2 research outputs found
Quantum picturalism for topological cluster-state computing
Topological quantum computing is a way of allowing precise quantum
computations to run on noisy and imperfect hardware. One implementation uses
surface codes created by forming defects in a highly-entangled cluster state.
Such a method of computing is a leading candidate for large-scale quantum
computing. However, there has been a lack of sufficiently powerful high-level
languages to describe computing in this form without resorting to single-qubit
operations, which quickly become prohibitively complex as the system size
increases. In this paper we apply the category-theoretic work of Abramsky and
Coecke to the topological cluster-state model of quantum computing to give a
high-level graphical language that enables direct translation between quantum
processes and physical patterns of measurement in a computer - a "compiler
language". We give the equivalence between the graphical and topological
information flows, and show the applicable rewrite algebra for this computing
model. We show that this gives us a native graphical language for the design
and analysis of topological quantum algorithms, and finish by discussing the
possibilities for automating this process on a large scale.Comment: 18 pages, 21 figures. Published in New J. Phys. special issue on
topological quantum computin
The GHZ/W-calculus contains rational arithmetic
Graphical calculi for representing interacting quantum systems serve a number
of purposes: compositionally, intuitive graphical reasoning, and a logical
underpinning for automation. The power of these calculi stems from the fact
that they embody generalized symmetries of the structure of quantum operations,
which, for example, stretch well beyond the Choi-Jamiolkowski isomorphism. One
such calculus takes the GHZ and W states as its basic generators. Here we show
that this language allows one to encode standard rational calculus, with the
GHZ state as multiplication, the W state as addition, the Pauli X gate as
multiplicative inversion, and the Pauli Z gate as additive inversion.Comment: In Proceedings HPC 2010, arXiv:1103.226