New Research in Physics

Exploring Quantum Adiabatic Conditions in a Generalized Quantum Algorithm

Authors

Arash Karimkhani
َAmir Ghale’e

Tafresh University

https://doi.org/10.61882/jmrph.9.2.15
Abstract
Quantum adiabatic computing provides a framework for simulating quantum algorithms grounded in established quantum mechanics theorems. The quantum adiabatic theorem defines the conditions for the adiabatic transformation of quantum systems, but verifying these conditions demands careful scrutiny. This study focuses on the generalized Deutsch algorithm within the realm of quantum adiabatic computing. The time-dependent Hamiltonian is analyzed by evaluating the system's input and output states. The input state is a two-particle quantum entangled state, while the four output states represent the system's computational results. The allowed energy levels of the computational system are derived as the eigenstates of the Hamiltonian. By plotting these energy levels, the differences between them are quantified. Standard runtime functions are employed to validate the computational system, and various scheduled time functions are used to examine the applicability of the quantum adiabatic theorem to the generalized Deutsch algorithm. Analysis of the energy gaps between excited states and the ground state confirms that the proposed Hamiltonian satisfies adiabatic conditions throughout the algorithm's execution.

Keywords

generalized Deutsch algorithm
Energy level
Quantum Computing
Quantum Adiabatic Computing
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