
• 2-D Compass Codes
• Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
• Fault-tolerance thresholds for the surface code with fabrication errors
• Fault-tolerant interface between quantum memories and quantum processors
• Leakage mitigation for quantum error correction using a mixed qubit scheme
• Handling Leakage with Subsystem Codes
• A decoder for the triangular color code by matching on a Möbius strip
• Error Thresholds for Arbitrary Pauli Noise
• General tensor network decoding of 2D Pauli codes
• Quantum Computation with Topological Codes: from qubit to topological fault-tolerance
• Optimal local unitary encoding circuits for the surface code
• Determination of the Semion Code Threshold using Neural Decoders
• A Scalable Decoder Micro-architecture for Fault-Tolerant Quantum Computing
• Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• The Implications of Ignorance for Quantum Error Correction Thresholds
• Frustration in vicinity of transition point of Ising spin glasses
• Fundamental thresholds for computational and erasure errors via the coherent information
• A simple relation between frustration and transition points in diluted spin glasses
• Homology-changing percolation transitions on finite graphs
• Quantum information and statistical mechanics: an introduction to frontier
• Decoding Quantum Error Correction Codes with Local Variation