Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm

Abstract

We introduce a correlated measurement noise model that can be efficiently described and characterized, and which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation can be performed up to some error for which we derive upper bounds. Characterization of the model is done efficiently using Diagonal Detector Overlapping Tomography -- a generalization of the recently introduced Quantum Overlapping Tomography to the problem of reconstruction of readout noise with restricted locality. The procedure allows to characterize $k$-local measurement cross-talk on $N$-qubit device using $O(k{2}^{k}log(N))$ circuits containing random combinations of X and identity gates. We perform experiments on 15 (23) qubits using IBM's (Rigetti's) devices to test both the noise model and the error-mitigation scheme, and obtain an average reduction of errors by a factor $>22$ ($>5.5$) compared to no mitigation. Interestingly, we find that correlations in the measurement noise do not correspond to the physical layout of the device. Furthermore, we study numerically the effects of readout noise on the performance of the Quantum Approximate Optimization Algorithm (QAOA). We observe in simulations that for numerous objective Hamiltonians, including random MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the noise-mitigation improves the quality of the optimization. Finally, we provide arguments why in the course of QAOA optimization the estimates of the local energy (or cost) terms often behave like uncorrelated variables, which greatly reduces sampling complexity of the energy estimation compared to the pessimistic error analysis. We also show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits.

27+25 pages, 6+2 figures, 0+3 table, 0+3 algorithmic boxes; v2: fixed typos, added omitted references, expanded acknowledgments; v3: updated to version accepted in Quantum, improved main narration, fixed typos;comments and suggestions are welcome

References in corpus (23)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Charge insensitive qubit design derived from the Cooper pair box
• A Quantum Approximate Optimization Algorithm
• Integrated Photonic Quantum Technologies
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
• Measuring measurement
• Mitigating measurement errors in multi-qubit experiments
• Virtual Distillation for Quantum Error Mitigation
• Mitigating realistic noise in practical noisy intermediate-scale quantum devices
• The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: A Typical Case
• Measurement Error Mitigation in Quantum Computers Through Classical Bit-Flip Correction
• Efficient correction of multiqubit measurement errors
• Rigorous measurement error correction
• Next-Generation Topology of D-Wave Quantum Processors
• Characterizing local noise in QAOA circuits
• A hybrid quantum-classical approach to mitigating measurement errors
• Measurement Error Mitigation for Variational Quantum Algorithms
• Modeling Noisy Quantum Circuits Using Experimental Characterization
• Analysis of Quantum Approximate Optimization Algorithm under Realistic Noise in Superconducting Qubits
• Scalable Bayesian Hamiltonian learning
• Compressively certifying quantum measurements
• Compressed variational quantum eigensolver for the Fermi-Hubbard model

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• A Review on Quantum Approximate Optimization Algorithm and its Variants
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• Characterizing the Reproducibility of Noisy Quantum Circuits
• Estimating gate-set properties from random sequences
• Analyzing the impact of time-correlated noise on zero-noise extrapolation
• Efficiently improving the performance of noisy quantum computers
• Implementation of quantum measurements using classical resources and only a single ancillary qubit
• The Unified Effect of Data Encoding, Ansatz Expressibility and Entanglement on the Trainability of HQNNs
• Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables
• Self-consistent quantum measurement tomography based on semidefinite programming
• Operational Quantum Average-Case Distances
• Mitigating Quantum Errors via Truncated Neumann Series
• Exploring Quantum Average-Case Distances: proofs, properties, and examples
• Improving the Performance of Digitized Counterdiabatic Quantum Optimization via Algorithm-Oriented Qubit Mapping
• Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping
• Experimental demonstration of Quantum Overlapping Tomography
• Practical techniques for high-precision measurements on near-term quantum hardware and applications in molecular energy estimation
• Benchmarking the quality of multiplexed qubit readout beyond assignment fidelity
• Detecting and Eliminating Quantum Noise of Quantum Measurements
• Mitigation of correlated readout errors without randomized measurements
• Photonic variational quantum eigensolver for NISQ-compatible quantum technology
• Qubit Readout Error Mitigation with Bit-flip Averaging
• Circuit-Noise-Resilient Virtual Distillation
• Data-Efficient Quantum Noise Modeling via Machine Learning