PT - JOURNAL ARTICLE
AU - Castagnoli, Giuseppe
AU - Finkelstein, David Ritz
TI - Quantum ground–state computation with kinematical gates
DP - 2003 Dec 08
TA - Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
PG - 3099--3108
VI - 459
IP - 2040
4099 - http://rspa.royalsocietypublishing.org/content/459/2040/3099.short
4100 - http://rspa.royalsocietypublishing.org/content/459/2040/3099.full
AB - 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.