Mathematical Foundations of Holonomic Quantum Computer

Abstract

We make a brief review of (optical) Holonomic Quantum Computer (or Computation) proposed by Zanardi and Rasetti (quant-ph/9904011) and Pachos and Chountasis (quant-ph/9912093), and give a mathematical reinforcement to their works.

Latex file, 11 pages

References in corpus (3)

• Holonomic Quantum Computation
• Geometric quantum computation with NMR
• Note on Coherent States and Adiabatic Connections, Curvatures

Cited by in corpus (11)

• Exchange Gate on the Qudit Space and Fock Space
• Realization of Arbitrary Gates in Holonomic Quantum Computation
• Exact Solutions of Holonomic Quantum Computation
• Control aspects of holonomic quantum computation
• Holonomic Gates in Pseudo-Hermitian Quantum Systems
• Chow's theorem and universal holonomic quantum computation
• Implementation of holonomic quantum gates by an isospectral deformation of an Ising dimer chain
• Semiclassical propagation of spin coherent states
• Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime
• Exact solutions for universal holonomic quantum gates
• Geometric and holonomic quantum computation