🤖 AI Summary
This work introduces the paradigm of *agnostic process tomography*: given query access to an unknown quantum channel Φ—without assuming Φ belongs to any prespecified model class—we select, from a given concept class ℂ, the channel that best approximates Φ. Our core techniques include Pauli spectrum analysis, superoperator spectral estimation, ancilla-enhanced state-tomography transfer, and efficient query sampling. We establish, for the first time, an agnostic learning transfer framework from quantum states to quantum processes, applicable to broad learnable classes including Pauli channels, quantum juntas, and QAC⁰ circuits. We design polynomial-time agnostic learning algorithms for Clifford circuits and circuits with few T-gates. Furthermore, we provide a theoretical characterization of sufficient conditions for agnostic learnability of quantum processes. These results advance foundational tools for quantum machine learning and error mitigation.
📝 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 $Phi$ and a known concept class $mathcal{C}$ of channels, output a quantum channel that approximates $Phi$ as well as any channel in the concept class $mathcal{C}$, 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 $mathsf{QAC}^0$ 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.