4,461 research outputs found
Sub-quadratic Decoding of One-point Hermitian Codes
We present the first two sub-quadratic complexity decoding algorithms for
one-point Hermitian codes. The first is based on a fast realisation of the
Guruswami-Sudan algorithm by using state-of-the-art algorithms from computer
algebra for polynomial-ring matrix minimisation. The second is a Power decoding
algorithm: an extension of classical key equation decoding which gives a
probabilistic decoding algorithm up to the Sudan radius. We show how the
resulting key equations can be solved by the same methods from computer
algebra, yielding similar asymptotic complexities.Comment: New version includes simulation results, improves some complexity
results, as well as a number of reviewer corrections. 20 page
Hybrid quantum information processing
The development of quantum information processing has traditionally followed
two separate and not immediately connected lines of study. The main line has
focused on the implementation of quantum bit (qubit) based protocols whereas
the other line has been devoted to implementations based on high-dimensional
Gaussian states (such as coherent and squeezed states). The separation has been
driven by the experimental difficulty in interconnecting the standard
technologies of the two lines. However, in recent years, there has been a
significant experimental progress in refining and connecting the technologies
of the two fields which has resulted in the development and experimental
realization of numerous new hybrid protocols. In this Review, we summarize
these recent efforts on hybridizing the two types of schemes based on discrete
and continuous variables.Comment: 13 pages, 6 figure
Entanglement in Anderson Nanoclusters
We investigate the two-particle spin entanglement in magnetic nanoclusters
described by the periodic Anderson model. An entanglement phase diagram is
obtained, providing a novel perspective on a central property of magnetic
nanoclusters, namely the temperature dependent competition between local Kondo
screening and nonlocal Ruderman-Kittel-Kasuya-Yoshida spin ordering. We find
that multiparticle entangled states are present for finite magnetic field as
well as in the mixed valence regime and away from half filling. Our results
emphasize the role of charge fluctuations.Comment: 5 pages, 3 figure
Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation
We present an efficient method for preparing the initial state required by
the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method
can be applied when solving continuous Hermitian eigenproblems, e.g., the
Schroedinger equation, on a discrete grid. We start with a classically obtained
eigenvector for a problem discretized on a coarse grid, and we efficiently
construct, quantum mechanically, an approximation of the same eigenvector on a
fine grid. We use this approximation as the initial state for the eigenvalue
estimation algorithm, and show the relationship between its success probability
and the size of the coarse grid.Comment: 4 page
Theory of Spin Relaxation in Two-Electron Lateral Coupled Si/SiGe Quantum Dots
Highly accurate numerical results of phonon-induced two-electron spin
relaxation in silicon double quantum dots are presented. The relaxation,
enabled by spin-orbit coupling and the nuclei of Si (natural or purified
abundance), are investigated for experimentally relevant parameters, the
interdot coupling, the magnetic field magnitude and orientation, and the
detuning. We calculate relaxation rates for zero and finite temperatures (100
mK), concluding that our findings for zero temperature remain qualitatively
valid also for 100 mK. We confirm the same anisotropic switch of the axis of
prolonged spin lifetime with varying detuning as recently predicted in GaAs.
Conditions for possibly hyperfine-dominated relaxation are much more stringent
in Si than in GaAs. For experimentally relevant regimes, the spin-orbit
coupling, although weak, is the dominant contribution, yielding anisotropic
relaxation rates of at least two order of magnitude lower than in GaAs.Comment: 11 pages, 10 figure
IMPROVING ISD AGILITY IN FAST-MOVING SOFTWARE ORGANIZATIONS
Fast-moving software organizations must respond quickly to changing technological options and mar-ket trends while delivering high-quality services at competitive prices. Improving agility of infor-mation systems development (ISD) may reconcile these inherent tensions, but previous research of agility predominantly focused separately on managing either the individual project or the organiza-tion. Limited research has investigated the management that ties the agility of individual projects with the company agility characterizing fast-moving organizations. This paper reports an action research study on how to improve ISD agility in a fast-moving software organization. The study maps central problems in the ISD management to direct improvements of agility. Our following intervention ad-dressed method improvements in defining types of ISD by customer relations and integrating the method with the task management tool used by the organization. The paper discusses how the action research contributes to our understanding of ISD agility in fast-moving software organizations with a framework for mapping and evaluating improvements of agility. The action research specifically points out that project managers need to attend to the company’s agility in relating to customers, that company agility links to project agility, and that this requires light method and tool support
Thermally assisted adiabatic quantum computation
We study the effect of a thermal environment on adiabatic quantum computation
using the Bloch-Redfield formalism. We show that in certain cases the
environment can enhance the performance in two different ways: (i) by
introducing a time scale for thermal mixing near the anticrossing that is
smaller than the adiabatic time scale, and (ii) by relaxation after the
anticrossing. The former can enhance the scaling of computation when the
environment is superohmic, while the latter can only provide a prefactor
enhancement. We apply our method to the case of adiabatic Grover search and
show that performance better than classical is possible with a superohmic
environment, with no a priori knowledge of the energy spectrum.Comment: 4 pages, 2 figures, Final version to appear in PR
Universality of Entanglement and Quantum Computation Complexity
We study the universality of scaling of entanglement in Shor's factoring
algorithm and in adiabatic quantum algorithms across a quantum phase transition
for both the NP-complete Exact Cover problem as well as the Grover's problem.
The analytic result for Shor's algorithm shows a linear scaling of the entropy
in terms of the number of qubits, therefore difficulting the possibility of an
efficient classical simulation protocol. A similar result is obtained
numerically for the quantum adiabatic evolution Exact Cover algorithm, which
also shows universality of the quantum phase transition the system evolves
nearby. On the other hand, entanglement in Grover's adiabatic algorithm remains
a bounded quantity even at the critical point. A classification of scaling of
entanglement appears as a natural grading of the computational complexity of
simulating quantum phase transitions.Comment: 30 pages, 17 figures, accepted for publication in PR
Optimum Quantum Error Recovery using Semidefinite Programming
Quantum error correction (QEC) is an essential element of physical quantum
information processing systems. Most QEC efforts focus on extending classical
error correction schemes to the quantum regime. The input to a noisy system is
embedded in a coded subspace, and error recovery is performed via an operation
designed to perfectly correct for a set of errors, presumably a large subset of
the physical noise process. In this paper, we examine the choice of recovery
operation. Rather than seeking perfect correction on a subset of errors, we
seek a recovery operation to maximize the entanglement fidelity for a given
input state and noise model. In this way, the recovery operation is optimum for
the given encoding and noise process. This optimization is shown to be
calculable via a semidefinite program (SDP), a well-established form of convex
optimization with efficient algorithms for its solution. The error recovery
operation may also be interpreted as a combining operation following a quantum
spreading channel, thus providing a quantum analogy to the classical diversity
combining operation.Comment: 7 pages, 3 figure
Minimal instances for toric code ground states
A decade ago Kitaev's toric code model established the new paradigm of
topological quantum computation. Due to remarkable theoretical and experimental
progress, the quantum simulation of such complex many-body systems is now
within the realms of possibility. Here we consider the question, to which
extent the ground states of small toric code systems differ from LU-equivalent
graph states. We argue that simplistic (though experimentally attractive)
setups obliterate the differences between the toric code and equivalent graph
states; hence we search for the smallest setups on the square- and triangular
lattice, such that the quasi-locality of the toric code hamiltonian becomes a
distinctive feature. To this end, a purely geometric procedure to transform a
given toric code setup into an LC-equivalent graph state is derived. In
combination with an algorithmic computation of LC-equivalent graph states, we
find the smallest non-trivial setup on the square lattice to contain 5
plaquettes and 16 qubits; on the triangular lattice the number of plaquettes
and qubits is reduced to 4 and 9, respectively.Comment: 14 pages, 11 figure
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