Performance of a measurement-driven 'adiabatic-like' quantum 3-SAT solver

Abstract: I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a non-orthogonal basis. If the basis slowly evolves then there is a strong analogy to adiabatic quantum computing, although the approach is entirely circuit-based. To solve a 3-SAT problem of n variables requires a quantum register of $n$ qubits, or more precisely rebits i.e. qubits whose phase need only be real. For cases of up to n=26 qubits numerical simulations indicate that the algorithm runs fast, outperforming Grover's algorithm and having a scaling with n that is superior to the best reported classical algorithms. There are indications that the approach has an inherent robustness versus imperfections in the elementary operations.