47 research outputs found
Single-step controlled-NOT logic from any exchange interaction
A self-contained approach to studying the unitary evolution of coupled qubits
is introduced, capable of addressing a variety of physical systems described by
exchange Hamiltonians containing Rabi terms. The method automatically
determines both the Weyl chamber steering trajectory and the accompanying local
rotations. Particular attention is paid to the case of anisotropic exchange
with tracking controls, which is solved analytically. It is shown that, if
computational subspace is well isolated, any exchange interaction can always
generate high-fidelity, single-step controlled-NOT (CNOT) logic, provided that
both qubits can be individually manipulated. The results are then applied to
superconducting qubit architectures, for which several CNOT gate
implementations are identified. The paper concludes with consideration of two
CNOT gate designs having high efficiency and operating with no significant
leakage to higher-lying non-computational states.Comment: 12 pages + 7 figures; revised version; title change
Derivation of the Lorentz transformation without the use of Einstein's second postulate
Derivation of the Lorentz transformation without the use of Einstein's Second
Postulate is provided along the lines of Ignatowsky, Terletskii, and others.
This is a write-up of the lecture first delivered in PHYS 4202 E&M class during
the Spring semester of 2014 at the University of Georgia. The main motivation
for pursuing this approach was to develop a better understanding of why the
faster-than-light neutrino controversy (OPERA experiment, 2011) was much ado
about nothing.Comment: 8 pages, 6 figures; introductory special relativity; lecture note
Tunneling out of metastable vacuum in a system consisting of two capacitively coupled phase qubits
Using a powerful combination of Coleman's instanton technique and the method
of Banks and Bender, the exponential factor for the zero temperature rate of
tunneling out of metastable vacuum in a system of two identical capacitively
coupled phase qubits is calculated in closed form to second order in asymmetry
parameter for a special case of intermediate coupling C=C_J/2.Comment: 10 pages, 5 figures (select PostScript to download Fig. 1). Corrected
version, to appear in PR