Data-Driven Inference of Physical Devices: Theory and Implementation

TL;DR

This paper presents a data-driven method for inferring the behavior of unknown physical devices without prior knowledge of measurement apparatus, enabling high-precision reconstruction solely from observed input-output data.

Contribution

It introduces an analytical and algorithmic approach to learn qubit channels without relying on full tomographic knowledge of the measurement setup.

Findings

High-precision inference of unknown devices from data

Analytical solution for qubit channel learning

Algorithm implementation demonstrated effectiveness

Abstract

Given a physical device as a black box, one can in principle fully reconstruct its input-output transfer function by repeatedly feeding different input probes through the device and performing different measurements on the corresponding outputs. However, for such a complete tomographic reconstruction to work, full knowledge of both input probes and output measurements is required. Such an assumption is not only experimentally demanding, but also logically questionable, as it produces a circular argument in which the characterization of unknown devices appears to require other devices to have been already characterized beforehand. Here, we introduce a method to overcome such limitations present in usual tomographic techniques. We show that, even without any knowledge about the tomographic apparatus, it is still possible to infer the unknown device to a high degree of precision, solely relying on the observed data. This is achieved by employing a criterion that singles out the minimal explanation compatible with the observed data. Our method, that can be seen as a data-driven analogue of tomography, is solved analytically and implemented as an algorithm for the learning of qubit channels.