Projected gradient descent algorithms for quantum state tomography

TL;DR

This paper introduces three new quantum state tomography algorithms based on projected gradient descent, demonstrating their advantages in speed and scalability over existing methods for high-dimensional quantum states.

Contribution

The paper proposes novel projected gradient descent algorithms for quantum state tomography and compares their performance with existing methods, showing improved speed and scalability.

Findings

Projected gradient descent methods are faster than traditional algorithms.

The new algorithms perform well on large quantum states.

They are applicable under a wider range of conditions.

Abstract

Accurate quantum tomography is a vital tool in both fundamental and applied quantum science. It is a task that involves processing a noisy measurement record in order to construct a reliable estimate of an unknown quantum state, and is central to quantum computing, metrology, and communication. To date, many different approaches to quantum state estimation have been developed, yet no one method fits all applications, and all fail relatively quickly as the dimensionality of the unknown state grows. In this work, we suggest that projected gradient descent is a method that can evade some of these shortcomings. We present three novel tomography algorithms that use projected gradient descent and compare their performance with state-of-the-art alternatives, i.e. the diluted iterative algorithm and convex programming. Our results find in favour of the general class of projected gradient descent methods due to their speed, applicability to large states, and the range of conditions in which they perform.