Evidence of scaling advantage on an NP-Complete problem with enhanced quantum solvers

TL;DR

This paper demonstrates empirical evidence of quantum speedup on an NP-complete problem by developing enhanced quantum solvers that outperform classical methods and scaling advantage is observed.

Contribution

The paper introduces a space reduction algorithm and enhanced quantum algorithms that improve resource efficiency and demonstrate scaling advantage on an NP-complete problem.

Findings

Enhanced quantum solvers outperform classical counterparts on problem instances up to 65 variables.

Quantum advantage observed in scaling behavior of the solvers.

Experimental implementation on a 13-qubit quantum processor confirms performance improvements.

Abstract

Achieving quantum advantage remains a key milestone in the noisy intermediate-scale quantum era. Without rigorous complexity proofs, scaling advantage-where quantum resource requirements grow more slowly than their classical counterparts-serves as the primary indicator. However, direct applications of quantum optimization algorithms to classically intractable problems have yet to demonstrate this advantage. To address this challenge, we develop enhanced quantum solvers for the NP-complete one-in-three Boolean satisfiability problem. We propose a restricting space reduction algorithm (RSRA) that achieves optimal search space dimensionality, thereby reducing both qubits and time complexity for various quantum solvers. Extensive numerical investigations on problem instances with up to 65 variables demonstrate that our enhanced quantum approximate optimization algorithm (QAOA) and quantum adiabatic algorithm (QAA)-based solvers outperform state-of-the-art classical solvers, with the QAA-based solver providing a lower bound for our method while exhibiting scaling advantage. Furthermore, we experimentally implement our enhanced solvers on a superconducting quantum processor with 13 qubits, confirming the predicted performance improvements. Collectively, our results provide empirical evidence of quantum speedup for an NP-complete problem.