2,561 research outputs found
Error threshold estimates for surface code with loss of qubits
We estimate optimal thresholds for surface code in the presence of loss via
an analytical method developed in statistical physics. The optimal threshold
for the surface code is closely related to a special critical point in a
finite-dimensional spin glass, which is disordered magnetic material. We
compare our estimations to the heuristic numerical results reported in earlier
studies. Further application of our method to the depolarizing channel, a
natural generalization of the noise model, unveils its wider robustness even
with loss of qubits.Comment: 4 pages, 3 figures, 2 tables, title change
New varieties of Gowdy spacetimes
Gowdy spacetimes are generalized to admit two commuting spatial "local"
Killing vectors, and some new varieties of them are presented, which are all
closely related to Thurston's geometries. Explicit spatial compactifications,
as well as the boundary conditions for the metrics are given in a systematic
way. A short comment on an implication to their dynamics toward the initial
singularity is made.Comment: 13 pages with no figure. A reference added, and typos corrected. To
appear in J.Math.Phy
Fluctuation Theorems on Nishimori Line
The distribution of the performed work for spin glasses with gauge symmetry
is considered. With the aid of the gauge symmetry, which leads to the
exact/rigorous results in spin glasses, we find a fascinating relation of the
performed work as the fluctuation theorem. The integral form of the resultant
relation reproduces the Jarzynski-type equation for spin glasses we have
obtained. We show that similar relations can be established not only for the
distribution of the performed work but also that of the free energy of spin
glasses with gauge symmetry, which provides another interpretation of the phase
transition in spin glasses.Comment: 10 pages, and 1 figur
Locations of multicritical points for spin glasses on regular lattices
We present an analysis leading to precise locations of the multicritical
points for spin glasses on regular lattices. The conventional technique for
determination of the location of the multicritical point was previously derived
using a hypothesis emerging from duality and the replica method. In the present
study, we propose a systematic technique, by an improved technique, giving more
precise locations of the multicritical points on the square, triangular, and
hexagonal lattices by carefully examining relationship between two partition
functions related with each other by the duality. We can find that the
multicritical points of the Ising model are located at
on the square lattice, where means the probability of ,
at on the triangular lattice, and at on the
hexagonal lattice. These results are in excellent agreement with recent
numerical estimations.Comment: 17pages, this is the published version with some minnor corrections.
Previous title was "Precise locations of multicritical points for spin
glasses on regular lattices
Dynamics of compact homogeneous universes
A complete description of dynamics of compact locally homogeneous universes
is given, which, in particular, includes explicit calculations of Teichm\"uller
deformations and careful counting of dynamical degrees of freedom. We regard
each of the universes as a simply connected four dimensional spacetime with
identifications by the action of a discrete subgroup of the isometry group. We
then reduce the identifications defined by the spacetime isometries to ones in
a homogeneous section, and find a condition that such spatial identifications
must satisfy. This is essential for explicit construction of compact
homogenoeus universes. Some examples are demonstrated for Bianchi II, VI,
VII, and I universal covers.Comment: 32 pages with 2 figures (LaTeX with epsf macro package
Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices
Accuracy thresholds of quantum error correcting codes, which exploit
topological properties of systems, defined on two different arrangements of
qubits are predicted. We study the topological color codes on the hexagonal
lattice and on the square-octagonal lattice by the use of mapping into the spin
glass systems. The analysis for the corresponding spin glass systems consists
of the duality, and the gauge symmetry, which has succeeded in deriving
locations of special points, which are deeply related with the accuracy
thresholds of topological error correcting codes. We predict that the accuracy
thresholds for the topological color codes would be for the
hexagonal lattice and for the square-octagonal lattice,
where denotes the error probability on each qubit. Hence both of them are
expected to be slightly lower than the probability for the
quantum Gilbert-Varshamov bound with a zero encoding rate.Comment: 6 pages, 4 figures, the previous title was "Threshold of topological
color code". This is the published version in Phys. Rev.
Measurement-Based Quantum Computation on Symmetry Breaking Thermal States
We consider measurement-based quantum computation (MBQC) on thermal states of
the interacting cluster Hamiltonian containing interactions between the cluster
stabilizers that undergoes thermal phase transitions. We show that the
long-range order of the symmetry breaking thermal states below a critical
temperature drastically enhance the robustness of MBQC against thermal
excitations. Specifically, we show the enhancement in two-dimensional cases and
prove that MBQC is topologically protected below the critical temperature in
three-dimensional cases. The interacting cluster Hamiltonian allows us to
perform MBQC even at a temperature an order of magnitude higher than that of
the free cluster Hamiltonian.Comment: 8 pages, 7 figure
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