Efficient Quantum State Tracking in Noisy Environments

TL;DR

This paper introduces a new online quantum state tomography method, matrix-exponentiated gradient tomography, which efficiently tracks evolving quantum states in noisy environments with high fidelity, demonstrated experimentally on a photonic qutrit system.

Contribution

The paper presents the first experimental implementation of matrix-exponentiated gradient tomography for real-time quantum state tracking in noisy conditions.

Findings

Achieved around 95% fidelity in state estimation.

Effectively tracked both stationary and evolving states.

Performed well under significant environmental noise.

Abstract

Quantum state tomography, which aims to find the best description of a quantum state -- the density matrix, is an essential building block in quantum computation and communication. Standard techniques for state tomography are incapable of tracking changing states and often perform poorly in the presence of environmental noise. Although there are different approaches to solve these problems theoretically, experimental demonstrations have so far been sparse. Our approach, matrix-exponentiated gradient tomography, is an online tomography method that allows for state tracking, updates the estimated density matrix dynamically from the very first measurements, is computationally efficient, and converges to a good estimate quickly even with noisy data. The algorithm is controlled via a single parameter, its learning rate, which determines the performance and can be tailored in simulations to the individual experiment. We present an experimental implementation of matrix-exponentiated gradient tomography on a qutrit system encoded in the transverse spatial mode of photons. We investigate the performance of our method on stationary and evolving states, as well as significant environmental noise, and find fidelities of around 95% in all cases.