Learning mixed quantum states in large-scale experiments

TL;DR

This paper introduces a protocol for efficiently learning the MPO representation of large-scale quantum states from classical shadows, enabling accurate state reconstruction and fidelity estimation in experimental quantum systems.

Contribution

The authors develop a scalable method to learn quantum states as MPOs from classical shadows, with proven efficiency and experimental validation on 96-qubit states.

Findings

Successfully learned entangled states of 96 qubits

Achieved high fidelity in state reconstruction

Demonstrated practical applicability in superconducting quantum processors

Abstract

We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and outputs the tensors of a MPO which maximizes a suitably-defined fidelity with the experimental state. The tensor optimization is carried out sequentially, similarly to the well-known density matrix renormalization group algorithm. Our approach is provably efficient under certain technical conditions which are expected to be met in short-range correlated states and in typical noisy experimental settings. Under the same conditions, we also provide an efficient scheme to estimate fidelities between the learned and the experimental states. We experimentally demonstrate our protocol by learning entangled quantum states of up to $N = 96$ qubits in a superconducting quantum processor. Our method upgrades classical shadows to large-scale quantum computation and simulation experiments.