# Fast Quantum Process Tomography via Riemannian Gradient Descent

arXiv: https://arxiv.org/abs/2404.18840 · HTML: https://mlsanity.com/paper/2404.18840/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 29 Apr 2024.

## Builds on (most cited first, 4 of 4)

- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Gradient-descent quantum process tomography by learning Kraus operators](https://mlsanity.com/paper/2208.00812/) (2022)
- [Partial Trace Regression and Low-Rank Kraus Decomposition](https://mlsanity.com/paper/2007.00935/) (2020)

## Built on by (most cited first, 1 of 1)

- [Comprehensive characterization of three-qubit Grover search algorithm on IBM's 127-qubit superconducting quantum computers](https://mlsanity.com/paper/2406.16018/) (2024)

## Abstract (arXiv)

Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process tomography, in which the goal is to retrieve the underlying quantum process based on a given set of measurement data. In this paper, we introduce a modified version of stochastic gradient descent on a Riemannian manifold that integrates recent advancements in numerical methods for Riemannian optimization. This approach inherently supports the physically driven constraints of a quantum process, takes advantage of state-of-the-art large-scale stochastic objective optimization, and has superior performance to traditional approaches such as maximum likelihood estimation and projected least squares. The data-driven approach enables accurate, order-of-magnitude faster results, and works with incomplete data. We demonstrate our approach on simulations of quantum processes and in hardware by characterizing an engineered process on quantum computers.