# Identification of Time-varying in situ Signals in Quantum Circuits

## TL;DR

This paper develops a theoretical framework and algorithms for identifying time-varying signals in quantum circuits from measurement data, applicable to both open and closed systems, with demonstrated numerical success.

## Contribution

It introduces an algebraic identifiability criterion and a numerical algorithm for in situ quantum signal identification, filling a gap in theoretical analysis.

## Key findings

- The criterion determines when signals can be uniquely identified.
- The algorithm successfully recovers signals in numerical simulations.
- Applicable to both open and closed quantum systems.

## Abstract

The identification of time-varying \textit{in situ} signals is crucial for characterizing the dynamics of quantum processes occurring in highly isolated environments. Under certain circumstances, they can be identified from time-resolved measurements via Ramsey interferometry experiments, but only with very special probe systems can the signals be explicitly read out, and a theoretical analysis is lacking on whether the measurement data are sufficient for unambiguous identification. In this paper, we formulate this problem as the invertibility of the underlying quantum input-output system, and derive the algebraic identifiability criterion and the algorithm for numerically identifying the signals. The criterion and algorithm can be applied to both closed and open quantum systems, and their effectiveness is demonstrated by numerical examples.