Constrained Shadow Tomography for Molecular Simulation on Quantum Devices

TL;DR

This paper introduces a constrained shadow tomography method using semidefinite programming to accurately reconstruct physically consistent two-particle reduced density matrices in quantum simulations, even with noisy data.

Contribution

It develops a bi-objective optimization framework that incorporates N-representability constraints and regularization, improving the physical validity and robustness of quantum state reconstructions.

Findings

Enhanced accuracy and noise resilience demonstrated in numerical simulations.

Significant improvements in scalability and physical consistency of fermionic state reconstruction.

Robust performance on hardware experiments with realistic quantum data.

Abstract

Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and computational demands limit scalability, motivating efficient alternatives such as classical shadows, which enable accurate prediction of many observables from randomized measurements. In this work, we introduce a bi-objective semidefinite programming approach for constrained shadow tomography, designed to reconstruct the two-particle reduced density matrix (2-RDM) from noisy or incomplete shadow data. By integrating $N$-representability constraints and nuclear-norm regularization into the optimization, the method builds an $N$-representable 2-RDM that balances fidelity to the shadow measurements with energy minimization. This unified framework mitigates noise and sampling errors while enforcing physical consistency in the reconstructed states. Numerical and hardware results demonstrate that the approach significantly improves accuracy, noise resilience, and scalability, providing a robust foundation for physically consistent fermionic state reconstruction in realistic quantum simulations.