Comparison of a quantum error correction threshold for exact and approximate errors

Abstract

Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit, more accurate approximations that still allow for efficient simulation can be obtained by including Clifford operators and Pauli operators conditional on measurement in the noise model. We examine the feasibility of employing these expanded error approximations to obtain better threshold estimates. We calculate the level-1 pseudothreshold for the Steane [[7,1,3]] code for amplitude damping and dephasing along a non-Clifford axis. The expanded channels estimate the actual channel action more accurately than the Pauli channels before error correction. However, after error correction, the Pauli twirling approximation yields very accurate estimates of the performance of quantum error-correcting protocols in the presence of the actual noise channel.

10 pages, 4 figures, 7 tables (v2. fixes typos in references)

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• Coherence in quantum error-correcting codes
• Modeling coherent errors in quantum error correction
• Constructing Smaller Pauli Twirling Sets for Arbitrary Error Channels
• Mitigating Coherent Noise Using Pauli Conjugation
• Errors and pseudo-thresholds for incoherent and coherent noise
• Optimizing resource efficiencies for scalable full-stack quantum computers
• Unbiased Simulation of Near-Clifford Quantum Circuits
• Transversality and lattice surgery: exploring realistic routes towards coupled logical qubits with trapped-ion quantum processors
• Quantum Computing: An Overview Across the System Stack
• A taxonomy of small Markovian errors
• Network architecture for a topological quantum computer in silicon
• Fault Tolerance with Bare Ancillae for a [[7,1,3]] Code
• Hard decoding algorithm for optimizing thresholds under general Markovian noise
• QVECTOR: an algorithm for device-tailored quantum error correction
• Tailored codes for small quantum memories
• Efficient simulation of quantum error correction under coherent error based on non-unitary free-fermionic formalism
• A Silicon Surface Code Architecture Resilient Against Leakage Errors
• Parallel quantum trajectories via forking for sampling without redundancy
• Benchmarking quantum logic operations relative to thresholds for fault tolerance
• Analytical Error Analysis of Clifford Gates by the Fault-Path Tracer Method
• Non-Pauli errors can be efficiently sampled in qudit surface codes
• Efficient diagnostics for quantum error correction
• Modeling error correction with Lindblad dynamics and approximate channels
• Methods for Classically Simulating Noisy Networked Quantum Architectures
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
• Accurate and Honest Approximation of Correlated Qubit Noise
• Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction
• Unbiased observable estimation with approximate channels in fault-tolerant quantum computation
• Comparison of spin-qubit architectures for quantum error-correcting codes