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- W2337004845 abstract "We construct a planar vertex model that encodes the result of a universal reversible classical computation in its ground state. The approach involves Boolean variables (spins) placed on links of a two-dimensional lattice, with vertices representing logic gates. Large short-ranged interactions between at most two spins implement the operation of each gate. The lattice is anisotropic with one direction corresponding to time, and with transverse boundaries storing the computation's input and output. Our approach tackles both fixed input computations that proceed forward in computational time, but also, more interestingly, problems in which only partial information about both inputs and outputs is known. In that case, reaching the ground state requires flow of information both forwards and backwards across the lattice, processes that are naturally built into our mapping of reversible computations into the vertex model. This allows us to tackle a subclass of the Circuit Satisfiability (CSAT) problem and to solve factoring problems by using multiplication circuits with polynomial depth. While we show that the model displays no finite temperature phase transitions, independent of circuit, the computational complexity is encoded in the scaling of the relaxation rate into the ground state with the system size. To explore faster relaxation routes, we construct an explicit mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating a novel approach to reversible classical computation based on state-of-the-art implementations of quantum annealing." @default.
- W2337004845 created "2016-06-24" @default.
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- W2337004845 date "2016-04-18" @default.
- W2337004845 modified "2023-09-27" @default.
- W2337004845 title "Solving Classical Computational Problems by Annealing a Planar Quantum Vertex Model" @default.
- W2337004845 hasPublicationYear "2016" @default.
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