Theorem on the existence of a nonzero energy gap in adiabatic quantum computation

TL;DR

This paper presents a theorem that guarantees the existence of a nonzero energy gap in certain Hamiltonians used in adiabatic quantum computation, aiding in the design of reliable quantum algorithms.

Contribution

It introduces a theorem that helps identify Hamiltonians with a nonzero energy gap, ensuring the validity of adiabatic quantum algorithms.

Findings

The theorem confirms the existence of a nonzero energy gap for specific Hamiltonians.

It provides a method to identify Hamiltonians without energy-level crossing.

This work supports the development of more reliable adiabatic quantum algorithms.

Abstract

Adiabatic quantum computation, based on the adiabatic theorem, is a promising alternative to conventional quantum computation. The validity of an adiabatic algorithm depends on the existence of a nonzero energy gap between the ground and excited states. However, it is difficult to ascertain the exact value of the energy gap. In this paper, we put forward a theorem on the existence of nonzero energy gap for the Hamiltonians used in adiabatic quantum computation. It can help to effectively identify a large class of the Hamiltonians without energy-level crossing between the ground and excited states.