Related papers: On the Random Schrödinger Equation and Geometric Quantum Control

On the Random Schrödinger Equation and Geometric Quantum Control

URL: http://arxiv.org/abs/2503.04617v3
Date: Mon, 31 Mar 2025 09:41:50 GMT
Title: On the Random Schrödinger Equation and Geometric Quantum Control
Authors: Rufus Lawrence, Aleš Wodecki, Johannes Aspman, Jakub Mareček,
Abstract summary: We introduce the random Schr"odinger equation, with a noise term given by a random Hermitian matrix as a means to model noisy quantum systems.<n>We derive bounds on the error of the synthesised unitary in terms of bounds on the norm of the noise, and show that for certain noise processes these bounds are tight.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We introduce the random Schr\"odinger equation, with a noise term given by a random Hermitian matrix as a means to model noisy quantum systems. We derive bounds on the error of the synthesised unitary in terms of bounds on the norm of the noise, and show that for certain noise processes these bounds are tight. We then show that in certain situations, minimising the error is equivalent to finding a geodesic on SU (n) with respect to a Riemannian metric encoding the coupling between the control pulse and the noise process. Our work thus extends the series of seminal papers by Nielsen et al. on the geometry of quantum gate complexity.

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