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

A Logical Approach to Efficient Max-SAT solving

Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in finding efficient solving techniques. Most of this work focus on the computation of good quality lower bounds to be used within a branch and bound DPLL-like algorithm. Most often, these lower bounds are described in a procedural way. Because of that, it is difficult to realize the {\em logic} that is behind. In this paper we introduce an original framework for Max-SAT that stresses the parallelism with classical SAT. Then, we extend the two basic SAT solving techniques: {\em search} and {\em inference}. We show that many algorithmic {\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in {\em logic} terms with our framework in a unified manner. Besides, we introduce an original search algorithm that performs a restricted amount of {\em weighted resolution} at each visited node. We empirically compare our algorithm with a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-sat evaluation ever reported, show that our algorithm is generally orders of magnitude faster than any competitor

Quantum Search Algorithms for Constraint Satisfaction and Optimization Problems Using Grover\u27s Search and Quantum Walk Algorithms with Advanced Oracle Design

The field of quantum computing has emerged as a powerful tool for solving and optimizing combinatorial optimization problems. To solve many real-world problems with many variables and possible solutions for constraint satisfaction and optimization problems, the required number of qubits of scalable hardware for quantum computing is the bottleneck in the current generation of quantum computers. In this dissertation, we will demonstrate advanced, scalable building blocks for the quantum search algorithms that have been implemented in Grover\u27s search algorithm and the quantum walk algorithm. The scalable building blocks are used to reduce the required number of qubits in the design. The proposed architecture effectively scales and optimizes the number of qubits needed to solve large problems with a limited number of qubits. Thus, scaling and optimizing the number of qubits that can be accommodated in quantum algorithm design directly reflect on performance. Also, accuracy is a key performance metric related to how accurately one can measure quantum states. The search space of quantum search algorithms is traditionally created by using the Hadamard operator to create superposition. However, creating superpositions for problems that do not need all superposition states decreases the accuracy of the measured states. We present an efficient quantum circuit design that the user has control over to create the subspace superposition states for the search space as needed. Using only the subspace states as superposition states of the search space will increase the rate of correct solutions. In this dissertation, we will present the implementation of practical problems for Grover\u27s search algorithm and quantum walk algorithm in logic design, logic puzzles, and machine learning problems such as SAT, MAX-SAT, XOR-SAT, and like SAT problems in EDA, and mining frequent patterns for association rule mining