Finding solutions to the integer case constraint satisfiability problem using Grover's algorithm

TL;DR

This paper demonstrates how Grover's algorithm can be applied to solve constraint satisfiability problems on quantum computers, showing a quadratic speedup and analyzing noise effects on current NISQ hardware.

Contribution

It introduces methods for implementing constraint satisfiability problems with Grover's algorithm on IBM quantum hardware and simulators, including noise analysis.

Findings

Quadratic speedup over classical algorithms.

Successful implementation on IBM Qiskit simulator.

Noise levels currently hinder successful execution on NISQ processors.

Abstract

Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high probability for several cases and are illustrated for the cases involving two variables for both 3- and 4-bit numbers. Methods are defined for inequality comparisons, and these are combined according to the form of the satisfiability formula, to form the oracle for the algorithm. The circuit is constructed using IBM Qiskit and is verified on an IBM simulator. It is further executed on one of the Noisy Intermediate-Scale Quantum (NISQ) processors from IBM on the cloud. Noise levels in the processor at present are found to be too high for successful execution. Running the algorithm on the simulator with a custom noise model lets us identify the noise threshold for successful execution.