Scalable bayesian shadow tomography for quantum property estimation with set transformers

2025-09-23

AI Summary

This work addresses the efficient estimation of scalar properties—such as fidelity and Rényi entropy—of unknown quantum states under few-shot (low-copy) conditions, bypassing full density matrix reconstruction. We propose a scalable Bayesian machine learning framework that integrates classical shadow protocols with permutation-invariant set transformers. Given random Pauli or Clifford measurement outcomes as input, the model learns residual corrections to baseline estimators, thereby approximating the Bayesian posterior mean. Input feature dimensionality remains fixed, while computational complexity scales polynomially in system size and number of measurements. In benchmark tasks—GHZ-state fidelity and second-order Rényi entropy estimation—our method achieves substantially lower mean-squared error than standard classical shadows; in the low-copy regime, error reduction exceeds 99%. To our knowledge, this is the first demonstration of bias-corrected Bayesian estimation enabling significant accuracy gains with limited data.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

A scalable Bayesian machine learning framework is introduced for estimating scalar properties of an unknown quantum state from measurement data, which bypasses full density matrix reconstruction. This work is the first to integrate the classical shadows protocol with a permutation-invariant set transformer architecture, enabling the approach to predict and correct bias in existing estimators to approximate the true Bayesian posterior mean. Measurement outcomes are encoded as fixed-dimensional feature vectors, and the network outputs a residual correction to a baseline estimator. Scalability to large quantum systems is ensured by the polynomial dependence of input size on system size and number of measurements. On Greenberger-Horne-Zeilinger state fidelity and second-order Rényi entropy estimation tasks -- using random Pauli and random Clifford measurements -- this Bayesian estimator always achieves lower mean squared error than classical shadows alone, with more than a 99% reduction in the few copy regime.

Problem

• Estimating quantum state properties without full reconstruction
• Correcting bias in existing quantum estimators using transformers
• Achieving scalable quantum property estimation with fewer measurements

Innovation

• Bayesian machine learning with set transformers
• Integration of classical shadows with permutation-invariant architecture
• Residual correction network for bias prediction