Non adiabatic quantum search algorithms

TL;DR

This paper introduces two novel continuous-time quantum search algorithms that operate without adiabatic evolution, demonstrating broad parameter robustness and convergence to the target state over time.

Contribution

The paper proposes two new quantum search algorithms that do not rely on adiabatic processes, expanding the toolkit for quantum search methods.

Findings

Algorithms work for a wide range of Hamiltonian parameters

One algorithm converges to the searched state after a characteristic time

Demonstrates robustness and convergence properties

Abstract

We present two new continuous time quantum search algorithms similar to the adiabatic search algorithm, but now without an adiabatic evolution. We find that both algorithms work for a wide range of values of the parameters of the Hamiltonian, and one of them has, as an additional feature that, for values of time larger than a characteristic one, it will converge to a state which can be close to the searched state.