Quantum ground–state computation with kinematical gates
Giuseppe Castagnoli, David Finkelstein · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2003
We develop a computation model for solving Boolean networks that implements wires dynamically through quantum ground–state computation and implements gates kinematically through identities following from angular–momentum algebra and statistics. The gates are extra–dynamical in the sense that they contribute nothing to the Hamiltonian and hold as constants of the motion; only the wires are dynamical. Just as a spin ½ makes an ideal 1–bit memory element, a spin 1 makes an ideal 3–bit gate. Such gates cost no computation time; relaxing the wires alone solves the network. We compare computation time heuristically with that of an easier Boolean network where all the gate constraints are simply removed. This computation model is robust with respect to decoherence and yields a generalized quantum speed–up for all NP (non–deterministic–polynomial) problems. We give an Ising model for such a logical network composed of spins of 1 with bilinear couplings.