Limitations to Dynamical Error Suppression and Gate-Error Virtualization from Temporally Correlated Nonclassical Noise

Abstract

Realistic multi-qubit noise processes often result in error mechanisms that are not captured by the probabilistic, Markovian error models commonly employed in circuit-level analyses of quantum fault-tolerance. By working within an open-quantum system Hamiltonian formulation, we revisit the validity of the notion of a constant gate error in the presence of noise that is both temporally correlated and nonclassical, and whose impact is mitigated through perfect instantaneous dynamical decoupling subject to finite timing constraints. We study a minimal exactly solvable single-qubit model under Gaussian quantum dephasing noise, showing that the fidelity of a dynamically protected idling gate can depend strongly on its location in the circuit and the history of applied control, even when the system-side error propagation is fully removed through perfect reset operations. For digital periodic control, we prove that, under mild conditions on the low-frequency behavior of the nonclassical noise spectrum, the gate fidelity saturates at a value that is strictly smaller than the one attainable in the absence of control history; the presence of high-frequency noise peaks is also found as especially harmful, due to the possible onset of control-induced resonance effects. We explicitly relate these features to the evolution of the bath statistics during the computation, which has not been fully accounted for in existing treatments. We find that only if decoupling can keep the qubit highly pure over a timescale larger than the correlation time of the noise, the bath approximately converges to its original statistics and a stable-in-time control performance is recovered. Implications of this costly re-equilibration of the quantum bath statistics for layered quantum fault-tolerant architectures are discussed.

31 pages, 9 figures

References in corpus (37)

• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Fault-Tolerant Quantum Dynamical Decoupling
• How to Enhance Dephasing Time in Superconducting Qubits
• Decoherence-protected quantum gates for a hybrid solid-state spin register
• Exponential suppression of bit or phase flip errors with repetitive error correction
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Correlated Charge Noise and Relaxation Errors in Superconducting Qubits
• Demonstrating a Driven Reset Protocol of a Superconducting Qubit
• Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences
• Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
• High fidelity quantum gates via dynamical decoupling
• Experimental noise filtering by quantum control
• Observation of classical-quantum crossover of 1/f flux noise and its paramagnetic temperature dependence
• Multiqubit Spectroscopy of Gaussian Quantum Noise
• A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control
• Dynamical Quantum Error Correction of Unitary Operations with Bounded Controls
• Matching and maximum likelihood decoding of a multi-round subsystem quantum error correction experiment
• Fault-tolerant quantum computation versus Gaussian noise
• Noise-correlation spectrum for a pair of spin qubits in silicon
• Demonstration of algorithmic quantum speedup
• Optimizing quantum gates towards the scale of logical qubits
• Open systems with error bounds: spin boson model with spectral density variations
• Rigorous Bounds on the Performance of a Hybrid Dynamical Decoupling-Quantum Computing Scheme
• Limits on Preserving Quantum Coherence using Multi-Pulse Control
• Spatial noise correlations beyond nearest-neighbor in ${}^{28}$Si/SiGe spin qubits
• Surface Code Threshold in the Presence of Correlated Errors
• Decoherence by Correlated Noise and Quantum Error Correction
• Predicting non-Markovian superconducting qubit dynamics from tomographic reconstruction
• Randomized benchmarking for non-Markovian noise
• Resilient Quantum Computation in Correlated Environments: A Quantum Phase Transition Perspective
• Dynamically corrected gates suppress spatio-temporal error correlations as measured by randomized benchmarking
• Effective qubit dephasing induced by spectator-qubit relaxation
• Designing dynamically corrected gates robust to multiple noise sources using geometric space curves
• SPAM-Robust Multi-axis Quantum Noise Spectroscopy in Temporally Correlated Environments
• Frequency estimation under non-Markovian spatially correlated quantum noise: Restoring superclassical precision scaling
• Nonergodic measurements of qubit frequency noise
• How coherence measurements of a qubit steer its quantum environment

Cited by in corpus (2)

• Temporally correlated quantum noise in driven quantum systems
• Efficient learning and optimizing non-Gaussian correlated noise in digitally controlled qubit systems