2,111 research outputs found
The expressive power of quantum walks in terms of language acceptance
Discrete time quantum walks are known to be universal for quantum
computation. This has been proven by showing that they can simulate a universal
quantum gate set. In this paper, we examine computation by quantum walks in
terms of language acceptance, and present two ways in which discrete time
quantum walks can accept some languages with certainty. These walks can take
quantum as well as classical inputs, and we show that when the input is
quantum, the walks can also be interpreted as performing the task of quantum
state discrimination.Comment: In Proceedings QPL 2012, arXiv:1407.842
Decoherence in Discrete Quantum Walks
We present an introduction to coined quantum walks on regular graphs, which
have been developed in the past few years as an alternative to quantum Fourier
transforms for underpinning algorithms for quantum computation. We then
describe our results on the effects of decoherence on these quantum walks on a
line, cycle and hypercube. We find high sensitivity to decoherence, increasing
with the number of steps in the walk, as the particle is becoming more
delocalised with each step. However, the effect of a small amount of
decoherence can be to enhance the properties of the quantum walk that are
desirable for the development of quantum algorithms, such as fast mixing times
to uniform distributions.Comment: 15 pages, Springer LNP latex style, submitted to Proceedings of DICE
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Dairying in the Waikato Region of New Zealand: An overview of historical statistics
The dairy industry is an important contributor to the economy of the Waikato region of New Zealand. An understanding of the history and development of the dairy sector in the different districts of the Waikato region is important in terms of informing future policy. Unfortunately there are currently no consistent long-run spatially disaggregated data sets available for the districts of the Waikato region that extend any further back than 1990. In this paper, we present the current state of dairy farming data available for the territorial local authorities within the Waikato region, and briefly discuss a set of methods that will be employed to develop consistent long-run spatially disaggregated data series for (i) milk production; (ii) total number of productive dairy cattle; (iii) total number of dairy farms; and (iv) total effective hectares devoted to dairy production
Optimal computation with non-unitary quantum walks
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times, respectively. Non-unitary quantum walks can provide a useful optimisation of these properties, producing a more uniform distribution on the line, and faster mixing times on the cycle. We investigate the interplay between quantum and random dynamics by comparing the resources required, and examining numerically how the level of quantum correlations varies during the walk. We show numerically that the optimal non-unitary quantum walk proceeds such that the quantum correlations are nearly all removed at the point of the final measurement. This requires only O(logT) random bits for a quantum walk of T steps
Entanglement and its Role in Shor's Algorithm
Entanglement has been termed a critical resource for quantum information
processing and is thought to be the reason that certain quantum algorithms,
such as Shor's factoring algorithm, can achieve exponentially better
performance than their classical counterparts. The nature of this resource is
still not fully understood: here we use numerical simulation to investigate how
entanglement between register qubits varies as Shor's algorithm is run on a
quantum computer. The shifting patterns in the entanglement are found to relate
to the choice of basis for the quantum Fourier transform.Comment: 15 pages, 4 eps figures, v1-3 were for conference proceedings (not
included in the end); v4 is improved following referee comments, expanded
explanations and added reference
The QWalk Simulator of Quantum Walks
Several research groups are giving special attention to quantum walks
recently, because this research area have been used with success in the
development of new efficient quantum algorithms. A general simulator of quantum
walks is very important for the development of this area, since it allows the
researchers to focus on the mathematical and physical aspects of the research
instead of deviating the efforts to the implementation of specific numerical
simulations. In this paper we present QWalk, a quantum walk simulator for one-
and two-dimensional lattices. Finite two-dimensional lattices with generic
topologies can be used. Decoherence can be simulated by performing measurements
or by breaking links of the lattice. We use examples to explain the usage of
the software and to show some recent results of the literature that are easily
reproduced by the simulator.Comment: 21 pages, 11 figures. Accepted in Computer Physics Communications.
Simulator can be downloaded from http://qubit.lncc.br/qwal
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