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Boolean satisfiability (SAT) solving is a fundamental problem in computer science. Finding efficient algorithms for SAT solving has broad implications in many areas of computer science and beyond. Quantum SAT solvers have been proposed in the literature based on Grover's algorithm. Although existing quantum SAT solvers can consider all possible inputs at once, they evaluate each clause in the formula one by one sequentially, making the time complexity O(m) -- linear to the number of clauses m -- per Grover iteration. In this work, we develop a parallel quantum SAT solver, which reduces the time complexity in each iteration from linear time O(m) to constant time O(1) by utilising extra entangled qubits. To further improve the scalability of our solution in case of extremely large problems, we develop a distributed version of the proposed parallel SAT solver based on quantum teleportation such that the total qubits required are shared and distributed among a set of quantum computers (nodes), and the quantum SAT solving is accomplished collaboratively by all the nodes. We have proved the correctness of our approaches and demonstrated them in simulations.

Given a formula $F$ of satisfiability modulo theory (SMT), the classical SMT solver tries to (1) abstract $F$ as a Boolean formula $F_B$, (2) find a Boolean solution to $F_B$, and (3) check whether the Boolean solution is consistent with the theory. Steps~{(2)} and (3) may need to be performed back and forth until a consistent solution is found. In this work, we develop a quantum SMT solver for the bit-vector theory. With the characteristic of superposition in quantum system, our solver is able to consider all the inputs simultaneously and check their consistency between Boolean and the theory domains in one shot.