Classical dissipative search of unstructured database
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Abstract
We propose a physical realization of the unstructured database search that works via classical, dissipative model of spherical spins. The database is implemented via spin-spin couplings, where the selected coupling refers to a larger ferromagnetic interaction between two selected spins. The low-temperature equilibrium of this model leads to magnetization strongly concentrated on the selected spins, which means that the search is complete. The search time refers to the relaxation time to equilibrium from a homogeneous initial state, and is described via Langevin equations. This time scales as ${\cal O}(M^a)$ with $a<1/2$, where $M$ is the database volume. This is faster than Grover's search, showing how a dissipative, classical analog computer can overcome the quantum unitary computer.