1,785 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
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
Modal expansions and non-perturbative quantum field theory in Minkowski space
We introduce a spectral approach to non-perturbative field theory within the
periodic field formalism. As an example we calculate the real and imaginary
parts of the propagator in 1+1 dimensional phi^4 theory, identifying both
one-particle and multi-particle contributions. We discuss the computational
limits of existing diagonalization algorithms and suggest new quasi-sparse
eigenvector methods to handle very large Fock spaces and higher dimensional
field theories.Comment: new material added, 12 pages, 6 figure
Quantum computing with nearest neighbor interactions and error rates over 1%
Large-scale quantum computation will only be achieved if experimentally
implementable quantum error correction procedures are devised that can tolerate
experimentally achievable error rates. We describe a quantum error correction
procedure that requires only a 2-D square lattice of qubits that can interact
with their nearest neighbors, yet can tolerate quantum gate error rates over
1%. The precise maximum tolerable error rate depends on the error model, and we
calculate values in the range 1.1--1.4% for various physically reasonable
models. Even the lowest value represents the highest threshold error rate
calculated to date in a geometrically constrained setting, and a 50%
improvement over the previous record.Comment: 4 pages, 8 figure
Measurable quantum geometric phase from a rotating single spin
We demonstrate that the internal magnetic states of a single nitrogen-vacancy
defect, within a rotating diamond crystal, acquire geometric phases. The
geometric phase shift is manifest as a relative phase between components of a
superposition of magnetic substates. We demonstrate that under reasonable
experimental conditions a phase shift of up to four radians could be measured.
Such a measurement of the accumulation of a geometric phase, due to macroscopic
rotation, would be the first for a single atom-scale quantum system.Comment: 5 pages, 2 figures: Accepted for publication in Physical Review
Letter
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
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