48 research outputs found
Quantum Cellular Automata Pseudo-Random Maps
Quantum computation based on quantum cellular automata (QCA) can greatly
reduce the control and precision necessary for experimental implementations of
quantum information processing. A QCA system consists of a few species of
qubits in which all qubits of a species evolve in parallel. We show that, in
spite of its inherent constraints, a QCA system can be used to study complex
quantum dynamics. To this aim, we demonstrate scalable operations on a QCA
system that fulfill statistical criteria of randomness and explore which
criteria of randomness can be fulfilled by operators from various QCA
architectures. Other means of realizing random operators with only a few
independent operators are also discussed.Comment: 7 pages, 8 figures, submitted to PR
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
Quantum Causal Graph Dynamics
Consider a graph having quantum systems lying at each node. Suppose that the
whole thing evolves in discrete time steps, according to a global, unitary
causal operator. By causal we mean that information can only propagate at a
bounded speed, with respect to the distance given by the graph. Suppose,
moreover, that the graph itself is subject to the evolution, and may be driven
to be in a quantum superposition of graphs---in accordance to the superposition
principle. We show that these unitary causal operators must decompose as a
finite-depth circuit of local unitary gates. This unifies a result on Quantum
Cellular Automata with another on Reversible Causal Graph Dynamics. Along the
way we formalize a notion of causality which is valid in the context of quantum
superpositions of time-varying graphs, and has a number of good properties.
Keywords: Quantum Lattice Gas Automata, Block-representation,
Curtis-Hedlund-Lyndon, No-signalling, Localizability, Quantum Gravity, Quantum
Graphity, Causal Dynamical Triangulations, Spin Networks, Dynamical networks,
Graph Rewriting.Comment: 8 pages, 1 figur
On the digraph of a unitary matrix
Given a matrix M of size n, a digraph D on n vertices is said to be the
digraph of M, when M_{ij} is different from 0 if and only if (v_{i},v_{j}) is
an arc of D. We give a necessary condition, called strong quadrangularity, for
a digraph to be the digraph of a unitary matrix. With the use of such a
condition, we show that a line digraph, LD, is the digraph of a unitary matrix
if and only if D is Eulerian. It follows that, if D is strongly connected and
LD is the digraph of a unitary matrix then LD is Hamiltonian. We conclude with
some elementary observations. Among the motivations of this paper are coined
quantum random walks, and, more generally, discrete quantum evolution on
digraphs.Comment: 6 page
Quantum-Information Processing with Semiconductor Macroatoms
An all optical implementation of quantum information processing with
semiconductor macroatoms is proposed. Our quantum hardware consists of an array
of semiconductor quantum dots and the computational degrees of freedom are
energy-selected interband optical transitions. The proposed quantum-computing
strategy exploits exciton-exciton interactions driven by ultrafast sequences of
multi-color laser pulses. Contrary to existing proposals based on charge
excitations, the present all-optical implementation does not require the
application of time-dependent electric fields, thus allowing for a
sub-picosecond, i.e. decoherence-free, operation time-scale in realistic
state-of-the-art semiconductor nanostructures.Comment: 11 pages, 5 figures, to be published in Phys. Rev. Lett., significant
changes in the text and new simulations (figure 3
Quantum Walks and Reversible Cellular Automata
We investigate a connection between a property of the distribution and a
conserved quantity for the reversible cellular automaton derived from a
discrete-time quantum walk in one dimension. As a corollary, we give a detailed
information of the quantum walk.Comment: 15 pages, minor corrections, some references adde
A Logic Simplification Approach for Very Large Scale Crosstalk Circuit Designs
Crosstalk computing, involving engineered interference between nanoscale
metal lines, offers a fresh perspective to scaling through co-existence with
CMOS. Through capacitive manipulations and innovative circuit style, not only
primitive gates can be implemented, but custom logic cells such as an Adder,
Subtractor can be implemented with huge gains. Our simulations show over 5x
density and 2x power benefits over CMOS custom designs at 16nm [1]. This paper
introduces the Crosstalk circuit style and a key method for large-scale circuit
synthesis utilizing existing EDA tool flow. We propose to manipulate the CMOS
synthesis flow by adding two extra steps: conversion of the gate-level netlist
to Crosstalk implementation friendly netlist through logic simplification and
Crosstalk gate mapping, and the inclusion of custom cell libraries for
automated placement and layout. Our logic simplification approach first
converts Cadence generated structured netlist to Boolean expressions and then
uses the majority synthesis tool to obtain majority functions, which is further
used to simplify functions for Crosstalk friendly implementations. We compare
our approach of logic simplification to that of CMOS and majority logic-based
approaches. Crosstalk circuits share some similarities to majority synthesis
that are typically applied to Quantum Cellular Automata technology. However,
our investigation shows that by closely following Crosstalk's core circuit
styles, most benefits can be achieved. In the best case, our approach shows 36%
density improvements over majority synthesis for MCNC benchmark