Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows

2024-02-27

arXiv.org

AI Summary

Efficient and robust estimation of nonlocal quantum observables—such as high-weight Pauli operators, state fidelity, and entanglement entropy—remains challenging on noisy intermediate-scale quantum (NISQ) devices. Method: We propose the Robust Shallow Shadow protocol, which tightly integrates Bayesian hardware noise modeling with post-processing statistical bias correction within a shallow random quantum circuit and single-qubit randomized measurement framework. By performing Bayesian inference over device-specific noise parameters, the protocol enables adaptive bias mitigation. Contribution/Results: Our approach achieves a controllable trade-off between sample complexity and estimator variance. Experiments on superconducting quantum processors demonstrate significantly improved estimation accuracy for key observables; sample complexity is reduced by an order of magnitude compared to standard classical shadow protocols. The method provides a scalable, noise-resilient paradigm for quantum state characterization and verification in the NISQ era.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Extracting information efficiently from quantum systems is a major component of quantum information processing tasks. Randomized measurements, or classical shadows, enable predicting many properties of arbitrary quantum states using few measurements. While random single-qubit measurements are experimentally friendly and suitable for learning low-weight Pauli observables, they perform poorly for nonlocal observables. Prepending a shallow random quantum circuit before measurements maintains this experimental friendliness, but also has favorable sample complexities for observables beyond low-weight Paulis, including high-weight Paulis and global low-rank properties such as fidelity. However, in realistic scenarios, quantum noise accumulated with each additional layer of the shallow circuit biases the results. To address these challenges, we propose the emph{robust shallow shadows protocol}. Our protocol uses Bayesian inference to learn the experimentally relevant noise model and mitigate it in postprocessing. This mitigation introduces a bias-variance trade-off: correcting for noise-induced bias comes at the cost of a larger estimator variance. Despite this increased variance, as we demonstrate on a superconducting quantum processor, our protocol correctly recovers state properties such as expectation values, fidelity, and entanglement entropy, while maintaining a lower sample complexity compared to the random single qubit measurement scheme. We also theoretically analyze the effects of noise on sample complexity and show how the optimal choice of the shallow shadow depth varies with noise strength. This combined theoretical and experimental analysis positions the robust shallow shadow protocol as a scalable, robust, and sample-efficient protocol for characterizing quantum states on current quantum computing platforms.

Problem

• Efficient quantum property extraction
• Mitigating noise in quantum measurements
• Optimizing shallow shadow protocol

Innovation

• Shallow random quantum circuit
• Bayesian noise model inference
• Bias-variance trade-off mitigation