1,195 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, and
, asymptotic forms and can be defined in
terms of a new parameter ( is the Lanczos iteration and 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 .Comment: 10 pages REVTex3.0, 3 PS figure
Sensing of Fluctuating Nanoscale Magnetic Fields Using NV Centres in Diamond
New magnetometry techniques based on Nitrogen-Vacancy (NV) defects in diamond
allow for the imaging of static (DC) and oscillatory (AC) nanoscopic magnetic
systems. However, these techniques require accurate knowledge and control of
the sample dynamics, and are thus limited in their ability to image fields
arising from rapidly fluctuating (FC) environments. We show here that FC fields
place restrictions on the DC field sensitivity of an NV qubit magnetometer, and
that by probing the dephasing rate of the qubit in a magnetic FC environment,
we are able to measure fluctuation rates and RMS field strengths that would be
otherwise inaccessible with the use of DC and AC magnetometry techniques. FC
sensitivities are shown to be comparable to those of AC fields, whilst
requiring no additional experimental overheads or control over the sample.Comment: 5 pages, 4 figure
Effects of J-gate potential and interfaces on donor exchange coupling in the Kane quantum computer architecture
We calculate the electron exchange coupling for a phosphorus donor pair in
silicon perturbed by a J-gate potential and the boundary effects of the silicon
host geometry. In addition to the electron-electron exchange interaction we
also calculate the contact hyperfine interaction between the donor nucleus and
electron as a function of the varying experimental conditions. Donor
separation, depth of the P nuclei below the silicon oxide layer and J-gate
voltage become decisive factors in determining the strength of both the
exchange coupling and the hyperfine interaction - both crucial components for
qubit operations in the Kane quantum computer. These calculations were
performed using an anisotropic effective-mass Hamiltonian approach. The
behaviour of the donor exchange coupling as a function of the device parameters
varied provides relevant information for the experimental design of these
devices.Comment: 15 pages, 15 figures. Accepted for Journal of Physics: Condensed
Matte
Towards visualisation of central-cell-effects in scanning-tunnelling-microscope images of subsurface dopant qubits in silicon
Atomic-scale understanding of phosphorous donor wave functions underpins the
design and optimisation of silicon based quantum devices. The accuracy of
large-scale theoretical methods to compute donor wave functions is dependent on
descriptions of central-cell-corrections, which are empirically fitted to match
experimental binding energies, or other quantities associated with the global
properties of the wave function. Direct approaches to understanding such
effects in donor wave functions are of great interest. Here, we apply a
comprehensive atomistic theoretical framework to compute scanning tunnelling
microscopy (STM) images of subsurface donor wave functions with two
central-cell-correction formalisms previously employed in the literature. The
comparison between central-cell models based on real-space image features and
the Fourier transform profiles indicate that the central-cell effects are
visible in the simulated STM images up to ten monolayers below the silicon
surface. Our study motivates a future experimental investigation of the
central-cell effects via STM imaging technique with potential of fine tuning
theoretical models, which could play a vital role in the design of donor-based
quantum systems in scalable quantum computer architectures.Comment: Nanoscale 201
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 , 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
Scheme for direct measurement of a general two-qubit Hamiltonian
The construction of two-qubit gates appropriate for universal quantum
computation is of enormous importance to quantum information processing.
Building such gates is dependent on accurate knowledge of the interaction
dynamics between two qubit systems. This letter will present a systematic
method for reconstructing the full two-qubit interaction Hamiltonian through
experimental measures of concurrence. This not only gives a convenient method
for constructing two qubit quantum gates, but can also be used to
experimentally determine various Hamiltonian parameters in physical systems. We
show explicitly how this method can be employed to determine the first and
second order spin-orbit corrections to the exchange coupling in quantum dots.Comment: 4 Pages, 1 Figur
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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