3,556 research outputs found
A first-order purely frame-formulation of General Relativity
In the gauge natural bundle framework a new space is introduced and a
first-order purely frame-formulation of General Relativity is obtained.Comment: 9 Pages, Submitted to Classical and Quantum Gravit
Kitaev's Z_d-Codes Threshold Estimates
We study the quantum error correction threshold of Kitaev's toric code over
the group Z_d subject to a generalized bit-flip noise. This problem requires
novel decoding techniques, and for this purpose we generalize the
renormalization group method we previously introduced for Z_2 topological
codes.Comment: 5 pages, 5 figure
General Relativity as a constrained Gauge Theory
The formulation of General Relativity presented in math-ph/0506077 and the
Hamiltonian formulation of Gauge theories described in math-ph/0507001 are made
to interact. The resulting scheme allows to see General Relativity as a
constrained Gauge theory.Comment: 8 Pages, Submitted to International Journal of Geometric Methods in
Modern Physic
Critical exact solutions for self-gravitating Dirac fields
We consider the Einstein-Dirac field equations describing a self-gravitating
massive neutrino, looking for axially-symmetric exact solutions; in the search
of general solutions, we find some that are specific and which have critical
features, such as the fact that the space-time curvature turns out to be flat
and the spinor field gives rise to a vanishing bi-linear scalar
with non-vanishing bi-linear pseudo-scalar
: because in quantum field theory general
computational methods are built on plane-wave solutions, for which bi-linear
pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the
solutions we found cannot be treated with the usual machinery of quantum field
theory. This means that for the Einstein-Dirac system there exist admissible
solutions which nevertheless cannot be quantized with the common prescriptions;
we regard this situation as yet another issue of tension between Einstein
gravity and quantum principles. Possible ways to quench this tension can be
seen either in enlarging the validity of quantum field theory or by restricting
the space of the solutions of the Einstein-Dirac system of field equations.Comment: 12 page
On the Hamiltonian formulation of Yang--Mills gauge theories
The Hamiltonian formulation of the theory of J-bundles is given both in the
Hamilton--De Donder and in the Multimomentum Hamiltonian geometrical
approaches. (3+3) Yang-Mills gauge theories are dealt with explicitly in order
to restate them in terms of Einstein-Cartan like field theories.Comment: 18 Pages, Submitted to International Journal of Geometric Methods in
Modern Physic
A State Distillation Protocol to Implement Arbitrary Single-qubit Rotations
An important task required to build a scalable, fault-tolerant quantum
computer is to efficiently represent an arbitrary single-qubit rotation by
fault-tolerant quantum operations. Traditionally, the method for decomposing a
single-qubit unitary into a discrete set of gates is Solovay-Kitaev
decomposition, which in practice produces a sequence of depth
O(\log^c(1/\epsilon)), where c~3.97 is the state-of-the-art. The proven lower
bound is c=1, however an efficient algorithm that saturates this bound is
unknown. In this paper, we present an alternative to Solovay-Kitaev
decomposition employing state distillation techniques which reduces c to
between 1.12 and 2.27, depending on the setting. For a given single-qubit
rotation, our protocol significantly lowers the length of the approximating
sequence and the number of required resource states (ancillary qubits). In
addition, our protocol is robust to noise in the resource states.Comment: 10 pages, 18 figures, 5 table
Exact solutions for Weyl fermions with gravity
We consider the single-handed spinor field in interaction with its own
gravitational field described by the set of field equations given by Weyl field
equations written in terms of derivatives that are covariant with respect to
the gravitational connection plus Einstein field equations soured with the
energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of
Weyl-Lewis-Papapetrou structure, we will find all exact solutions. The obtained
solution for the metric tensor is that of a PP-wave spacetime while the spinor
field is a flag-dipole.Comment: 12 page
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