Analytic asymptotic performance of topological codes

Abstract

Topological quantum error correction codes are extremely practical, typically requiring only a 2-D lattice of qubits with tunable nearest neighbor interactions yet tolerating high physical error rates p. It is computationally expensive to simulate the performance of such codes at low p, yet this is a regime we wish to study as low physical error rates lead to low qubit overhead. We present a very general method of analytically estimating the low p performance of the most promising class of topological codes. Our method can handle arbitrary periodic quantum circuits implementing the error detection associated with this class of codes, and arbitrary Pauli error models for each type of quantum gate. Our analytic expressions take only seconds to obtain, versus hundreds of hours to perform equivalent low p simulations.

4 pages, 2 figures

References in corpus (10)

• Surface codes: Towards practical large-scale quantum computation
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Towards fault-tolerant quantum computing with trapped ions
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Randomized Benchmarking of Multi-Qubit Gates
• Two-Dimensional Arrays of RF Ion Traps with Addressable Interactions
• Proof of finite surface code threshold for matching
• Quantum Circuits for Measuring Levin-Wen Operators

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• Convolutional neural network based decoders for surface codes
• Color code decoder with improved scaling for correcting circuit-level noise
• Noise threshold and resource cost of fault-tolerant quantum computing with Majorana fermions in hybrid systems
• Accurate simulations of planar topological codes cannot use cyclic boundaries
• Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancilla-register interaction
• Dynamical subset sampling of quantum error correcting protocols
• Segmented Composite Design of Robust Single-Qubit Quantum Gates
• Magic State Injection with Erasure Qubits
• Constructions of Pure Asymmetric Quantum Alternant Codes Based on Subclasses of Alternant Codes
• Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds
• Quantum stabilizer codes from Abelian and non-Abelian groups association schemes