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.
Highlights
The satisfiability problem involving conjunctive inequalities is one of the widely encountered problems in database systems, forming a central part of several database problems
We consider conjunctive formulas of arithmetic inequalities of the form (X op C) and (X op Y ), where C is a constant in the domain of X; X and Y are attributes/variables from the integer domain; and op ∈ {} [8]
Motivated by the importance of finding solutions for conjunctive formulas in classical computation problems of practical importance, we explored the solution of such formulas in noisy intermediate-scale quantum (NISQ) devices
Summary
The satisfiability problem involving conjunctive inequalities is one of the widely encountered problems in database systems, forming a central part of several database problems. We consider conjunctive formulas of arithmetic inequalities of the form (X op C) and (X op Y ), where C is a constant in the domain of X; X and Y are attributes/variables from the integer domain; and op ∈ {} [8]. A conjunctive normal form is a product of sums or an and of ors Such a formula is satisfiable by an assignment of variables if it evaluates to true under the particular assignment. The general satisfiability problem of checking if a formula evaluates to true under any of the assignments of variables from its domain has been shown to be NP-hard in the integer case [9]. The aim is to find the solutions in addition to checking for satisfiability, i.e., searching for assignments of variables satisfying S. Vinod and Shaji: FINDING SOLUTIONS TO INTEGER CASE CONSTRAINT SATISFIABILITY PROBLEM
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