Quantum Algorithms for Unate and Binate Covering Problems with Application to Finite State Machine Minimization

Covering problems find applications in many areas of computer science and engineering, such that numerous combinatorial problems can be formulated as covering problems. Combinatorial optimization problems are generally NPhard problems that require an extensive search to find the optimal solution. Exploiting the benefits of quantum computing, we present a quantum oracle design for covering problems, taking advantage of Grover’s search algorithm to achieve quadratic speedup. This paper also discusses applications of the quantum counter in unate covering problems and binate covering problems with some important practical applications, such as finding prime implicants of a Boolean function, implication graphs, and minimization of incompletely specified Finite State Machines

Quantum Algorithm for Variant Maximum Satisfiability

In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover’s algorithm with a new block called quantum counter in the oracle circuit. The proposed circuit can be adapted for various forms of satisfiability expressions and several satisfiability-like problems. Using the quantum counter and mirrors for SAT terms reduces the need for ancilla qubits and realizes a large Toffoli gate that is then not needed. Our circuit reduces the number of ancilla qubits for the terms T of the Boolean function from T of ancilla qubits to ≈⌈log2⁡T⌉+1. We analyzed and compared the quantum cost of the traditional oracle design with our design which gives a low quantum cost

Grover-based Ashenhurst-Curtis Decomposition Using Quantum Language Quipper

Functional decomposition plays a key role in several areas such as system design, digital circuits, database systems, and Machine Learning. This paper presents a novel quantum computing approach based on Grover’s search algorithm for a generalized Ashenhurst-Curtis decomposition. The method models the decomposition problem as a search problem and constructs the oracle circuit based on the set-theoretic partition algebra. A hybrid quantum-based algorithm takes advantage of the quadratic speedup achieved by Grover’s search algorithm with quantum oracles for finding the minimum-cost decomposition. The method is implemented and simulated in the quantum programming language Quipper. This work constitutes the first attempt to apply quantum computing to functional decompositio