4,110 research outputs found
Intrinsically universal one-dimensional quantum cellular automata in two flavours
We give a one-dimensional quantum cellular automaton (QCA) capable of
simulating all others. By this we mean that the initial configuration and the
local transition rule of any one-dimensional QCA can be encoded within the
initial configuration of the universal QCA. Several steps of the universal QCA
will then correspond to one step of the simulated QCA. The simulation preserves
the topology in the sense that each cell of the simulated QCA is encoded as a
group of adjacent cells in the universal QCA. The encoding is linear and hence
does not carry any of the cost of the computation. We do this in two flavours:
a weak one which requires an infinite but periodic initial configuration and a
strong one which needs only a finite initial configuration. KEYWORDS: Quantum
cellular automata, Intrinsic universality, Quantum computation.Comment: 27 pages, revtex, 23 figures. V3: The results of V1-V2 are better
explained and formalized, and a novel result about intrinsic universality
with only finite initial configurations is give
Entanglement Dynamics in 1D Quantum Cellular Automata
Several proposed schemes for the physical realization of a quantum computer
consist of qubits arranged in a cellular array. In the quantum circuit model of
quantum computation, an often complex series of two-qubit gate operations is
required between arbitrarily distant pairs of lattice qubits. An alternative
model of quantum computation based on quantum cellular automata (QCA) requires
only homogeneous local interactions that can be implemented in parallel. This
would be a huge simplification in an actual experiment. We find some minimal
physical requirements for the construction of unitary QCA in a 1 dimensional
Ising spin chain and demonstrate optimal pulse sequences for information
transport and entanglement distribution. We also introduce the theory of
non-unitary QCA and show by example that non-unitary rules can generate
environment assisted entanglement.Comment: 12 pages, 8 figures, submitted to Physical Review
The universe as quantum computer
This article reviews the history of digital computation, and investigates
just how far the concept of computation can be taken. In particular, I address
the question of whether the universe itself is in fact a giant computer, and if
so, just what kind of computer it is. I will show that the universe can be
regarded as a giant quantum computer. The quantum computational model of the
universe explains a variety of observed phenomena not encompassed by the
ordinary laws of physics. In particular, the model shows that the the quantum
computational universe automatically gives rise to a mix of randomness and
order, and to both simple and complex systems.Comment: 16 pages, LaTe
The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
In this Letter we show that an arbitrarily good approximation to the
propagator e^{itH} for a 1D lattice of n quantum spins with hamiltonian H may
be obtained with polynomial computational resources in n and the error
\epsilon, and exponential resources in |t|. Our proof makes use of the finitely
correlated state/matrix product state formalism exploited by numerical
renormalisation group algorithms like the density matrix renormalisation group.
There are two immediate consequences of this result. The first is that the
Vidal's time-dependent density matrix renormalisation group will require only
polynomial resources to simulate 1D quantum spin systems for logarithmic |t|.
The second consequence is that continuous-time 1D quantum circuits with
logarithmic |t| can be simulated efficiently on a classical computer, despite
the fact that, after discretisation, such circuits are of polynomial depth.Comment: 4 pages, 2 figures. Simplified argumen
Cellular Automata
Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented
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