Scalable bayesian shadow tomography for quantum property estimation with set transformers
This work addresses scalable quantum property estimation for quantum computing, offering a novel method that improves accuracy in resource-limited settings.
The authors tackled the problem of estimating quantum state properties from measurement data without full reconstruction, by integrating classical shadows with a set transformer to correct bias in estimators. Their Bayesian approach achieved over 99% reduction in mean squared error compared to classical shadows alone in few-copy regimes for tasks like GHZ state fidelity and Rényi entropy estimation.
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.