Quantum mechanical NMR implementation of DNA algorithm for satisfiability problem

TL;DR

This paper demonstrates a quantum mechanical implementation of a DNA-inspired algorithm for solving the SAT problem using NMR, highlighting reduced complexity through quantum parallelism.

Contribution

It introduces a quantum gate-based approach to emulate DNA computation for SAT, enabling more efficient problem solving with fewer qubits.

Findings

Successful NMR experiment for a one-variable SAT problem

Quantum approach reduces computational complexity compared to DNA methods

Implementation of DNA-like gates in quantum systems

Abstract

DNA computation could in principle solve the satisfiability (SAT) problem due to the operations in parallel on extremely large numbers of strands. We demonstrate some quantum gates corresponding to the DNA ones, based on which an implementation of DNA algorithm for SAT problem is available by quantum mechanical way. Since quantum computation owns the favorable feature of operations in parallel on 2$^{n}$ states by using only n qubits, instead of 2$^{n}$ strands in DNA computation, computational complexity is much reduced in treating the SAT problem quantum mechanically. We take a three-clause SAT problem with two variables as an example, and carry out a NMR experiment for solving a one-variable SAT problem.