Randomized benchmarking for non-Markovian noise

Abstract

Estimating the features of noise is the first step in a chain of protocols that will someday lead to fault tolerant quantum computers. The randomized benchmarking (RB) protocol is designed with this exact mindset, estimating the average strength of noise in a quantum processor with relative ease in practice. However, RB, along with most other benchmarking and characterization methods, is limited in scope because it assumes that the noise is temporally uncorrelated (Markovian), which is increasingly evident not to be the case. Here, we combine the RB protocol with a recent framework describing non-Markovian quantum phenomena to derive a general analytical expression of the average sequence fidelity (ASF) for non-Markovian RB with the Clifford group. We show that one can identify non-Markovian features of the noise directly from the ASF through its deviations from the Markovian case, proposing a set of methods to collectively estimate these deviations, non-Markovian memory time-scales, and diagnose (in)coherence of non-Markovian noise in an RB experiment. Finally, we demonstrate the efficacy of our proposal by means of several proof-of-principle examples. Our methods are directly implementable and pave the pathway to better understanding correlated noise in quantum processors.

arXiv commentPublished version, results unchanged. 11 + 16 pages, 14 figures

References in corpus (57)

• Improved Simulation of Stabilizer Circuits
• Quantum state tomography via compressed sensing
• Randomized Benchmarking of Quantum Gates
• Prescription for experimental determination of the dynamics of a quantum black box
• Robust randomized benchmarking of quantum processes
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Theoretical framework for quantum networks
• Scalable Noise Estimation with Random Unitary Operators
• Direct Fidelity Estimation from Few Pauli Measurements
• Characterizing Quantum Gates via Randomized Benchmarking
• Quantum Process Tomography: Resource Analysis of Different Strategies
• Efficient measurement of quantum gate error by interleaved randomized benchmarking
• Quantum Circuits Architecture
• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Practical characterization of quantum devices without tomography
• Characterization of addressability by simultaneous randomized benchmarking
• Operational Markov condition for quantum processes
• Quantum causal modelling
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Estimating the Coherence of Noise
• Quantum stochastic processes and quantum non-Markovian phenomena
• Randomized Benchmarking with Confidence
• Investigating the limits of randomized benchmarking protocols
• Completely Positive Divisibility Does Not Mean Markovianity
• What randomized benchmarking actually measures
• Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing
• Characterizing Universal Gate Sets via Dihedral Benchmarking
• Operational approach to open dynamics and quantifying initial correlations
• Randomized benchmarking with gate-dependent noise
• Simulation complexity of open quantum dynamics: Connection with tensor networks
• The effect of noise correlations on randomized benchmarking
• An introduction to operational quantum dynamics
• Characterizing quantum dynamics with initial system-environment correlations
• Non-exponential Fidelity Decay in Randomized Benchmarking with Low-Frequency Noise
• Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories
• Quantum Markov Order
• The Structure of Quantum Stochastic Processes with Finite Markov Order
• Efficient error characterization in Quantum Information Processing
• Probing context-dependent errors in quantum processors
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
• Recovering quantum gates from few average gate fidelities
• Experimental quantum verification in the presence of temporally correlated noise
• Distinguishing decoherence from alternative quantum theories by dynamical decoupling
• Practical experimental certification of computational quantum gates via twirling
• Real Randomized Benchmarking
• Witnessing quantum memory in non-Markovian processes
• Almost Markovian processes from closed dynamics
• Leakage mitigation for quantum error correction using a mixed qubit scheme
• Genuine Multipartite Entanglement in Time
• Dynamical Decoupling of Unbounded Hamiltonians
• Markovianization with approximate unitary designs
• Efficient Unitarity Randomized Benchmarking of Few-qubit Clifford Gates
• Randomized benchmarking of quantum gates implemented by electron spin resonance
• Memory Effects in Quantum Processes
• Randomized benchmarking in the presence of time-correlated dephasing noise

Cited by in corpus (26)

• Benchmarking and fidelity response theory of high-fidelity Rydberg entangling gates
• Benchmarking quantum computers
• Single-qubit gates with errors at the $10^{-7}$ level
• Non-Markovian Memory Strength Bounds Quantum Process Recoverability
• Filtering crosstalk from bath non-Markovianity via spacetime classical shadows
• Controlling NMR spin systems for quantum computation
• Quantifying Non-Markovianity in Open Quantum Dynamics
• Machine learning classification of non-Markovian noise disturbing quantum dynamics
• SPAM-Robust Multi-axis Quantum Noise Spectroscopy in Temporally Correlated Environments
• Maxwell's two-demon engine under pure dephasing noise
• Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise
• Operational Markovianization in Randomized Benchmarking
• Quantum processes as thermodynamic resources: the role of non-Markovianity
• Benchmarking bosonic modes for quantum information with randomized displacements
• Randomised benchmarking for characterizing and forecasting correlated processes
• Noise-Agnostic Quantum Error Mitigation with Data Augmented Neural Models
• Hidden Quantum Memory: Is Memory There When Somebody Looks?
• Limitations to Dynamical Error Suppression and Gate-Error Virtualization from Temporally Correlated Nonclassical Noise
• Relations between Markovian and non-Markovian correlations in multitime quantum processes
• Emergent non-Markovianity and dynamical quantification of the quantum switch
• Process tensor distinguishability measures
• Multi-time quantum process tomography on a superconducting qubit
• Dual Map Framework for Noise Characterization of Quantum Computers
• Robust Error Accumulation Suppression for Quantum Circuits
• Blind-spots of Randomized Benchmarking Under Temporal Correlations
• Efficient learning and optimizing non-Gaussian correlated noise in digitally controlled qubit systems