374 research outputs found
Fidelity of the surface code in the presence of a bosonic bath
We study the resilience of the surface code to decoherence caused by the
presence of a bosonic bath. This approach allows us to go beyond the standard
stochastic error model commonly used to quantify decoherence and error
threshold probabilities in this system. The full quantum mechanical system-bath
dynamics is computed exactly over one quantum error correction cycle. Since all
physical qubits interact with the bath, space-time correlations between errors
are taken into account. We compute the fidelity of the surface code as a
function of the quantum error correction time. The calculation allows us to map
the problem onto an Ising-like statistical spin model with two-body
interactions and a fictitious temperature which is related to the inverse bath
coupling constant. The model departs from the usual Ising model in the sense
that interactions can be long ranged and can involve complex exchange
couplings; in addition, the number of allowed configurations is restricted by
the syndrome extraction. Using analytical estimates and numerical calculations,
we argue that, in the limit of an infinite number of physical qubits, the spin
model sustain a phase transition which can be associated to the existence of an
error threshold in the surface code. An estimate of the transition point is
given for the case of nearest-neighbor interactions.Comment: 15 pages, 5 figure
Properties of magnetic nanodots with perpendicular anisotropy
Nanodots with magnetic vortices have many potential applications, such as
magnetic memories (VRAMs) and spin transfer nano-oscillators (STNOs). Adding a
perpendicular anisotropy term to the magnetic energy of the nanodot it becomes
possible to tune the vortex core properties. This can be obtained, e.g., in Co
nanodots by varying the thickness of the Co layer in a Co/Pt stack. Here we
discuss the spin configuration of circular and elliptical nanodots for
different perpendicular anisotropies; we show for nanodisks that micromagnetic
simulations and analytical results agree. Increasing the perpendicular
anisotropy, the vortex core radii increase, the phase diagrams are modified and
new configurations appear; the knowledge of these phase diagrams is relevant
for the choice of optimum nanodot dimensions for applications. MFM measurements
on Co/Pt multilayers confirm the trend of the vortex core diameters with
varying Co layer thicknesses.Comment: 7 pages, 8 figure
Resilient Quantum Computation in Correlated Environments: A Quantum Phase Transition Perspective
We analyze the problem of a quantum computer in a correlated environment
protected from decoherence by QEC using a perturbative renormalization group
approach. The scaling equation obtained reflects the competition between the
dimension of the computer and the scaling dimension of the correlations. For an
irrelevant flow, the error probability is reduced to a stochastic form for long
time and/or large number of qubits; thus, the traditional derivation of the
threshold theorem holds for these error models. In this way, the ``threshold
theorem'' of quantum computing is rephrased as a dimensional criterion.Comment: 4.1 pages, minor correction and an improved discussion of Eqs. (4)
and (14
Uncertainty in context-aware systems: A case study for intelligent environments
Data used be context-aware systems is naturally incomplete and not always reflect real situations. The dynamic nature of intelligent environments leads to the need of analysing and handling uncertain information. Users can change their acting patterns within a short space of time. This paper presents a case study for a better understanding of concepts related to context awareness and the problem of dealing with inaccurate data. Through the analysis of identification of elements that results in the construction of unreliable contexts, it is aimed to identify patterns to minimize incompleteness. Thus, it will be possible to deal with flaws caused by undesired execution of applications.Programa Operacional Temático Factores de Competitividade (POCI-01-0145-
Hamiltonian Formulation of Quantum Error Correction and Correlated Noise: The Effects Of Syndrome Extraction in the Long Time Limit
We analyze the long time behavior of a quantum computer running a quantum
error correction (QEC) code in the presence of a correlated environment.
Starting from a Hamiltonian formulation of realistic noise models, and assuming
that QEC is indeed possible, we find formal expressions for the probability of
a faulty path and the residual decoherence encoded in the reduced density
matrix. Systems with non-zero gate times (``long gates'') are included in our
analysis by using an upper bound on the noise. In order to introduce the local
error probability for a qubit, we assume that propagation of signals through
the environment is slower than the QEC period (hypercube assumption). This
allows an explicit calculation in the case of a generalized spin-boson model
and a quantum frustration model. The key result is a dimensional criterion: If
the correlations decay sufficiently fast, the system evolves toward a
stochastic error model for which the threshold theorem of fault-tolerant
quantum computation has been proven. On the other hand, if the correlations
decay slowly, the traditional proof of this threshold theorem does not hold.
This dimensional criterion bears many similarities to criteria that occur in
the theory of quantum phase transitions.Comment: 19 pages, 5 figures. Includes response to arXiv:quant-ph/0702050. New
title and an additional exampl
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