9,255 research outputs found
Quantum dynamics, dissipation, and asymmetry effects in quantum dot arrays
We study the role of dissipation and structural defects on the time evolution
of quantum dot arrays with mobile charges under external driving fields. These
structures, proposed as quantum dot cellular automata, exhibit interesting
quantum dynamics which we describe in terms of equations of motion for the
density matrix. Using an open system approach, we study the role of asymmetries
and the microscopic electron-phonon interaction on the general dynamical
behavior of the charge distribution (polarization) of such systems. We find
that the system response to the driving field is improved at low temperatures
(and/or weak phonon coupling), before deteriorating as temperature and
asymmetry increase. In addition to the study of the time evolution of
polarization, we explore the linear entropy of the system in order to gain
further insights into the competition between coherent evolution and
dissipative processes.Comment: 11pages,9 figures(eps), submitted to PR
Simulating Markovian open quantum systems using higher-order series expansion
We present an efficient quantum algorithm for simulating the dynamics of
Markovian open quantum systems. The performance of our algorithm is similar to
the previous state-of-the-art quantum algorithm, i.e., it scales linearly in
evolution time and poly-logarithmically in inverse precision. However, our
algorithm is conceptually cleaner, and it only uses simple quantum primitives
without compressed encoding. Our approach is based on a novel mathematical
treatment of the evolution map, which involves a higher-order series expansion
based on Duhamel's principle and approximating multiple integrals using scaled
Gaussian quadrature. Our method easily generalizes to simulating quantum
dynamics with time-dependent Lindbladians. Furthermore, our method of
approximating multiple integrals using scaled Gaussian quadrature could
potentially be used to produce a more efficient approximation of time-ordered
integrals, and therefore can simplify existing quantum algorithms for
simulating time-dependent Hamiltonians based on a truncated Dyson series.Comment: 28 pages, various minor changes. To appear in the 50th EATCS
International Colloquium on Automata, Languages and Programming (ICALP 2023
Information flow in one-dimensional non-unitary quantum cellular automata
The information flow in a quantum system is a fundamental feature of its
dynamics. An important class of dynamics are quantum cellular automata (QCA),
systems with discrete updates invariant in time and space, for which an index
theory has been proposed for the quantification of the net flow of quantum
information across a boundary. While the index is rigid in the sense of begin
invariant under finite-depth local circuits, it is not defined when the system
is coupled to an environment, i.e. for non-unitary time evolution of open
quantum systems. We propose a new measure of information flow for non-unitary
QCA denoted the information current which is not rigid, but can be computed
locally based on the matrix-product operator representation of the map.Comment: 21 pages, 23 figure
Quantum Cellular Automata
Quantum cellular automata (QCA) are reviewed, including early and more recent
proposals. QCA are a generalization of (classical) cellular automata (CA) and
in particular of reversible CA. The latter are reviewed shortly. An overview is
given over early attempts by various authors to define one-dimensional QCA.
These turned out to have serious shortcomings which are discussed as well.
Various proposals subsequently put forward by a number of authors for a general
definition of one- and higher-dimensional QCA are reviewed and their properties
such as universality and reversibility are discussed.Comment: 12 pages, 3 figures. To appear in the Springer Encyclopedia of
Complexity and Systems Scienc
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