4,702 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
On the state complexity of semi-quantum finite automata
Some of the most interesting and important results concerning quantum finite
automata are those showing that they can recognize certain languages with
(much) less resources than corresponding classical finite automata
\cite{Amb98,Amb09,AmYa11,Ber05,Fre09,Mer00,Mer01,Mer02,Yak10,ZhgQiu112,Zhg12}.
This paper shows three results of such a type that are stronger in some sense
than other ones because (a) they deal with models of quantum automata with very
little quantumness (so-called semi-quantum one- and two-way automata with one
qubit memory only); (b) differences, even comparing with probabilistic
classical automata, are bigger than expected; (c) a trade-off between the
number of classical and quantum basis states needed is demonstrated in one case
and (d) languages (or the promise problem) used to show main results are very
simple and often explored ones in automata theory or in communication
complexity, with seemingly little structure that could be utilized.Comment: 19 pages. We improve (make stronger) the results in section
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
From Quantum Query Complexity to State Complexity
State complexity of quantum finite automata is one of the interesting topics
in studying the power of quantum finite automata. It is therefore of importance
to develop general methods how to show state succinctness results for quantum
finite automata. One such method is presented and demonstrated in this paper.
In particular, we show that state succinctness results can be derived out of
query complexity results.Comment: Some typos in references were fixed. To appear in Gruska Festschrift
(2014). Comments are welcome. arXiv admin note: substantial text overlap with
arXiv:1402.7254, arXiv:1309.773
What is a quantum computer, and how do we build one?
The DiVincenzo criteria for implementing a quantum computer have been seminal
in focussing both experimental and theoretical research in quantum information
processing. These criteria were formulated specifically for the circuit model
of quantum computing. However, several new models for quantum computing
(paradigms) have been proposed that do not seem to fit the criteria well. The
question is therefore what are the general criteria for implementing quantum
computers. To this end, a formal operational definition of a quantum computer
is introduced. It is then shown that according to this definition a device is a
quantum computer if it obeys the following four criteria: Any quantum computer
must (1) have a quantum memory; (2) facilitate a controlled quantum evolution
of the quantum memory; (3) include a method for cooling the quantum memory; and
(4) provide a readout mechanism for subsets of the quantum memory. The criteria
are met when the device is scalable and operates fault-tolerantly. We discuss
various existing quantum computing paradigms, and how they fit within this
framework. Finally, we lay out a roadmap for selecting an avenue towards
building a quantum computer. This is summarized in a decision tree intended to
help experimentalists determine the most natural paradigm given a particular
physical implementation
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