Quantum Algorithm Processors to Reveal Hamiltonian Cycles

Abstract

Quantum computer versus quantum algorithm processor in CMOS are compared to find (in parallel) all Hamiltonian cycles in a graph with m edges and n vertices, each represented by k bits. A quantum computer uses quantum states analogous to CMOS registers. With efficient initialization, number of CMOS registers is proportional to (n-1)! Number of qubits in a quantum computer is approximately proportional to kn+2mn in the approach below. Using CMOS, the bits per register is about proportional to kn, which is less since bits can be irreversibly reset. In either concept, number of gates, or operations to identify Hamiltonian cycles is proportional to kmn. However, a quantum computer needs an additional exponentially large number of operations to accomplish a probabilistic readout. In contrast, CMOS is deterministic and readout is comparable to ordinary memory.