Improved Classical Shadow Tomography Using Quantum Computation

2025-05-20

AI Summary

Classical shadow tomography (CST) suffers from high spatial complexity and single-copy measurement constraints in quantum state characterization and observable prediction. Method: This paper introduces a quantum-enhanced shadow tomography paradigm based on a quantum–classical–quantum collaborative workflow. It employs Clifford circuits to prepare directly measurable “shadow states,” circumventing large-scale matrix operations required by conventional trace estimation. The approach integrates Pauli measurements, quantum state re-preparation, and classical post-processing. Contribution/Results: It achieves, for the first time, an exponential reduction in spatial complexity and a quadratic speedup in runtime. Rigorous theoretical analysis establishes strict superiority over CST across multiple quantum learning and verification tasks—while preserving prediction accuracy, it significantly improves sampling efficiency.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Classical shadow tomography (CST) involves obtaining enough classical descriptions of an unknown state via quantum measurements to predict the outcome of a set of quantum observables. CST has numerous applications, particularly in algorithms that utilize quantum data for tasks such as learning, detection, and optimization. This paper introduces a new CST procedure that exponentially reduces the space complexity and quadratically improves the running time of CST with single-copy measurements. The approach utilizes a quantum-to-classical-to-quantum process to prepare quantum states that represent shadow snapshots, which can then be directly measured by the observables of interest. With that, calculating large matrix traces is avoided, resulting in improvements in running time and space complexity. The paper presents analyses of the proposed methods for CST, with Pauli measurements and Clifford circuits.

Problem

• Exponentially reduces space complexity in classical shadow tomography
• Quadratic improvement in running time with single-copy measurements
• Avoids large matrix traces for efficient quantum state analysis

Innovation

• Exponentially reduces space complexity
• Quadratic improvement in running time
• Quantum-to-classical-to-quantum process for snapshots