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IEEE Conference on Decision and Control (CDC)

Holonomic quantum computation with squeezed coherent states

Dennis G. Lucarelli, TZYH JONG TARN

Published Aug 27, 2003• 1 citation
Publisher

Abstract

Control theoretic aspects of holonomic quantum computation are presented. A generating set of holonomic transformations is constructed from the product bundle arising from the two-qubit system of holonomic quantum computation with squeezed coherent states.
DOI
10.1109/cdc.2002.1184537

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A unifying framework for the control of quantum systems with non-Abelian holonomy is presented. It is shown that, from a control theoretic point of view, holonomic quantum computation can be treated as a control system evolving on a principal fiber bundle. An extension of methods developed for these classical systems may be applied to quantum holonomic systems to obtain insight into the control properties of such systems and to construct control algorithms for two established examples of the computing paradigm.
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Abstract We propose a protocol for nonadiabatic holonomic quantum computation based on squeezed cat states. By exponentially enhancing the Kerr nonlinearity of a harmonic oscillator via a tailored driving scheme, we enable the fast, nonadiabatic generation of squeezed coherent states through shortcuts to adiabaticity. These squeezed coherent states serve as the building blocks for squeezed cat states, which are then utilized as logical qubits in our holonomic framework. Numerical simulations show that our state-preparation mechanism is approximately five times faster than conventional adiabatic approaches, thereby providing a practical route to accelerate the realization of holonomic gates. Leveraging the robustness of geometric phases and the nonclassical features of squeezed cat states, our scheme offers a promising platform for high-speed, fault-tolerant quantum computation.
In this paper the idea of holonomic quantum computation is realized within quantum optics. In a nonlinear 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 in logical gates acting on the states of the combined degenerate subspaces of the lasers, producing any one qubit rotations and interactions between any two qubits. Issues such as universality, complexity, scalability, and reversibility are addressed and several steps are taken towards the physical implementation of this model.
We in this paper consider a further generalization of the (optical) holonomic quantum computation proposed by Zanardi and Rasetti (quant-ph/9904011), and reinforced by Fujii (quant-ph/9910069) and Pachos and Chountasis (quant-ph/9912093). We construct a quantum computational bundle on some parameter space, and calculate non-abelian Berry connections and curvatures explicitly in the special cases. Our main tool is unitary coherent operators based on Lie algebras su(n+1) and su(n,1), where the case of n = 1 is the previous one.