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Geometry of quantum computation

Gia Giorgadze

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Preface Basic of Quantum Computation Quantum Computers Based on Exactly Solvable Models & Geometric Phases Quantum Processor Based on the Three-Level Quantum System Methods of Geometric Control Theory for Quantum Computations Analytic Methods in Quantum Computation References Index.

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Abstract We present a new approach for generating arbitrary analytically solvable two-level systems. This method offers the ability to completely derive all analytically solvable Hamiltonians for any analytical evolutions of two-level systems. To demonstrate the effectiveness of this approach, we reconstruct the Rosen–Zener model and generate several new exact solutions. Using this approach, we present the exact evolution of the semi-classical Rabi model with new analytical properties. The parameters used to generate Hamiltonians have direct physical interpretations within the Bloch sphere, the quantum speed limit, and the geometric phase. As a result, the physical properties of the generated Hamiltonian are highly controllable, which plays a significant role in the fields of quantum control, quantum computing, and quantum information.
In the present paper, we study the geometric phase by considering a model that closely describes a realistic experimental scenario. We present an active way to control and quench the variation of the geometric phase using ultra-short strong pulses for a two-level quantum system with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we study the variation of the geometric phase with a few cycles pulse and a smooth phase jump over a finite time intervals. The control of the variation rate of the geometric phase is obtained by acting on the shape of the phase transient and other parameters of the considered system. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.