Learning quantum processes without input control

• URL: http://arxiv.org/abs/2211.05005v3
• Date: Tue, 5 Mar 2024 14:48:53 GMT
• Title: Learning quantum processes without input control
• Authors: Marco Fanizza, Yihui Quek, Matteo Rosati
• Abstract summary: We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. This framework is applicable to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer.
• Score: 2.6089354079273512
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process governed by classical parameters that are out of one's control. This framework is applicable, for example, to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer. We provide an algorithm for learning with high probability in this setting with a finite amount of samples, even if the concept class is infinite. To do this, we review and adapt existing algorithms for shadow tomography and hypothesis selection, and combine their guarantees with the uniform convergence on the data of the loss functions of interest. As a by-product we obtain sufficient conditions for performing shadow tomography of classical-quantum states with a number of copies which depends on the dimension of the quantum register, but not on the dimension of the classical one. We give concrete examples of processes that can be learned in this manner, based on quantum circuits or physically motivated classes, such as systems governed by Hamiltonians with random perturbations or data-dependent phase-shifts.

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