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  • Open Access

Efficiently Learning Global Quantum Channels with Local Tomography

Zidu Liu1,* and Dominik S. Wild1,2

  • *Contact author: zidu.liu@mpq.mpg.de
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PRX Quantum 7, 043015 – Published 22 October, 2026

DOI: https://doi.org/10.1103/51mt-ghpn

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 inverse of the desired global reconstruction error, which we quantify by the trace-norm distance between the true and the reconstructed Choi states. 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 network 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 of local shadow tomography to scalable channel characterization with access to global properties.

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Popular Summary

A central challenge in quantum computing is learning how noise affects systems with many qubits. As devices grow larger, the quantum processes that govern their behavior become exponentially more complex, making complete characterization impractical. Existing scalable tools can often probe only local properties, leaving open the question of how to obtain a reliable global picture of a noisy device. This gap limits our ability to diagnose errors, understand correlated effects, and improve the performance of quantum technologies. Our work shows that, under physically motivated conditions, global properties of a many-qubit quantum process can be inferred from local measurement data. In other words, one does not always need prohibitively expensive full tomography to extract meaningful global information. We develop a scalable framework that combines local tomography with a reconstruction procedure that stitches local data into a globally consistent description. By extending quantum process characterization beyond strictly local observables, this work opens a practical route toward studying, validating, and benchmarking larger quantum devices.

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PRX Quantum 7, 043015– Published 22 October, 2026
  • Received 13 March 2026
  • Revised 11 August 2026
  • Accepted 21 September 2026
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