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QGOpt: Riemannian optimization for quantum technologies

by Ilia A. Luchnikov, Alexander Ryzhov, Sergey N. Filippov, Henni Ouerdane

Submission summary

As Contributors: Ilia Luchnikov · Henni Ouerdane · Alexander Ryzhov
Preprint link: scipost_202011_00008v1
Code repository: https://github.com/LuchnikovI/QGOpt
Date submitted: 2020-11-07 20:44
Submitted by: Ouerdane, Henni
Submitted to: SciPost Physics Codebases
Academic field: Physics
Specialties:
  • Quantum Physics
Approaches: Theoretical, Computational

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.

Current status:
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Submission scipost_202011_00008v1 on 7 November 2020

Reports on this Submission

Anonymous Report 1 on 2020-11-24 Invited Report

Report

Dear Editor,
please find here enclosed my review of the manuscript entitled
QGOpt: Riemannian optimization for quantum technologies, submitted for publication in SciPost Physics.
The authors introduce a new optimization method for solving problems in constrained quantum dynamics. This approach is based on the Riemannian structure of the optimization problem which allows to apply a standard gradient algorithm, while preserving the physical constraints. Two examples in quantum technologies are discussed, namely gate decomposition and quantum tomography.

The development of efficient and versatile numerical optimization procedures is a subject of fundamental interest in quantum technologies both from a physical and mathematical point of view. The proposed method and the results are very interesting. The formulation is compact and seems straightforward to use. This paper seems sound mathematically and numerically. The different results are described in detail. I think that this paper is a significant contribution to this research area. It provides a complete and original investigation. I support the publication of this paper.

I have also minor comments about this manuscript. In the two examples presented by the authors, it would be interesting to describe briefly the computational cost of the algorithm. This information could be useful for the interested reader. In the same direction, is it possible to estimate the maximum dimension of the quantum system in which this approach can be applied? Another idea to discuss maybe in the conclusion of the paper: The authors use in this manuscript a first-order gradient algorithm. Would it be possible or interesting to extend this approach to second-order gradient algorithms? In the conclusion, the authors mention that "\emph{the complex Stiefel manifold can
be used to address different control problems, where one needs to find an optimal set of unitary gates driving a quantum system to a desirable quantum state}". In this perspective, would it be possible to combine this approach with optimal control theory? The authors should complete the bibliography of this paper about quantum optimal control. Quantum optimal control is for instance a very efficient procedure for generating quantum gates in a minimum time. They should cite a recent review paper (1) which gives the current state-of-the-art of optimal control in different domains, such as quantum information science. This review paper completes the other references mentioned in the current version of the manuscript.
(1)- S. J. Glaser et al., \emph{Training Schr\"odinger's cat: Quantum optimal control}, Eur. Phys. J. D (2015) 69, 279 [DOI: 10.1140/epjd/e2015-60464-1]

  • validity: high
  • significance: good
  • originality: good
  • clarity: good
  • formatting: good
  • grammar: good

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