3,771 research outputs found
Fast Decoders for Topological Quantum Codes
We present a family of algorithms, combining real-space renormalization
methods and belief propagation, to estimate the free energy of a topologically
ordered system in the presence of defects. Such an algorithm is needed to
preserve the quantum information stored in the ground space of a topologically
ordered system and to decode topological error-correcting codes. For a system
of linear size L, our algorithm runs in time log L compared to L^6 needed for
the minimum-weight perfect matching algorithm previously used in this context
and achieves a higher depolarizing error threshold.Comment: 4 pages, 4 figure
Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes
Foliated quantum codes are a resource for fault-tolerant measurement-based
quantum error correction for quantum repeaters and for quantum computation.
They represent a general approach to integrating a range of possible quantum
error correcting codes into larger fault-tolerant networks. Here we present an
efficient heuristic decoding scheme for foliated quantum codes, based on
message passing between primal and dual code 'sheets'. We test this decoder on
two different families of sparse quantum error correcting code: turbo codes and
bicycle codes, and show reasonably high numerical performance thresholds. We
also present a construction schedule for building such code states.Comment: 23 pages, 15 figures, accepted for publication in Phys. Rev.
An NPZ Model with State-Dependent Delay due to Size-Structure in Juvenile Zooplankton
The study of planktonic ecosystems is important as they make up the bottom
trophic levels of aquatic food webs. We study a closed
Nutrient-Phytoplankton-Zooplankton (NPZ) model that includes size structure in
the juvenile zooplankton. The closed nature of the system allows the
formulation of a conservation law of biomass that governs the system. The model
consists of a system of nonlinear ordinary differential equation coupled to a
partial differential equation. We are able to transform this system into a
system of delay differential equations where the delay is of threshold type and
is state-dependent. The system of delay differential equations can be further
transformed into one with fixed delay. Using the different forms of the model
we perform a qualitative analysis of the solutions, which includes studying
existence and uniqueness, positivity and boundedness, local and global
stability, and conditions for extinction. Key parameters that are explored are
the total biomass in the system and the maturity level at which the juvenile
zooplankton reach maturity. Numerical simulations are also performed to verify
our analytical results
Relational time for systems of oscillators
Using an elementary example based on two simple harmonic oscillators, we show
how a relational time may be defined that leads to an approximate Schrodinger
dynamics for subsystems, with corrections leading to an intrinsic decoherence
in the energy eigenstates of the subsystem.Comment: Contribution to the Int. J. of Quant. Info. issue dedicated to the
memory of Asher Pere
Allee Effects May Slow the Spread of Parasites in a Coastal Marine Ecosystem
Allee effects are thought to mediate the dynamics of population colonization, particularly for invasive species. However, Allee effects acting on parasites have rarely been considered in the analogous process of infectious disease establishment and spread. We studied the colonization of uninfected wild juvenile Pacific salmon populations by ectoparasitic salmon lice (Lepeophtheirus salmonis) over a 4-year period. In a data set of 68,376 fish, we observed 85 occurrences of precopular pair formation among 1,259 preadult female and 613 adult male lice. The probability of pair formation was dependent on the local abundance of lice, but this mate limitation is likely offset somewhat by mate-searching dispersal of males among host fish. A mathematical model of macroparasite population dynamics that incorporates the empirical results suggests a high likelihood of a demographic Allee effect, which can cause the colonizing parasite populations to die out. These results may provide the first empirical evidence for Allee effects in a macroparasite. Furthermore, the data give a rare detailed view of Allee effects in colonization dynamics and suggest that Allee effects may dampen the spread of parasites in a coastal marine ecosystem
Alien Registration- Poulin, Marie A. (Waterville, Kennebec County)
https://digitalmaine.com/alien_docs/14770/thumbnail.jp
Alien Registration- Poulin, Marie A. (Lewiston, Androscoggin County)
https://digitalmaine.com/alien_docs/27961/thumbnail.jp
A Quantum-Quantum Metropolis Algorithm
Recently, the idea of classical Metropolis sampling through Markov chains has
been generalized for quantum Hamiltonians. However, the underlying Markov chain
of this algorithm is still classical in nature. Due to Szegedy's method, the
Markov chains of classical Hamiltonians can achieve a quadratic quantum speedup
in the eigenvalue gap of the corresponding transition matrix. A natural
question to ask is whether Szegedy's quantum speedup is merely a consequence of
employing classical Hamiltonians, where the eigenstates simply coincide with
the computational basis, making cloning of the classical information possible.
We solve this problem by introducing a quantum version of the method of
Markov-chain quantization combined with the quantum simulated annealing (QSA)
procedure, and describe explicitly a novel quantum Metropolis algorithm, which
exhibits a quadratic quantum speedup in the eigenvalue gap of the corresponding
Metropolis Markov chain for any quantum Hamiltonian. This result provides a
complete generalization of the classical Metropolis method to the quantum
domain.Comment: 7 page
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