A geometrical approach to quantum holonomic computing algorithms

DOI10.1016/j.matcom.2004.01.017zbMath1151.81320OpenAlexW2130171848MaRDI QIDQ596303

Anatoliy K. Prykarpatsky, A. M. Samoilenko, D. L. Blackmore, Ufuk Taneri, Yarema A. Prykarpatsky

Publication date: 10 August 2004

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2004.01.017

zbMATH Keywords

manifoldsDynamical systemsGrassmannConnectionsHolonomy groupsLax type integrable flowsQuantum algorithmsQuantum computersSymplectic structures

Mathematics Subject Classification ID

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Cites Work

• Parallel transport and ``quantum holonomy along density operators
• Reduction of Hamiltonian systems, affine Lie algebra, and Lax equations. II
• Lax-type flows on Grassmann manifolds and dual momentum mappings
• Holonomic quantum computation
• On a connection governing parallel transport along \(2 \times{}2\) density matrices
• On the geometry of soliton equations
• A completely integrable Hamiltonian system associated with line fitting in complex vector spaces
• Symplectic manifolds, coherent states, and semiclassical approximation
• The Finite-Dimensional Moser Type Reduction of Modified Boussinesq and Super-Korteweg-de Vries Hamiltonian Systems via the Gradient-Holonomic Algorithm and Dual Moment Maps. Part I
• The Integrability of Lie-invariant Geometric Objects Generated by Ideals in the Grassmann Algebra
• A Theorem on Holonomy
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