153 research outputs found

    Analytic Solution for the Ground State Energy of the Extensive Many-Body Problem

    Full text link
    A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, αn(N)\alpha_n(N) and βn(N)\beta_n(N), asymptotic forms α(z)\alpha(z) and β(z)\beta(z) can be defined in terms of a new parameter zn/Nz\equiv n/N (nn is the Lanczos iteration and NN is the size of the system). By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given in general by E0=inf[α(z)2β(z)]{\cal E}_0 = {\rm inf}\,\left[\alpha(z) - 2\,\beta(z)\right].Comment: 10 pages REVTex3.0, 3 PS figure

    Optimising Matrix Product State Simulations of Shor's Algorithm

    Get PDF
    We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on rr, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.Comment: 8 pages, 2 figures, 2 tables. v2 using PDFLaTeX compiler. v3 to include extra references. v4 for publication in Quantu

    A multiplexed single electron transistor for application in scalable solid-state quantum computing

    Get PDF
    Single Electron Transistors (SETs) are nanoscale electrometers of unprecedented sensitivity, and as such have been proposed as read-out devices in a number of quantum computer architectures. We show that the functionality of a standard SET can be multiplexed so as to operate as both read-out device and control gate for a solid-state qubit. Multiplexing in this way may be critical in lowering overall gate densities in scalable quantum computer architectures.Comment: 3 pages 3 figure