Quantum Computing Inspired Approach for Self-Avoiding Walk (SAWs): 2D lattice and 3D lattice SAWs for single chain enumeration

TL;DR

This paper introduces a quantum computing algorithm based on quantum amplitude estimation to efficiently enumerate self-avoiding walks on 2D and 3D lattices, significantly reducing computational time compared to classical methods.

Contribution

The paper develops a novel quantum algorithm for SAW enumeration on 2D and 3D lattices, achieving larger N and faster runtimes than classical algorithms.

Findings

2D SAWs up to N=71 enumerated in 26.9 minutes

3D SAWs up to N=40 enumerated in 13.06 minutes

Quantum approach outperforms classical algorithms in speed

Abstract

We investigate the application of quantum computing algorithms to enhance the efficiency of enumerating self-avoiding walks (SAWs), utilizing quantum properties such as superposition and interference. A Quantum Amplitude Estimation (QAE)-based algorithm is developed to enumerate SAWs on both 2D and 3D lattices. In case of 2D square lattice, SAWs up to N=71 steps are successfully enumerated within 26.9 minutes - significantly improving upon the classical algorithm, which required approximately 231 hours(Jensen et al., 2012, J. Phys. A: Math. Theor. 45, 115202). The algorithm is further extended to 3D cubic lattices, where SAWs up to N=40 steps are enumerated in 13.06 minutes, compared to the classical result of N=36 in 250 hours (Schram et al., 2011, J. Stat. Mech. P06019). These results demonstrate a substantial reduction in computational time, highlighting the potential of quantum computing for combinatorial enumeration problems.