The Travelling Salesman Problem and Adiabatic Quantum Computation: An Algorithm

TL;DR

This paper presents an adiabatic quantum algorithm for solving the travelling salesman problem, focusing on the construction of Hamiltonians and analyzing the computational complexity and energy resources involved.

Contribution

It introduces a specific adiabatic quantum algorithm for TSP with explicit Hamiltonian design and complexity estimates, advancing quantum approaches to combinatorial optimization.

Findings

The initial Hamiltonian admits canonical coherent states as ground states.

The target Hamiltonian encodes the shortest tour as its ground state.

Complexity bounds are provided for energy, space, and time resources.

Abstract

An explicit algorithm for the travelling salesman problem is constructed in the framework of adiabatic quantum computation, AQC. The initial Hamiltonian for the AQC process admits canonical coherent states as the ground state, and the target Hamiltonian has the shortest tour as the desirable ground state. Some estimates/bounds are also given for the computational complexity of the algorithm with particular emphasis on the required energy resources, besides the space and time complexity, for the physical process of (quantum) computation in general.