  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.
