QGOpt: Riemannian optimization for quantum technologies

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,...

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Bibliographic Details
Published inarXiv.org
Main Authors Luchnikov, I A, Ryzhov, A, Filippov, S N, Ouerdane, H
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.11.2021
Subjects
Constraints
Optimization
Optimization techniques
Orthogonality
Physics - Quantum Physics
Quantum mechanics
Quotients
Riemann manifold
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2011.01894