Realization of commonly used quantum gates using perturbed harmonic oscillator

This paper deals with the approximate design of quantum unitary gates using perturbed harmonic oscillator dynamics. The harmonic oscillator dynamics is perturbed by a small time-varying electric field which leads to time-dependent Schrödinger equation. The corresponding unitary evolution after time T is obtained by approximately solving the time-dependent Schrödinger equation. The aim of this work is to minimize the discrepancy between a given unitary gate and the gate obtained by evolving the oscillator in the weak electric field over [0, T]. The proposed algorithm shows that the approximate design is able to realize the Hadamard gate and controlled unitary gate on three-qubit arrays with high accuracy.

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