Multiparameter estimation of continuous-time Quantum Walk Hamiltonians through Machine Learning

TL;DR

This paper introduces a machine learning approach to estimate Hamiltonian parameters of continuous-time quantum walks from experimental data, achieving near-optimal accuracy and enabling better characterization of quantum systems.

Contribution

The authors develop a deep neural network method for multiparameter estimation of quantum walk Hamiltonians, outperforming traditional bounds and applicable to complex multi-parameter scenarios.

Findings

Neural network estimates Hamiltonian parameters with near-optimal accuracy.

Method is effective for multiple parameters simultaneously.

Results match theoretical bounds for estimation precision.

Abstract

The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum walks, the parameters themselves may not be directly accessible, thus it is necessary to find alternative estimation strategies exploiting other observables. Here, we perform the multiparameter estimation of the Hamiltonian parameters characterizing a continuous-time quantum walk over a line graph with $n$-neighbour interactions using a deep neural network model fed with experimental probabilities at a given evolution time. We compare our results with the bounds derived from estimation theory and find that the neural network acts as a nearly optimal estimator both when the estimation of two or three parameters is performed.