QGOpt: Riemannian optimization for quantum technologies

TL;DR

QGOpt is a TensorFlow-based library that applies Riemannian optimization techniques to solve constrained quantum problems like quantum gate decomposition and tomography, ensuring quantum constraints are preserved.

Contribution

The paper introduces QGOpt, a novel library leveraging Riemannian optimization for quantum constraints, enabling standard gradient methods in quantum applications.

Findings

Successfully applied to quantum gate decomposition

Effective in quantum tomography tasks

Preserves quantum constraints during optimization

Abstract

Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP property of quantum channels, and conditions on density matrices, can be seen as quotient or embedded Riemannian manifolds. This allows to use Riemannian optimization techniques for solving quantum-mechanical constrained optimization problems. In the present work, we introduce QGOpt, the library for constrained optimization in quantum technology. QGOpt relies on the underlying Riemannian structure of quantum-mechanical constraints and permits application of standard gradient based optimization methods while preserving quantum mechanical constraints. Moreover, QGOpt is written on top of TensorFlow, which enables automatic differentiation to calculate necessary gradients for optimization. We show two application examples: quantum gate decomposition and quantum tomography.