Coherence in quantum error-correcting codes

Abstract

Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively unknown. Here, we prove that encoding a system in a stabilizer code and measuring error syndromes decoheres errors, that is, causes coherent errors to converge toward probabilistic Pauli errors, even when no recovery operations are applied. Two practical consequences are that the error rate in a logical circuit is well quantified by the average gate fidelity at the logical level and that essentially optimal recovery operators can be determined by independently optimizing the logical fidelity of the effective noise per syndrome.

arXiv comment6 pages + references. See related work by Huang, Doherty, and Flammia

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Cited by in corpus (48)

• Fault-Tolerant Logical Gates in the IBM Quantum Experience
• Efficient estimation of Pauli channels
• Performance of quantum error correction with coherent errors
• Benchmarking Coherent Errors in Controlled-Phase Gates due to Spectator Qubits
• Coherence in logical quantum channels
• Mitigating Coherent Noise Using Pauli Conjugation
• A taxonomy of small Markovian errors
• Fast Estimation of Sparse Quantum Noise
• Coherent error threshold for surface codes from Majorana delocalization
• Hidden Inverses: Coherent Error Cancellation at the Circuit Level
• Stabilizer Slicing: Coherent Error Cancellations in LDPC Codes
• Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers
• Bell sampling from quantum circuits
• Pauli channels can be estimated from syndrome measurements in quantum error correction
• Coherent errors and readout errors in the surface code
• Tailoring three-dimensional topological codes for biased noise
• Improved quantum error correction with randomized compiling
• Statistically Characterising Robustness and Fidelity of Quantum Controls and Quantum Control Algorithms
• Optimizing Stabilizer Parities for Improved Logical Qubit Memories
• Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes
• Benchmarking universal quantum gates via channel spectrum
• Mitigating Coherent Noise by Balancing Weight-2 $Z$-Stabilizers
• Scalable noise characterization of syndrome-extraction circuits with averaged circuit eigenvalue sampling
• Testing a Quantum Error-Correcting Code on Various Platforms
• Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics
• Non-Pauli errors can be efficiently sampled in qudit surface codes
• Modeling error correction with Lindblad dynamics and approximate channels
• Spectator Errors in Tunable Coupling Architectures
• Strategies for single-shot discrimination of process matrices
• Coherent errors in stabilizer codes caused by quasistatic phase damping
• Effect of quantum error correction on detection-induced coherent errors
• Robustness of the concatenated quantum error-correction protocol against noise for channels affected by fluctuation
• Non-Pauli Errors in the Three-Dimensional Surface Code
• A new error-modeling of Hardy's paradox for superconducting qubits and its experimental verification
• Estimating the bias of CX gates via character randomized benchmarking
• Characterization of coherent errors in gate layers with robustness to Pauli noise
• Efficiently computing logical noise in quantum error correcting codes
• The resource cost of large scale quantum computing
• Vulnerability of fault-tolerant topological quantum error correction to quantum deviations in code space
• Logical Error Rates for the Surface Code Under a Mixed Coherent and Stochastic Circuit-Level Noise Model Inspired by Trapped Ions
• Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes
• From Magic State Distillation to Dynamical Systems
• Logical Noise Bias in Magic State Injection
• Robustly decorrelating errors with mixed quantum gates
• Optimal number of stabilizer measurement rounds in an idling surface code patch
• Symmetric channel verification for purifying noisy quantum channels
• Implementation of Finite state logic machines via the dynamics of atomic systems
• Unbiased observable estimation with approximate channels in fault-tolerant quantum computation