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Mathematical Foundations of Holonomic Quantum Computer Kazuyuki FUJII

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. ∗E-mail address : [email protected]

Quantum Squeezed Light Propagation in an Optical Parity-Time (PT)-Symmetric Structure

We investigate the medium effect of a parity-time (PT)-symmetric bilayer on the quantum optical properties of an incident squeezed light at zero temperature (T=0 K). To do so, we use the canonical quantization approach and describe the amplification and dissipation properties of the constituent layers of the bilayer structure by Lorentz model to analyze the quadrature squeezing of the outgoing ...

Optical holonomic single quantum gates with a geometric spin under a zero field

Chow’s theorem and universal holonomic quantum computation

A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra are presented by taking covariant derivatives of the curvature associated to a non-Abelian gauge connection. When applied to the Optical Holonomic Computer, ...

Optical Holonomic Quantum Computer

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a non-linear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices and interferometers provide the classical control parameter space where the adiabatic loops are performed. This results into logical gates acting on the states of the combined ...