Gradient-descent quantum process tomography by learning Kraus operators

TL;DR

This paper introduces a gradient-descent based quantum process tomography method using Kraus operators, which efficiently reconstructs quantum processes with fewer measurements and scales to larger systems, outperforming traditional techniques.

Contribution

The paper presents a novel GD-QPT method that combines advantages of compressed sensing and least-squares approaches, enabling efficient, scalable quantum process reconstruction.

Findings

Matches performance of CS and PLS in benchmarks

Reconstructs processes from fewer measurements

Scales to systems with up to five qubits

Abstract

We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems by learning a process representation using Kraus operators. The Kraus form ensures that the reconstructed process is completely positive. To make the process trace-preserving, we use a constrained gradient-descent (GD) approach on the so-called Stiefel manifold during optimization to obtain the Kraus operators. Our ansatz uses a few Kraus operators to avoid direct estimation of large process matrices, e.g., the Choi matrix, for low-rank quantum processes. The GD-QPT matches the performance of both compressed-sensing (CS) and projected least-squares (PLS) QPT in benchmarks with two-qubit random processes, but shines by combining the best features of these two methods. Similar to CS (but unlike PLS), GD-QPT can reconstruct a process from just a small number of random measurements, and similar to PLS (but unlike CS) it also works for larger system sizes, up to at least five qubits. We envisage that the data-driven approach of GD-QPT can become a practical tool that greatly reduces the cost and computational effort for QPT in intermediate-scale quantum systems.