1,463 research outputs found
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
Definition and evolution of quantum cellular automata with two qubits per cell
Studies of quantum computer implementations suggest cellular quantum computer
architectures. These architectures can simulate the evolution of quantum
cellular automata, which can possibly simulate both quantum and classical
physical systems and processes. It is however known that except for the trivial
case, unitary evolution of one-dimensional homogeneous quantum cellular
automata with one qubit per cell is not possible. Quantum cellular automata
that comprise two qubits per cell are defined and their evolution is studied
using a quantum computer simulator. The evolution is unitary and its linearity
manifests itself as a periodic structure in the probability distribution
patterns.Comment: 13 pages, 4 figure
On the structure of Clifford quantum cellular automata
We study reversible quantum cellular automata with the restriction that these
are also Clifford operations. This means that tensor products of Pauli
operators (or discrete Weyl operators) are mapped to tensor products of Pauli
operators. Therefore Clifford quantum cellular automata are induced by
symplectic cellular automata in phase space. We characterize these symplectic
cellular automata and find that all possible local rules must be, up to some
global shift, reflection invariant with respect to the origin. In the one
dimensional case we also find that every uniquely determined and
translationally invariant stabilizer state can be prepared from a product state
by a single Clifford cellular automaton timestep, thereby characterizing these
class of stabilizer states, and we show that all 1D Clifford quantum cellular
automata are generated by a few elementary operations. We also show that the
correspondence between translationally invariant stabilizer states and
translationally invariant Clifford operations holds for periodic boundary
conditions.Comment: 28 pages, 2 figures, LaTe
Local Unitary Quantum Cellular Automata
In this paper we present a quantization of Cellular Automata. Our formalism
is based on a lattice of qudits, and an update rule consisting of local unitary
operators that commute with their own lattice translations. One purpose of this
model is to act as a theoretical model of quantum computation, similar to the
quantum circuit model. It is also shown to be an appropriate abstraction for
space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains
and others. Some results that show the benefits of basing the model on local
unitary operators are shown: universality, strong connections to the circuit
model, simple implementation on quantum hardware, and a wealth of applications.Comment: To appear in Physical Review
Models of Quantum Cellular Automata
In this paper we present a systematic view of Quantum Cellular Automata
(QCA), a mathematical formalism of quantum computation. First we give a general
mathematical framework with which to study QCA models. Then we present four
different QCA models, and compare them. One model we discuss is the traditional
QCA, similar to those introduced by Shumacher and Werner, Watrous, and Van Dam.
We discuss also Margolus QCA, also discussed by Schumacher and Werner. We
introduce two new models, Coloured QCA, and Continuous-Time QCA. We also
compare our models with the established models. We give proofs of computational
equivalence for several of these models. We show the strengths of each model,
and provide examples of how our models can be useful to come up with
algorithms, and implement them in real-world physical devices
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