QGOpt: Riemannian optimization for quantum technologies

Luchnikov, Ilia; Ryzhov, Alexander; Filippov, Sergey; Ouerdane, Henni

doi:10.21468/SciPostPhys.10.3.079

SciPost Physics

QGOpt: Riemannian optimization for quantum technologies

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

SciPost Phys. 10, 079 (2021) · published 30 March 2021

doi: 10.21468/SciPostPhys.10.3.079
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.10.3.079
TI  - QGOpt: Riemannian optimization for quantum technologies
PY  - 2021/03/30
UR  - https://www.scipost.org/SciPostPhys.10.3.079
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 10
IS  - 3
SP  - 079
A1  - Luchnikov, Ilia
AU  - Ryzhov, Alexander
AU  - Filippov, Sergey
AU  - Ouerdane, Henni
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.10.3.079,
	title={{QGOpt: Riemannian optimization for quantum technologies}},
	author={Ilia A. Luchnikov and Alexander Ryzhov and Sergey N. Filippov and Henni Ouerdane},
	journal={SciPost Phys.},
	volume={10},
	pages={079},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.10.3.079},
	url={https://scipost.org/10.21468/SciPostPhys.10.3.079},
}

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