115 research outputs found
Quantum Walks of SU(2)_k Anyons on a Ladder
We study the effects of braiding interactions on single anyon dynamics using
a quantum walk model on a quasi-1-dimensional ladder filled with stationary
anyons. The model includes loss of information of the coin and nonlocal fusion
degrees of freedom on every second time step, such that the entanglement
between the position states and the exponentially growing auxiliary degrees of
freedom is lost. The computational complexity of numerical calculations reduces
drastically from the fully coherent anyonic quantum walk model, allowing for
relatively long simulations for anyons which are spin-1/2 irreps of SU(2)_k
Chern-Simons theory. We find that for Abelian anyons, the walk retains the
ballistic spreading velocity just like particles with trivial braiding
statistics. For non-Abelian anyons, the numerical results indicate that the
spreading velocity is linearly dependent on the number of time steps. By
approximating the Kraus generators of the time evolution map by circulant
matrices, it is shown that the spatial probability distribution for the k=2
walk, corresponding to Ising model anyons, is equal to the classical unbiased
random walk distribution.Comment: 12 pages, 4 figure
Anyonic Quantum Walks
The one dimensional quantum walk of anyonic systems is presented. The anyonic
walker performs braiding operations with stationary anyons of the same type
ordered canonically on the line of the walk. Abelian as well as non-Abelian
anyons are studied and it is shown that they have very different properties.
Abelian anyonic walks demonstrate the expected quadratic quantum speedup.
Non-Abelian anyonic walks are much more subtle. The exponential increase of the
system's Hilbert space and the particular statistical evolution of non-Abelian
anyons give a variety of new behaviors. The position distribution of the walker
is related to Jones polynomials, topological invariants of the links created by
the anyonic world-lines during the walk. Several examples such as the SU(2)
level k and the quantum double models are considered that provide insight to
the rich diffusion properties of anyons.Comment: 17 pages, 10 figure
Deterministic generation of an on-demand Fock state
We theoretically study the deterministic generation of photon Fock states
on-demand using a protocol based on a Jaynes Cummings quantum random walk which
includes damping. We then show how each of the steps of this protocol can be
implemented in a low temperature solid-state quantum system with a
Nitrogen-Vacancy centre in a nano-diamond coupled to a nearby high-Q optical
cavity. By controlling the coupling duration between the NV and the cavity via
the application of a time dependent Stark shift, and by increasing the decay
rate of the NV via stimulated emission depletion (STED) a Fock state with high
photon number can be generated on-demand. Our setup can be integrated on a chip
and can be accurately controlled.Comment: 13 pages, 9 figure
Realization of Arbitrary Gates in Holonomic Quantum Computation
Among the many proposals for the realization of a quantum computer, holonomic
quantum computation (HQC) is distinguished from the rest in that it is
geometrical in nature and thus expected to be robust against decoherence. Here
we analyze the realization of various quantum gates by solving the inverse
problem: Given a unitary matrix, we develop a formalism by which we find loops
in the parameter space generating this matrix as a holonomy. We demonstrate for
the first time that such a one-qubit gate as the Hadamard gate and such
two-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier
transformation can be obtained with a single loop.Comment: 8 pages, 6 figure
Geometric phase in open systems
We calculate the geometric phase associated to the evolution of a system
subjected to decoherence through a quantum-jump approach. The method is general
and can be applied to many different physical systems. As examples, two main
source of decoherence are considered: dephasing and spontaneous decay. We show
that the geometric phase is completely insensitive to the former, i.e. it is
independent of the number of jumps determined by the dephasing operator.Comment: 4 pages, 2 figures, RevTe
An expectation value expansion of Hermitian operators in a discrete Hilbert space
We discuss a real-valued expansion of any Hermitian operator defined in a
Hilbert space of finite dimension N, where N is a prime number, or an integer
power of a prime. The expansion has a direct interpretation in terms of the
operator expectation values for a set of complementary bases. The expansion can
be said to be the complement of the discrete Wigner function.
We expect the expansion to be of use in quantum information applications
since qubits typically are represented by a discrete, and finite-dimensional
physical system of dimension N=2^p, where p is the number of qubits involved.
As a particular example we use the expansion to prove that an intermediate
measurement basis (a Breidbart basis) cannot be found if the Hilbert space
dimension is 3 or 4.Comment: A mild update. In particular, I. D. Ivanovic's earlier derivation of
the expansion is properly acknowledged. 16 pages, one PS figure, 1 table,
written in RevTe
SafeDrones: Real-Time Reliability Evaluation of UAVs using Executable Digital Dependable Identities
The use of Unmanned Arial Vehicles (UAVs) offers many advantages across a
variety of applications. However, safety assurance is a key barrier to
widespread usage, especially given the unpredictable operational and
environmental factors experienced by UAVs, which are hard to capture solely at
design-time. This paper proposes a new reliability modeling approach called
SafeDrones to help address this issue by enabling runtime reliability and risk
assessment of UAVs. It is a prototype instantiation of the Executable Digital
Dependable Identity (EDDI) concept, which aims to create a model-based solution
for real-time, data-driven dependability assurance for multi-robot systems. By
providing real-time reliability estimates, SafeDrones allows UAVs to update
their missions accordingly in an adaptive manner
Quantum Computation and Information: Multi-Particle Aspects
This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers
Factorizations and Physical Representations
A Hilbert space in M dimensions is shown explicitly to accommodate
representations that reflect the prime numbers decomposition of M.
Representations that exhibit the factorization of M into two relatively prime
numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)),
and related representations termed representations (together with
their conjugates) are analysed, as well as a representation that exhibits the
complete factorization of M. In this latter representation each quantum number
varies in a subspace that is associated with one of the prime numbers that make
up M
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