Quantum Adiabatic Evolution Algorithms with Different Paths

TL;DR

This paper explores alternative paths in quantum adiabatic evolution algorithms, proposing random path generation methods that can improve success rates over traditional linear paths.

Contribution

It introduces novel methods for constructing non-linear paths in quantum adiabatic algorithms, demonstrating potential to convert failures into successes.

Findings

Random path generation can enhance algorithm success

Non-linear paths outperform straight-line paths in some cases

Proposed methods are versatile and adaptable

Abstract

In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes the solution of the computational problem. These algorithms have generally been studied in the case where the "straight line" path from initial to final Hamiltonian is taken. But there is no reason not to try paths involving terms that are not linear combinations of the initial and final Hamiltonians. We give several proposals for randomly generating new paths. Using one of these proposals, we convert an algorithmic failure into a success.