698 research outputs found
Adiabatic Gate Teleportation
The difficulty in producing precisely timed and controlled quantum gates is a
significant source of error in many physical implementations of quantum
computers. Here we introduce a simple universal primitive, adiabatic gate
teleportation, which is robust to timing errors and many control errors and
maintains a constant energy gap throughout the computation above a degenerate
ground state space. Notably this construction allows for geometric robustness
based upon the control of two independent qubit interactions. Further, our
piecewise adiabatic evolution easily relates to the quantum circuit model,
enabling the use of standard methods from fault-tolerance theory for
establishing thresholds.Comment: 4 pages, 1 figure, with additional 3 pages and 2 figures in an
appendix. v2 Refs added. Video abstract available at
http://www.quantiki.org/video_abstracts/0905090
The Stability of Quantum Concatenated Code Hamiltonians
Protecting quantum information from the detrimental effects of decoherence
and lack of precise quantum control is a central challenge that must be
overcome if a large robust quantum computer is to be constructed. The
traditional approach to achieving this is via active quantum error correction
using fault-tolerant techniques. An alternative to this approach is to engineer
strongly interacting many-body quantum systems that enact the quantum error
correction via the natural dynamics of these systems. Here we present a method
for achieving this based on the concept of concatenated quantum error
correcting codes. We define a class of Hamiltonians whose ground states are
concatenated quantum codes and whose energy landscape naturally causes quantum
error correction. We analyze these Hamiltonians for robustness and suggest
methods for implementing these highly unnatural Hamiltonians.Comment: 18 pages, small corrections and clarification
Trans-Planckian Tail in a Theory with a Cutoff
Trans-planckian frequencies can be mimicked outside a black-hole horizon as a
tail of an exponentially large amplitude wave that is mostly hidden behind the
horizon. The present proposal requires implementing a final state condition.
This condition involves only frequencies below the cutoff scale. It may be
interpreted as a condition on the singularity. Despite the introduction of the
cutoff, the Hawking radiation is restored for static observers. Freely falling
observers see empty space outside the horizon, but are "heated" as they cross
the horizon.Comment: 17 pages, RevTe
The hidden horizon and black hole unitarity
We motivate through a detailed analysis of the Hawking radiation in a
Schwarzschild background a scheme in accordance with quantum unitarity. In this
scheme the semi-classical approximation of the unitary quantum - horizonless -
black hole S-matrix leads to the conventional description of the Hawking
radiation from a classical black hole endowed with an event horizon. Unitarity
is borne out by the detailed exclusive S-matrix amplitudes. There, the fixing
of generic out-states, in addition to the in-state, yields in asymptotic
Minkowski space-time saddle-point contributions which are dominated by
Planckian metric fluctuations when approaching the Schwarzschild radius. We
argue that these prevent the corresponding macroscopic "exclusive backgrounds"
to develop an event horizon. However, if no out-state is selected, a distinct
saddle-point geometry can be defined, in which Planckian fluctuations are
tamed. Such "inclusive background" presents an event horizon and constitutes a
coarse-grained average over the aforementioned exclusive ones. The classical
event horizon appears as a coarse-grained structure, sustaining the
thermodynamic significance of the Bekenstein-Hawking entropy. This is
reminiscent of the tentative fuzzball description of extremal black holes: the
role of microstates is played here by a complete set of out-states. Although
the computations of unitary amplitudes would require a detailed theory of
quantum gravity, the proposed scheme itself, which appeals to the metric
description of gravity only in the vicinity of stationary points, does not.Comment: 29 pages, 4 figures. Typos corrected. Two footnotes added (footnotes
3 and 5
Observable Dirac-type singularities in Berry's phase and the monopole
The physical reality and observability of 2n\pi Berry phases, as opposed to
the usually considered modulo 2\pi topological phases is demonstrated with the
help of computer simulation of a model adiabatic evolution whose parameters are
varied along a closed loop in the parameter space. Using the analogy of Berry's
phase with the Dirac monopole, it is concluded that an interferometer loop
taken around a magnetic monopole of strength n/2 yields an observable 2n\pi
phase shift, where n is an integer. An experiment to observe the effect is
proposed.Comment: 12 pages Latex, 3 postscript figures; submitted to Physical Review
Letters 15 September 2000; revised 19 November 200
Pre- and post-selection, weak values, and contextuality
By analyzing the concept of contextuality (Bell-Kochen-Specker) in terms of
pre-and-post-selection (PPS), it is possible to assign definite values to
observables in a new and surprising way. Physical reasons are presented for
restrictions on these assignments. When measurements are performed which do not
disturb the pre- and post-selection (i.e. weak measurements), then novel
experimental aspects of contextuality can be demonstrated including a proof
that every PPS-paradox with definite predictions implies contextuality. Certain
results of these measurements (eccentric weak values with e.g. negative values
outside the spectrum), however, cannot be explained by a "classical-like"
hidden variable theory.Comment: Identical content; stream-lined verbal presentatio
Correspondences and Quantum Description of Aharonov-Bohm and Aharonov-Casher Effects
We establish systematic consolidation of the Aharonov-Bohm and
Aharonov-Casher effects including their scalar counterparts. Their formal
correspondences in acquiring topological phases are revealed on the basis of
the gauge symmetry in non-simply connected spaces and the adiabatic condition
for the state of magnetic dipoles. In addition, investigation of basic two-body
interactions between an electric charge and a magnetic dipole clarifies their
appropriate relative motions and discloses physical interrelations between the
effects. Based on the two-body interaction, we also construct an exact
microscopic description of the Aharonov-Bohm effect, where all the elements are
treated on equal footing, i.e., magnetic dipoles are described
quantum-mechanically and electromagnetic fields are quantized. This microscopic
analysis not only confirms the conventional (semiclassical) results and the
topological nature but also allows one to explore the fluctuation effects due
to the precession of the magnetic dipoles with the adiabatic condition relaxed
Topological phase due to electric dipole moment and magnetic monopole interaction
We show that there is an anologous Aharonov-Casher effect on a neutral
particle with electric dipole moment interacting with a magnetic filed produced
by magnetic monopoles.Comment: 8 page
Weak Values with Decoherence
The weak value of an observable is experimentally accessible by weak
measurements as theoretically analyzed by Aharonov et al. and recently
experimentally demonstrated. We introduce a weak operator associated with the
weak values and give a general framework of quantum operations to the W
operator in parallel with the Kraus representation of the completely positive
map for the density operator. The decoherence effect is also investigated in
terms of the weak measurement by a shift of a probe wave function of continuous
variable. As an application, we demonstrate how the geometric phase is affected
by the bit flip noise.Comment: 17 pages, 3 figure
Following microscopic motion in a two dimensional glass-forming binary fluid
The dynamics of a binary mixture of large and small discs are studied at
temperatures approaching the glass transition using an analysis based on the
topology of the Voronoi polygon surrounding each atom. At higher temperatures
we find that dynamics is dominated by fluid-like motion that involves particles
entering and exiting the nearest-neighbour shells of nearby particles. As the
temperature is lowered, the rate of topological moves decreases and motion
becomes localised to regions of mixed pentagons and heptagons. In addition we
find that in the low temperature state particles may translate significant
distances without undergoing changes in their nearest neig hbour shell. These
results have implications for dynamical heterogeneities in glass forming
liquids.Comment: 12 pages, 7 figure
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