Machine Learning approach to the Floquet--Lindbladian problem

TL;DR

This paper explores using machine learning to determine if a quantum map can be generated by a time-independent Lindbladian, revealing spectral properties of the Choi matrix as key indicators.

Contribution

It introduces ML-based methods to analyze the Floquet--Lindbladian problem and links spectral features of the Choi matrix to Lindbladian generation.

Findings

ML methods can predict Lindbladian generation from quantum maps

Spectral properties of the Choi matrix encode Lindbladian information

Eigenvalues and eigenstates of the Choi matrix are key indicators

Abstract

Similar to its classical version, quantum Markovian evolution can be either time-discrete or time-continuous. Discrete quantum Markovian evolution is usually modeled with completely-positive trace-preserving maps while time-continuous evolution is often specified with superoperators referred to as "Lindbladians". Here we address the following question: Being given a quantum map, can we find a Lindbladian which generates an evolution identical -- when monitored at discrete instances of time -- to the one induced by the map? It was demonstrated that the problem of getting the answer to this question can be reduced to an NP-complete (in the dimension $N$ of the Hilbert space the evolution takes place in) problem. We approach this question from a different perspective by considering a variety of Machine Learning (ML) methods and trying to estimate their potential ability to give the correct answer. Complimentary, we use the performance of different ML methods as a tool to check the hypothesis that the answer to the question is encoded in spectral properties of the so-called Choi matrix, which can be constructed from the given quantum map. As a test bed, we use two single-qubit models for which the answer can be obtained by using the reduction procedure. The outcome of our experiment is that, for a given map, the property of being generated by a time-independent Lindbladian is encoded both in the eigenvalues and the eigenstates of the corresponding Choi matrix.