Performance Benchmarking of Quantum Algorithms for Hard Combinatorial Optimization Problems: A Comparative Study of non-FTQC Approaches

TL;DR

This paper benchmarks various non-fault-tolerant quantum algorithms and classical methods across multiple optimization problems, revealing no single approach excels universally and emphasizing the importance of tailored strategies for NISQ devices.

Contribution

It provides a comprehensive performance comparison of diverse non-FTQC quantum algorithms and classical methods on key optimization problems, establishing a baseline for future research.

Findings

No single algorithm outperforms others across all problems.

Classical simulated annealing and quantum annealing show competitive results.

Algorithm performance varies significantly with problem type.

Abstract

This study systematically benchmarks several non-fault-tolerant quantum computing algorithms across four distinct optimization problems: max-cut, number partitioning, knapsack, and quantum spin glass. Our benchmark includes noisy intermediate-scale quantum (NISQ) algorithms, such as the variational quantum eigensolver, quantum approximate optimization algorithm, quantum imaginary time evolution, and imaginary time quantum annealing, with both ansatz-based and ansatz-free implementations, alongside tensor network methods and direct simulations of the imaginary-time Schr\"odinger equation. For comparative analysis, we also utilize classical simulated annealing and quantum annealing on D-Wave devices. Employing default configurations, our findings reveal that no single non-FTQC algorithm performs optimally across all problem types, underscoring the need for tailored algorithmic strategies. This work provides an objective performance baseline and serves as a critical reference point for advancing NISQ algorithms and quantum annealing platforms.