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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 present a systematic implementation of differential renormalization to all orders in perturbation theory. The method is applied to individual Feynman graphs written in coordinate space. After isolating every singularity which appears in a bare diagram, we define a subtraction procedure which consists in replacing the core of the singularity by its… (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)

- José I Latorre
- 2008

The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum systems. Further applications of the techniques based on matrix product states, some of their spin-off and their recent… (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)

- Akira Saitoh, A Kawaguchi, K Shimizu, Y Tokura, N Imoto, M C Bañuls +4 others
- 2015

There have been many studies on matrix-product-state (MPS) simulation of quantum computing for more than a decade [1, 2, 3, 4, 5, 6]. Although it is widely believed to be unlikely, it is still an open problem if a practical simulation of a powerful quantum algorithm like Shor's factoring algorithm is possible. This situation is owing to the fact that not… (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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