Low depth measurement-based quantum computation beyond two-level systems
Abstract
Low depth measurement-based quantum computation with qudits (-level systems) is investigated and a precise relationship between this powerful model and qudit quantum circuits is derived in terms of computational depth and size complexity. To facilitate this investigation a qudit `unbounded fan-out' circuit model, in which a qudit may be quantum-copied into an arbitrary number of ancillas in a single time-step, is introduced and shown to be capable of implementing interesting -qudit unitaries in constant depth. A procedure for reducing the quantum computational depth in the measurement-based model is then proposed and using this it is then shown that there is a logarithmic depth separation between the depth complexity of qudit measurement-based computation and circuits composed of gates act on a bounded number of qudits. The relationship is made precise by showing that the depth complexity of the qudit measurement-based model is exactly equivalent to that of unbounded fan-out circuits. These results illustrate that the well-known advantages inherent in qubit measurement-based quantum computation are also applicable to the higher-dimensional generalisation. As qudits are both naturally available and have been shown to provide fundamental advantages over binary logic encodings, this then suggests that the qudit measurement-based model is a particularly appealing paradigm for universal quantum computation.
Cite
@article{arxiv.1510.06472,
title = {Low depth measurement-based quantum computation beyond two-level systems},
author = {Timothy J. Proctor},
journal= {arXiv preprint arXiv:1510.06472},
year = {2015}
}