Efficiently Learning Global Quantum Channels with Local Tomography

TL;DR

This paper presents a scalable method for reconstructing global quantum channels from local measurements, leveraging local shadow tomography and convex optimization, effective when correlations decay exponentially, enabling characterization of large quantum systems.

Contribution

Introduces a local-to-global reconstruction framework for quantum channels that is efficient under exponential decay of correlations, extending local shadow tomography to global properties.

Findings

Sample complexity scales polynomially with system size

Successfully reconstructs channels on up to 50 qubits

Accurately recovers global diagnostics like process fidelity

Abstract

Scalable characterization of quantum processors is crucial for mitigating noise and imperfections. While randomized measurement protocols enable efficient access to local observables, inferring a globally consistent description of multi-qubit processes remains challenging. Here we introduce a local-to-global reconstruction framework for one-dimensional multi-qubit states and channels. The method is efficient provided that correlations, as quantified by the conditional mutual information, decay exponentially. In particular, we prove that under this assumption, the required number of samples scales polynomially with the system size and the desired global reconstruction error. Our approach is based on combining local shadow tomography with locally optimal recovery maps obtained by convex optimization. We supplement these rigorous guarantees by studying the performance of the protocol numerically for a system evolving under a local Lindbladian and a noisy, shallow circuit. By employing a tensor networ representation, we reconstruct channels acting on up to 50 qubits and accurately recover global diagnostics such as the process fidelity, the Choi state purity, and Pauli-weight-resolved process matrix elements. Our work thus extends the powerful toolbox local shadow tomography to scalable channel characterization with access to global properties.