Quantum Optimization

TL;DR

This paper introduces a quantum algorithm for combinatorial optimization that shifts probability amplitudes towards lower-cost solutions, demonstrated through simulations on satisfiability and traveling salesman problems, and compared with classical heuristics.

Contribution

The paper presents a novel quantum algorithm leveraging cost structure to improve solution concentration in combinatorial optimization problems.

Findings

Algorithm shifts amplitude towards low-cost states in simulations.

Performance compares favorably with classical heuristics.

Demonstrates potential of quantum methods for combinatorial optimization.

Abstract

We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satisfiability and asymmetric traveling salesman problems. Simulations with randomly generated problem instances show each step of the algorithm shifts amplitude preferentially towards lower cost states, thereby concentrating amplitudes into low-cost states, on average. These results are compared with conventional heuristics for these problems.