Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems
This work addresses the problem of approximating complex input-output maps for machine learning applications, offering a quantum approach that is incremental but shows promise for future performance gains.
The paper develops a theory for learning nonlinear input-output maps with fading memory using dissipative quantum systems, proving universality for a specific class and showing numerically that small quantum systems can match classical methods with many parameters, with potential for quantum advantage due to exponential Hilbert space growth.
In this paper, we develop a theory of learning nonlinear input-output maps with fading memory by dissipative quantum systems, as a quantum counterpart of the theory of approximating such maps using classical dynamical systems. The theory identifies the properties required for a class of dissipative quantum systems to be {\em universal}, in that any input-output map with fading memory can be approximated arbitrarily closely by an element of this class. We then introduce an example class of dissipative quantum systems that is provably universal. Numerical experiments illustrate that with a small number of qubits, this class can achieve comparable performance to classical learning schemes with a large number of tunable parameters. Further numerical analysis suggests that the exponentially increasing Hilbert space presents a potential resource for dissipative quantum systems to surpass classical learning schemes for input-output maps.