120 research outputs found
The Multi-Agent Programming Contest: A r\'esum\'e
The Multi-Agent Programming Contest, MAPC, is an annual event organized since
2005 out of Clausthal University of Technology. Its aim is to investigate the
potential of using decentralized, autonomously acting intelligent agents, by
providing a complex scenario to be solved in a competitive environment. For
this we need suitable benchmarks where agent-based systems can shine. We
present previous editions of the contest and also its current scenario and
results from its use in the 2019 MAPC with a special focus on its suitability.
We conclude with lessons learned over the years.Comment: Submitted to the proceedings of the Multi-Agent Programming Contest
2019, to appear in Springer Lect. Notes Computer Challenges Series
https://www.springer.com/series/1652
Quantum Walks with Non-Orthogonal Position States
Quantum walks have by now been realized in a large variety of different
physical settings. In some of these, particularly with trapped ions, the walk
is implemented in phase space, where the corresponding position states are not
orthogonal. We develop a general description of such a quantum walk and show
how to map it into a standard one with orthogonal states, thereby making
available all the tools developed for the latter. This enables a variety of
experiments, which can be implemented with smaller step sizes and more steps.
Tuning the non-orthogonality allows for an easy preparation of extended states
such as momentum eigenstates, which travel at a well-defined speed with low
dispersion. We introduce a method to adjust their velocity by momentum shifts,
which allows to investigate intriguing effects such as the analog of Bloch
oscillations.Comment: 5 pages, 4 figure
Correlated Markov Quantum Walks
We consider the discrete time unitary dynamics given by a quantum walk on
performed by a particle with internal degree of freedom, called coin
state, according to the following iterated rule: a unitary update of the coin
state takes place, followed by a shift on the lattice, conditioned on the coin
state of the particle. We study the large time behavior of the quantum
mechanical probability distribution of the position observable in for
random updates of the coin states of the following form. The random sequences
of unitary updates are given by a site dependent function of a Markov chain in
time, with the following properties: on each site, they share the same
stationnary Markovian distribution and, for each fixed time, they form a
deterministic periodic pattern on the lattice.
We prove a Feynman-Kac formula to express the characteristic function of the
averaged distribution over the randomness at time in terms of the nth power
of an operator . By analyzing the spectrum of , we show that this
distribution posesses a drift proportional to the time and its centered
counterpart displays a diffusive behavior with a diffusion matrix we compute.
Moderate and large deviations principles are also proven to hold for the
averaged distribution and the limit of the suitably rescaled corresponding
characteristic function is shown to satisfy a diffusion equation.
An example of random updates for which the analysis of the distribution can
be performed without averaging is worked out. The random distribution displays
a deterministic drift proportional to time and its centered counterpart gives
rise to a random diffusion matrix whose law we compute. We complete the picture
by presenting an uncorrelated example.Comment: 37 pages. arXiv admin note: substantial text overlap with
arXiv:1010.400
Index theory of one dimensional quantum walks and cellular automata
If a one-dimensional quantum lattice system is subject to one step of a
reversible discrete-time dynamics, it is intuitive that as much "quantum
information" as moves into any given block of cells from the left, has to exit
that block to the right. For two types of such systems - namely quantum walks
and cellular automata - we make this intuition precise by defining an index, a
quantity that measures the "net flow of quantum information" through the
system. The index supplies a complete characterization of two properties of the
discrete dynamics. First, two systems S_1, S_2 can be pieced together, in the
sense that there is a system S which locally acts like S_1 in one region and
like S_2 in some other region, if and only if S_1 and S_2 have the same index.
Second, the index labels connected components of such systems: equality of the
index is necessary and sufficient for the existence of a continuous deformation
of S_1 into S_2. In the case of quantum walks, the index is integer-valued,
whereas for cellular automata, it takes values in the group of positive
rationals. In both cases, the map S -> ind S is a group homomorphism if
composition of the discrete dynamics is taken as the group law of the quantum
systems. Systems with trivial index are precisely those which can be realized
by partitioned unitaries, and the prototypes of systems with non-trivial index
are shifts.Comment: 38 pages. v2: added examples, terminology clarifie
Localization of the Grover walks on spidernets and free Meixner laws
A spidernet is a graph obtained by adding large cycles to an almost regular
tree and considered as an example having intermediate properties of lattices
and trees in the study of discrete-time quantum walks on graphs. We introduce
the Grover walk on a spidernet and its one-dimensional reduction. We derive an
integral representation of the -step transition amplitude in terms of the
free Meixner law which appears as the spectral distribution. As an application
we determine the class of spidernets which exhibit localization. Our method is
based on quantum probabilistic spectral analysis of graphs.Comment: 32 page
Implementation of Clifford gates in the Ising-anyon topological quantum computer
We give a general proof for the existence and realizability of Clifford gates
in the Ising topological quantum computer. We show that all quantum gates that
can be implemented by braiding of Ising anyons are Clifford gates. We find that
the braiding gates for two qubits exhaust the entire two-qubit Clifford group.
Analyzing the structure of the Clifford group for n \geq 3 qubits we prove that
the the image of the braid group is a non-trivial subgroup of the Clifford
group so that not all Clifford gates could be implemented by braiding in the
Ising topological quantum computation scheme. We also point out which Clifford
gates cannot in general be realized by braiding.Comment: 17 pages, 10 figures, RevTe
Random Time-Dependent Quantum Walks
We consider the discrete time unitary dynamics given by a quantum walk on the
lattice performed by a quantum particle with internal degree of freedom,
called coin state, according to the following iterated rule: a unitary update
of the coin state takes place, followed by a shift on the lattice, conditioned
on the coin state of the particle. We study the large time behavior of the
quantum mechanical probability distribution of the position observable in
when the sequence of unitary updates is given by an i.i.d. sequence of
random matrices. When averaged over the randomness, this distribution is shown
to display a drift proportional to the time and its centered counterpart is
shown to display a diffusive behavior with a diffusion matrix we compute. A
moderate deviation principle is also proven to hold for the averaged
distribution and the limit of the suitably rescaled corresponding
characteristic function is shown to satisfy a diffusion equation. A
generalization to unitary updates distributed according to a Markov process is
also provided. An example of i.i.d. random updates for which the analysis of
the distribution can be performed without averaging is worked out. The
distribution also displays a deterministic drift proportional to time and its
centered counterpart gives rise to a random diffusion matrix whose law we
compute. A large deviation principle is shown to hold for this example. We
finally show that, in general, the expectation of the random diffusion matrix
equals the diffusion matrix of the averaged distribution.Comment: Typos and minor errors corrected. To appear In Communications in
Mathematical Physic
Experimental simulation and limitations of quantum walks with trapped ions
We examine the prospects of discrete quantum walks (QWs) with trapped ions.
In particular, we analyze in detail the limitations of the protocol of
Travaglione and Milburn (PRA 2002) that has been implemented by several
experimental groups in recent years. Based on the first realization in our
group (PRL 2009), we investigate the consequences of leaving the scope of the
approximations originally made, such as the Lamb--Dicke approximation. We
explain the consequential deviations from the idealized QW for different
experimental realizations and an increasing number of steps by taking into
account higher-order terms of the quantum evolution. It turns out that these
become dominant after a few steps already, which is confirmed by experimental
results and is currently limiting the scalability of this approach. Finally, we
propose a new scheme using short laser pulses, derived from a protocol from the
field of quantum computation. We show that the new scheme is not subject to the
above-mentioned restrictions, and analytically and numerically evaluate its
limitations, based on a realistic implementation with our specific setup.
Implementing the protocol with state-of-the-art techniques should allow for
substantially increasing the number of steps to 100 and beyond and should be
extendable to higher-dimensional QWs.Comment: 29 pages, 15 figue
Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
Quantum walks subject to decoherence generically suffer the loss of their
genuine quantum feature, a quadratically faster spreading compared to classical
random walks. This intuitive statement has been verified analytically for
certain models and is also supported by numerical studies of a variety of
examples. In this paper we analyze the long-time behavior of a particular class
of decoherent quantum walks, which, to the best of our knowledge, was only
studied at the level of numerical simulations before. We consider a local coin
operation which is randomly and independently chosen for each time step and
each lattice site and prove that, under rather mild conditions, this leads to
classical behavior: With the same scaling as needed for a classical diffusion
the position distribution converges to a Gaussian, which is independent of the
initial state. Our method is based on non-degenerate perturbation theory and
yields an explicit expression for the covariance matrix of the asymptotic
Gaussian in terms of the randomness parameters
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
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