970 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
Surface code fidelity at finite temperatures
We study the dependence of the fidelity of the surface code in the presence
of a single finite-temperature massless bosonic environment after a quantum
error correction cycle. The three standard types of environment are considered:
super-Ohmic, Ohmic, and sub-Ohmic. Our results show that, for regimes relevant
to current experiments, quantum error correction works well even in the
presence of environment-induced, long-range inter-qubit interactions. A
threshold always exists at finite temperatures, although its temperature
dependence is very sensitive to the type of environment. For the super-Ohmic
case, the critical coupling constant separating high- from low-fidelity
decreases with increasing temperature. For both Ohmic and super-Ohmic cases,
the dependence of the critical coupling on temperature is weak. In all cases,
the critical coupling is determined by microscopic parameters of the
environment. For the sub-Ohmic case, it also depends strongly on the duration
of the QEC cycle.Comment: 13 pages, 6 figure
Surface Code Threshold in the Presence of Correlated Errors
We study the fidelity of the surface code in the presence of correlated
errors induced by the coupling of physical qubits to a bosonic environment. By
mapping the time evolution of the system after one quantum error correction
cycle onto a statistical spin model, we show that the existence of an error
threshold is related to the appearance of an order-disorder phase transition in
the statistical model in the thermodynamic limit. This allows us to relate the
error threshold to bath parameters and to the spatial range of the correlated
errors.Comment: 5 pages, 2 figure
From Edge State Physics to Entanglement Spectrum: Studying Interactions and Impurities in Two-Dimensional Topological Insulators
We present a novel theoretical approach to incorporate electronic
interactions in the study of two-dimensional topological insulators. By
exploiting the correspondence between edge state physics and entanglement
spectrum in gapped topological systems, we deconstruct the system into
one-dimensional channels. This framework enables a simple and elegant inclusion
of fermionic interactions into the discussion of topological insulators. We
apply this approach to the Kane-Mele model with interactions and magnetic
impurities.Comment: 5 pages, 3 figure
Fixed Points of the Dissipative Hofstadter Model
The phase diagram of a dissipative particle in a periodic potential and a
magnetic field is studied in the weak barrier limit and in the tight-biding
regime. For the case of half flux per plaquette, and for a wide range of values
of the dissipation, the physics of the model is determined by a non trivial
fixed point. A combination of exact and variational results is used to
characterize this fixed point. Finally, it is also argued that there is an
intermediate energy scale that separates the weak coupling physics from the
tight-binding solution.Comment: 4 pages 3 figure
Forest fires in Portugal: a study on determinants and the role of firefighters
A Work Project, presented as part of the requirements for the Award of a Masters Degree in Economics from the NOVA – School of Business and Economic
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