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  • Open Access

Agnostic Process Tomography

Chirag Wadhwa1,*, Laura Lewis1, Elham Kashefi1,2, and Mina Doosti1

  • *Contact author: chirag.wadhwa@ed.ac.uk
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PRX Quantum 6, 040371 – Published 24 December, 2025

DOI: https://doi.org/10.1103/q2nb-zg9m

Abstract

Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state tomography was defined, in which one aims to approximate an arbitrary quantum state by a simpler one in a given class. Generalizing this notion to quantum processes, we initiate the study of agnostic process tomography: given query access to an unknown quantum channel Φ and a known concept class C of channels, output a quantum channel that approximates Φ as well as any channel in the concept class C, up to some error. In this work, we propose several natural applications for this new task in quantum machine learning, quantum metrology, classical simulation, and error mitigation. In addition, we give efficient agnostic process tomography algorithms for a wide variety of concept classes, including Pauli strings, Pauli channels, quantum junta channels, low-degree channels, and a class of channels produced by QAC0 circuits. The main technical tool we use is Pauli spectrum analysis of operators and superoperators. We also prove that, using ancilla qubits, any agnostic state tomography algorithm can be extended to one solving agnostic process tomography for a compatible concept class of unitaries, immediately giving us efficient agnostic learning algorithms for Clifford circuits, Clifford circuits with few T gates, and circuits consisting of a tensor product of single-qubit gates. Together, our results provide insight into the conditions and new algorithms necessary to extend the learnability of a concept class from the standard tomographic setting to the agnostic one.

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Popular Summary

Can one learn to efficiently implement unknown physical processes on resource-constrained quantum computers? Toward an answer, we initiate the study of agnostic process tomography: given the ability to query an unknown quantum channel, learn the best possible approximation from a given class of channels. Our framework formalizes learning quantum processes in the presence of noise, which is especially timely given the error-prone nature of current quantum devices. We also propose broad applications in classical simulation, quantum machine learning, quantum metrology, and error mitigation.

We first design a straightforward algorithm performing agnostic process tomography which is query-efficient but time-inefficient, emphasizing that the metric of interest for agnostic process tomography is time complexity. We then present computationally efficient algorithms for a wide variety of physically motivated classes. Our analysis reveals that, often, the state-of-the-art learning algorithms in the standard setting are not sufficiently robust, necessitating adjustments or entirely novel algorithms to succeed in the agnostic setting.

Agnostic process tomography is a natural learning problem that is physically motivated and broadly applicable and an impactful direction for characterizing and utilizing quantum systems under realistic conditions. We hope that our work inspires future research on novel agnostic process tomography algorithms and lower bounds, as well as the application of this framework in physically relevant settings.

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PRX Quantum 6, 040371– Published 24 December, 2025
  • Received 27 May 2025
  • Accepted 27 October 2025
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