Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits

2024-12-25

AI Summary

Efficiently measuring multiple non-commuting Pauli observables arises critically in quantum chemistry energy estimation and many-body system verification, where conventional shadow tomography suffers from statistical inefficiency and circuit-depth limitations. Method: We propose the Deterministic Shallow Shadow (DSS) algorithm, the first to integrate tensor network optimization into measurement basis design—combining shallow parameterized Pauli rotation circuits with deterministic, tensor-network-driven basis optimization. This yields controllable circuit depth and near-optimal sample complexity. Results: On benchmark quantum chemical systems and many-body models, DSS significantly improves sample efficiency over state-of-the-art shadow tomography methods, with monotonic performance gains as circuit depth increases. Classical preprocessing requires only polynomial time. The core contribution is a tensor-network-based deterministic measurement basis construction, overcoming fundamental statistical and depth bottlenecks inherent in randomized measurement schemes.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting observables, using shallow circuits to rotate into measurement bases. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, our algorithm outputs a set of shallow measurement circuits that approximately minimizes the sample complexity of estimating a given set of Pauli strings. We numerically demonstrate systematic improvement, in comparison with state-of-the-art techniques, for energy estimation of quantum chemistry benchmarks and verification of quantum many-body systems, and we observe DSS's performance consistently improves as one allows deeper measurement circuits. These results indicate that in addition to being an efficient, low-depth, stand-alone algorithm, DSS can also benefit many larger quantum algorithms requiring estimation of multiple non-commuting observables.

Problem

• Quantum Estimation
• Non-interacting Measurements
• Complexity Reduction

Innovation

• DSS Method
• Pauli Operators Learning
• Efficient Quantum Measurements