16,793 research outputs found
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 to Reduce the Complexity of Simulating a Quantum Computer
Recently Quantum Computation has generated a lot of interest due to the
discovery of a quantum algorithm which can factor large numbers in polynomial
time. The usefulness of a quantum com puter is limited by the effect of errors.
Simulation is a useful tool for determining the feasibility of quantum
computers in the presence of errors. The size of a quantum computer that can be
simulat ed is small because faithfully modeling a quantum computer requires an
exponential amount of storage and number of operations. In this paper we define
simulation models to study the feasibility of quantum computers. The most
detailed of these models is based directly on a proposed imple mentation. We
also define less detailed models which are exponentially less complex but still
pro duce accurate results. Finally we show that the two different types of
errors, decoherence and inaccuracies, are uncorrelated. This decreases the
number of simulations which must be per formed.Comment: 25 page
Simulating chemistry efficiently on fault-tolerant quantum computers
Quantum computers can in principle simulate quantum physics exponentially
faster than their classical counterparts, but some technical hurdles remain.
Here we consider methods to make proposed chemical simulation algorithms
computationally fast on fault-tolerant quantum computers in the circuit model.
Fault tolerance constrains the choice of available gates, so that arbitrary
gates required for a simulation algorithm must be constructed from sequences of
fundamental operations. We examine techniques for constructing arbitrary gates
which perform substantially faster than circuits based on the conventional
Solovay-Kitaev algorithm [C.M. Dawson and M.A. Nielsen, \emph{Quantum Inf.
Comput.}, \textbf{6}:81, 2006]. For a given approximation error ,
arbitrary single-qubit gates can be produced fault-tolerantly and using a
limited set of gates in time which is or ; with sufficient parallel preparation of ancillas, constant average
depth is possible using a method we call programmable ancilla rotations.
Moreover, we construct and analyze efficient implementations of first- and
second-quantized simulation algorithms using the fault-tolerant arbitrary gates
and other techniques, such as implementing various subroutines in constant
time. A specific example we analyze is the ground-state energy calculation for
Lithium hydride.Comment: 33 pages, 18 figure
A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton
We describe a simple n-dimensional quantum cellular automaton (QCA) capable
of simulating all others, in that the initial configuration and the forward
evolution of any n-dimensional QCA can be encoded within the initial
configuration of the intrinsically universal QCA. Several steps of the
intrinsically universal QCA 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.Comment: 13 pages, 7 figures. In Proceedings of the 4th International
Conference on Language and Automata Theory and Applications (LATA 2010),
Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382
Complexity, parallel computation and statistical physics
The intuition that a long history is required for the emergence of complexity
in natural systems is formalized using the notion of depth. The depth of a
system is defined in terms of the number of parallel computational steps needed
to simulate it. Depth provides an objective, irreducible measure of history
applicable to systems of the kind studied in statistical physics. It is argued
that physical complexity cannot occur in the absence of substantial depth and
that depth is a useful proxy for physical complexity. The ideas are illustrated
for a variety of systems in statistical physics.Comment: 21 pages, 7 figure
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