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The pixel values of an image can be casted into a real ket of a Hilbert space using an appropriate block structured addressing. The resulting state can then be rewritten in terms of its matrix product state representation in such a way that quantum entanglement corresponds to classical correlations between different coarse-grained textures. A truncation of… (More)

We construct a tensor network that delivers an unnormalized quantum state whose coefficients are the solutions to a given instance of the 3SAT problem. The tensor network contraction that corresponds to the norm of the state counts the number of solutions to the instance. It follows that exact contractions of tensor networks are in the #P-complete… (More)

- Stefano Carrazza, Stefano Forte, Zahari Kassabov, José Ignacio Latorre, Juan Rojo
- 2015

We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a… (More)

In recent years, we have witnessed an explosion of experimental tools by which quantum systems can be manipulated in a controlled and coherent way. One of the most important goals now is to build quantum simulators, which would open up the possibility of exciting experiments probing various theories in regimes that are not achievable under normal lab… (More)

We propose a quantum circuit that creates a pure state corresponding to the quantum superposition of all prime numbers less than 2 n , where n is the number of qubits of the register. This Prime state can be built using Grover's algorithm, whose oracle is a quantum implementation of the classical Miller-Rabin primality test. The Prime state is highly… (More)

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