Theoretical realization of a two qubit quantum controlled-not logic gate and a single qubit Hadamard logic gate in the anti-Jaynes-Cummings model

TL;DR

This paper presents a theoretical scheme for implementing a Hadamard gate and a controlled-NOT gate using the anti-Jaynes-Cummings model, advancing quantum logic gate design in cavity QED systems.

Contribution

It introduces a novel theoretical approach for realizing key quantum gates within the anti-Jaynes-Cummings interaction framework.

Findings

Successful theoretical realization of Hadamard gate in anti-Jaynes-Cummings model.

Implementation of controlled-NOT gate with high success probability.

Precise interaction timing achieves ideal gate operation probabilities.

Abstract

We provide a theoretical scheme for realizing a Hadamard and a quantum controlled-NOT logic gates operations in the anti-Jaynes-Cummings interaction process. Standard Hadamard operation for a specified initial atomic state is achieved by setting a specific sum frequency and photon number in the anti-Jaynes-Cummings qubit state transition operation with the interaction component of the anti-Jaynes-Cummings Hamiltonian generating the state transitions. The quantum controlled-NOT logic gate is realized when a single atomic qubit defined in a two-dimensional Hilbert space is the control qubit and two non-degenerate and orthogonal polarized cavities defined in a two-dimensional Hilbert space make the target qubit. With precise choice of interaction time in the anti-Jaynes-Cummings qubit state transition operations defined in the anti-Jaynes-Cummings sub-space spanned by normalized but non-orthogonal basic qubit state vectors, we obtain ideal unit probabilities of success in the quantum controlled-NOT operations.