3 research outputs found
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
On Grover's Search Algorithm from a Quantum Information Geometry Viewpoint
We present an information geometric characterization of Grover's quantum
search algorithm. First, we quantify the notion of quantum distinguishability
between parametric density operators by means of the Wigner-Yanase quantum
information metric. We then show that the quantum searching problem can be
recast in an information geometric framework where Grover's dynamics is
characterized by a geodesic on the manifold of the parametric density operators
of pure quantum states constructed from the continuous approximation of the
parametric quantum output state in Grover's algorithm. We also discuss possible
deviations from Grover's algorithm within this quantum information geometric
setting.Comment: 18 pages and 0 figures. To appear in Physica
Decoherence in quantum walks - a review
The development of quantum walks in the context of quantum computation, as
generalisations of random walk techniques, led rapidly to several new quantum
algorithms. These all follow unitary quantum evolution, apart from the final
measurement. Since logical qubits in a quantum computer must be protected from
decoherence by error correction, there is no need to consider decoherence at
the level of algorithms. Nonetheless, enlarging the range of quantum dynamics
to include non-unitary evolution provides a wider range of possibilities for
tuning the properties of quantum walks. For example, small amounts of
decoherence in a quantum walk on the line can produce more uniform spreading (a
top-hat distribution), without losing the quantum speed up. This paper reviews
the work on decoherence, and more generally on non-unitary evolution, in
quantum walks and suggests what future questions might prove interesting to
pursue in this area.Comment: 52 pages, invited review, v2 & v3 updates to include significant work
since first posted and corrections from comments received; some non-trivial
typos fixed. Comments now limited to changes that can be applied at proof
stag