153 research outputs found

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

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, $\alpha_n(N)$ and
$\beta_n(N)$, asymptotic forms $\alpha(z)$ and $\beta(z)$ can be defined in
terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ 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 ${\cal E}_0 = {\rm inf}\,\left[\alpha(z) -
2\,\beta(z)\right]$.Comment: 10 pages REVTex3.0, 3 PS figure

### Optimising Matrix Product State Simulations of Shor's Algorithm

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 $r$, 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

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

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