1,835 research outputs found
Designing Robust Unitary Gates: Application to Concatenated Composite Pulse
We propose a simple formalism to design unitary gates robust against given
systematic errors. This formalism generalizes our previous observation [Y.
Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing
dynamical phase in some composite gates is essential to suppress amplitude
errors. By employing our formalism, we naturally derive a new composite unitary
gate which can be seen as a concatenation of two known composite unitary
operations. The obtained unitary gate has high fidelity over a wider range of
the error strengths compared to existing composite gates.Comment: 7 pages, 4 figures. Major revision: improved presentation in Sec. 3,
references and appendix adde
Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace
When the environmental disturbace to a quantum system has a wavelength much
larger than the system size, all qubits localized within a small area are under
action of the same error operators. Noiseless subsystem and decoherence free
subspace are known to correct such collective errors. We construct simple
quantum circuits, which implement these collective error correction codes, for
a small number of physical qubits. A single logical qubit is encoded with
and , while two logical qubits are encoded with . The recursive
relations among the subspaces employed in noiseless subsystem and decoherence
free subspace play essential r\^oles in our implementation. The recursive
relations also show that the number of gates required to encode logical
qubits increases linearly in .Comment: 9 pages, 3 figure
Improved perfluoroalkylether fluid development
The feasibility of transforming a commercial linear perfluoroalkylether fluid into a material stable in the presence of metals and metal alloys in oxidizing atmospheres at 300 C without the loss of the desirable viscosity temperature characteristics was determined. The approach consisted of thermal oxidative treatment in the presence of catalyst to remove weak links, followed by transformation of the created functional groups into phospha-s-triazine linkages. It it found that the experimental material obtained in 66% yield from the commercial fluid exhibits, over an 8 hr period at 300 C in the presence of Ti(4Al, 4Mn) alloy, thermal oxidative stability better by a factor of 2.6x1000 based on volatiles evolved than the commercial product. The viscosity and molecular weight of the developed fluid are unchanged and are essentially identical with the commercial material. No metal corrosion occurs with the experimental fluid at 300 C
Potential formulation of the dispersion relation for a uniform, magnetized plasma with stationary ions in terms of a vector phasor
The derivation of the helicon dispersion relation for a uniform plasma with
stationary ions subject to a constant background magnetic field is reexamined
in terms of the potential formulation of electrodynamics. Under the same
conditions considered by the standard derivation, the nonlinear self-coupling
between the perturbed electron flow and the potential it generates is
addressed. The plane wave solution for general propagation vector is determined
for all frequencies and expressed in terms of a vector phasor. The behavior of
the solution as described in vacuum units depends upon the ratio of
conductivity to the magnitude of the background field. Only at low conductivity
and below the cyclotron frequency can significant propagation occur as
determined by the ratio of skin depth to wavelength.Comment: 10 pages, 6 figures, major revision, final version, to appear in Po
Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model
We investigate the potential energy surface of a phi^4 model with infinite
range interactions. All stationary points can be uniquely characterized by
three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_-
= 1, provided that the interaction strength mu is smaller than a critical
value. The saddle index n_s is equal to alpha_0 and its distribution function
has a maximum at n_s^max = 1/3. The density p(e) of stationary points with
energy per particle e, as well as the Euler characteristic chi(e), are singular
at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu)
\neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per
particle at the thermodynamic phase transition point T_c. This proves that
previous claims that the topological and thermodynamic transition points
coincide is not valid, in general. Both types of singularities disappear for H
\neq 0. The average saddle index bar{n}_s as function of e decreases
monotonically with e and vanishes at the ground state energy, only. In
contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is
given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 >
upsilon_0, the ground state energy.Comment: 9 PR pages, 6 figure
Geometric Aspects of Composite Pulses
Unitary operations acting on a quantum system must be robust against
systematic errors in control parameters for reliable quantum computing.
Composite pulse technique in nuclear magnetic resonance (NMR) realises such a
robust operation by employing a sequence of possibly poor quality pulses. In
this article, we demonstrate that two kinds of composite pulses, one
compensates for a pulse length error in a one-qubit system and the other
compensates for a J-coupling error in a twoqubit system, have vanishing
dynamical phase and thereby can be seen as geometric quantum gates, which
implement unitary gates by the holonomy associated with dynamics of cyclic
vectors defined in the text.Comment: 20 pages, 4 figures. Accepted for publication in Philosophical
Transactions of the Royal Society
Soldered Bundle Background for the De Sitter Top
We prove that the mathematical framework for the de Sitter top system is the
de Sitter fiber bundle. In this context, the concept of soldering associated
with a fiber bundle plays a central role. We comment on the possibility that
our formalism may be of particular interest in different contexts including
MacDowell-Mansouri theory, two time physics and oriented matroid theory.Comment: 12 pages, Latex; some improvements introduced, reference added, typos
correcte
Kinematic Orbits and the Structure of the Internal Space for Systems of Five or More Bodies
The internal space for a molecule, atom, or other n-body system can be
conveniently parameterised by 3n-9 kinematic angles and three kinematic
invariants. For a fixed set of kinematic invariants, the kinematic angles
parameterise a subspace, called a kinematic orbit, of the n-body internal
space. Building on an earlier analysis of the three- and four-body problems, we
derive the form of these kinematic orbits (that is, their topology) for the
general n-body problem. The case n=5 is studied in detail, along with the
previously studied cases n=3,4.Comment: 38 pages, submitted to J. Phys.
A cosmological model in Weyl-Cartan spacetime: I. Field equations and solutions
In this first article of a series on alternative cosmological models we
present an extended version of a cosmological model in Weyl-Cartan spacetime.
The new model can be viewed as a generalization of a model developed earlier
jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e.
torsion and nonmetricity , are proportional to
the Weyl 1-form. The hypermomentum depends on our
ansatz for the nonmetricity and vice versa. We derive the explicit form of the
field equations for different cases and provide solutions for a broad class of
parameters. We demonstrate that it is possible to construct models in which the
non-Riemannian quantities die out with time. We show how our model fits into
the more general framework of metric-affine gravity (MAG).Comment: 22 pages, 2 figures, uses IOP preprint styl
Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
One of the defining properties of the conventional three-dimensional
("-", or "spin-orbit"-) topological insulator is its
characteristic magnetoelectric effect, as described by axion electrodynamics.
In this paper, we discuss an analogue of such a magnetoelectric effect in the
thermal (or gravitational) and the magnetic dipole responses in all symmetry
classes which admit topologically non-trivial insulators or superconductors to
exist in three dimensions. In particular, for topological superconductors (or
superfluids) with time-reversal symmetry which lack SU(2) spin rotation
symmetry (e.g. due to spin-orbit interactions), such as the B phase of He,
the thermal response is the only probe which can detect the non-trivial
topological character through transport. We show that, for such topological
superconductors, applying a temperature gradient produces a thermal- (or mass-)
surface current perpendicular to the thermal gradient. Such charge, thermal, or
magnetic dipole responses provide a definition of topological insulators and
superconductors beyond the single-particle picture. Moreover we find, for a
significant part of the 'ten-fold' list of topological insulators found in
previous work in the absence of interactions, that in general dimensions the
effective field theory describing the space-time responses is governed by a
field theory anomaly. Since anomalies are known to be insensitive to whether
the underlying fermions are interacting or not, this shows that the
classification of these topological insulators is robust to adiabatic
deformations by interparticle interactions in general dimensionality. In
particular, this applies to symmetry classes DIII, CI, and AIII in three
spatial dimensions, and to symmetry classes D and C in two spatial dimensions.Comment: 16 pages, 2 figure
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