11,103 research outputs found
Superiority of one-way and realtime quantum machines and new directions
In automata theory, the quantum computation has been widely examined for
finite state machines, known as quantum finite automata (QFAs), and less
attention has been given to the QFAs augmented with counters or stacks.
Moreover, to our knowledge, there is no result related to QFAs having more than
one input head. In this paper, we focus on such generalizations of QFAs whose
input head(s) operate(s) in one-way or realtime mode and present many
superiority of them to their classical counterparts. Furthermore, we propose
some open problems and conjectures in order to investigate the power of
quantumness better. We also give some new results on classical computation.Comment: A revised edition with some correction
Quantum counter automata
The question of whether quantum real-time one-counter automata (rtQ1CAs) can
outperform their probabilistic counterparts has been open for more than a
decade. We provide an affirmative answer to this question, by demonstrating a
non-context-free language that can be recognized with perfect soundness by a
rtQ1CA. This is the first demonstration of the superiority of a quantum model
to the corresponding classical one in the real-time case with an error bound
less than 1. We also introduce a generalization of the rtQ1CA, the quantum
one-way one-counter automaton (1Q1CA), and show that they too are superior to
the corresponding family of probabilistic machines. For this purpose, we
provide general definitions of these models that reflect the modern approach to
the definition of quantum finite automata, and point out some problems with
previous results. We identify several remaining open problems.Comment: A revised version. 16 pages. A preliminary version of this paper
appeared as A. C. Cem Say, Abuzer Yakary{\i}lmaz, and \c{S}efika
Y\"{u}zsever. Quantum one-way one-counter automata. In R\={u}si\c{n}\v{s}
Freivalds, editor, Randomized and quantum computation, pages 25--34, 2010
(Satellite workshop of MFCS and CSL 2010
Quantum computation with devices whose contents are never read
In classical computation, a "write-only memory" (WOM) is little more than an
oxymoron, and the addition of WOM to a (deterministic or probabilistic)
classical computer brings no advantage. We prove that quantum computers that
are augmented with WOM can solve problems that neither a classical computer
with WOM nor a quantum computer without WOM can solve, when all other resource
bounds are equal. We focus on realtime quantum finite automata, and examine the
increase in their power effected by the addition of WOMs with different access
modes and capacities. Some problems that are unsolvable by two-way
probabilistic Turing machines using sublogarithmic amounts of read/write memory
are shown to be solvable by these enhanced automata.Comment: 32 pages, a preliminary version of this work was presented in the 9th
International Conference on Unconventional Computation (UC2010
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
We prove new bounds on the quantum communication complexity of the
disjointness and equality problems. For the case of exact and non-deterministic
protocols we show that these complexities are all equal to n+1, the previous
best lower bound being n/2. We show this by improving a general bound for
non-deterministic protocols of de Wolf. We also give an O(sqrt{n}c^{log^*
n})-qubit bounded-error protocol for disjointness, modifying and improving the
earlier O(sqrt{n}log n) protocol of Buhrman, Cleve, and Wigderson, and prove an
Omega(sqrt{n}) lower bound for a large class of protocols that includes the
BCW-protocol as well as our new protocol.Comment: 11 pages LaTe
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
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