28,453 research outputs found
Appearance and Stability of Anomalously Fluctuating States in Shor's Factoring Algorithm
We analyze quantum computers which perform Shor's factoring algorithm, paying
attention to asymptotic properties as the number L of qubits is increased.
Using numerical simulations and a general theory of the stabilities of
many-body quantum states, we show the following: Anomalously fluctuating states
(AFSs), which have anomalously large fluctuations of additive operators, appear
in various stages of the computation. For large L, they decohere at anomalously
great rates by weak noises that simulate noises in real systems. Decoherence of
some of the AFSs is fatal to the results of the computation, whereas
decoherence of some of the other AFSs does not have strong influence on the
results of the computation. When such a crucial AFS decoheres, the probability
of getting the correct computational result is reduced approximately
proportional to L^2. The reduction thus becomes anomalously large with
increasing L, even when the coupling constant to the noise is rather small.
Therefore, quantum computations should be improved in such a way that all AFSs
appearing in the algorithms do not decohere at such great rates in the existing
noises.Comment: 11 figures. A few discussions were added in verion 2. Version 3 is
the SAME as version 2; only errors during the Web-upload were fixed. Version
4 is the publised version, in which several typos are fixed and the reference
list is update
Thermal Pure Quantum States at Finite Temperature
An equilibrium state can be represented by a pure quantum state, which we
call a thermal pure quantum (TPQ) state. We propose a new TPQ state and a
simple method of obtaining it. A single realization of the TPQ state suffices
for calculating all statistical-mechanical properties, including correlation
functions and genuine thermodynamic variables, of a quantum system at finite
temperature.Comment: 5 pages, 3 figures, A shortened version will appear in Phys. Rev.
Let
Cluster Property and Robustness of Ground States of Interacting Many Bosons
We study spatial correlation functions of local operators of interacting many
bosons confined in a box of a large, but volume V, for various `ground states'
whose energy densities are almost degenerate. The ground states include the
coherent state of interacting bosons (CSIB), the number state of interacting
bosons (NSIB), and the number-phase squeezed state of interacting bosons, which
interpolates between the CSIB and NSIB. It was shown previously that only the
CSIB is robust (i.e., does not decohere for a macroscopically long time)
against the leakage of bosons into an environment. We show that for the CSIB
the spatial correlation of any local operators A(r) and B(r') (which are
localized around r and r', respectively) vanishes as |r - r' | \sim V^{1/3} \to
\infty, i.e., the CSIB has the `cluster property.' In contrast, the other
ground states do not possess the cluster property. Therefore, we have
successfully shown that the robust state has the cluster property. This ensures
the consistency of the field theory of bosons with macroscopic theories.Comment: We have replaced the manuscript in order to update the reference list
and to fix typos. (5 pages, no figures) In the final manuscript, a few
sentences have added for more detailed explanation. Journal PDF at
http://jpsj.jps.or.jp/journal/JPSJ-71-1.htm
Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces
In this paper, we generalize Walcher's computation of the open Gromov-Witten
invariants of the quintic hypersurface to Fano and Calabi-Yau projective
hypersurfaces. Our main tool is the open virtual structure constants. We also
propose the generalized mirror transformation for the open Gromov-Witten
invariants, some parts of which are proven explicitly. We also discuss possible
modification of the multiple covering formula for the case of higher
dimensional Calabi-Yau manifolds. The generalized disk invariants for some
Calabi-Yau and Fano manifolds are shown and they are certainly integers after
re-summation by the modified multiple covering formula. This paper also
contains the direct integration method of the period integrals for higher
dimensional Calabi-Yau hypersurfaces in the appendix.Comment: 24pages, 5figure
Microscopic Description of Nuclear Wobbling Motion -- Rotation of traxially deformed nuclei --
The nuclear wobbling motion in the Lu region is studied by the microscopic
cranked mean-field plus RPA method. The Woods-Saxon potential is used as a
mean-field with a new parameterization which gives reliable description of
rapidly rotating nuclei. The prescription of symmetry-preserving residual
interaction makes the calculation of the RPA step parameter-free, and we find
the wobbling-like RPA solution if the triaxial deformation of the mean-field is
suitably chosen. It is shown that the calculated out-of-band of the
wobbling-like solution depends on the triaxial deformation in the same way as
in the macroscopic rotor model, and can be used to probe the triaxiality of the
nuclear mean-field.Comment: 10 pages, 8 figures, talk at International Conference on Nuclear
Structure Physics, Shanghai, June 200
A model study of cooperative binding of ionic surfactants to oppositely charged flexible polyions
A novel statistical model for the cooperative binding of monomeric ligands to
a linear lattice is developed to study the interaction of ionic surfactant
molecules with flexible polyion chain in dilute solution. Electrostatic binding
of a ligand to a site on the polyion and hydrophobic associations between the
neighboring bound ligands are assumed to be stochastic processes. Ligand
association separated by several lattice points within defined width is
introduced for the flexible polyion. Model calculations by the Monte Carlo
method are carried out to investigate the binding behavior. The hypothesis on
the ligand association and its width on the chain are of importance in
determining critical aggregation concentration and binding isotherm. The
results are reasonable for the interpretations of several surfactant-flexible
polyion binding experiments. The implications of the approach are presented and
discussed.Comment: 11 pages, 9 figure
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