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### Benjamin Russell, Susan Stepney.

Applications of Finsler Geometry to Speed Limits to Quantum Information Processing

#### International Journal of Foundations of Computer Science, **25**(4):489–505 2014

#### Abstract:

We are interested in fundamental limits to computation imposed by physical constraints.
In particular, the physical laws of motion constrain the speed at which a computer can
transition between well-defined states. Here, we discuss speed limits in the context of
quantum computing. We review some relevant parts of the theory of Finsler metrics
on Lie groups and homogeneous spaces such as the special unitary groups and complex
projective spaces. We show how these constructions can be applied to analysing the
limit to the speed of quantum information processing operations in constrained quantum
systems with finite dimensional Hilbert spaces of states. We demonstrate the approach
applied to a spin chain system.

preprint: PDF 421 K

journal doi: 10.1142/S0129054114400073

*this is a revised and extended version of the UCNC 2013 conference paper*

@article(SS-IJFCS14,
author = "Benjamin Russell and Susan Stepney",
title = "Applications of Finsler Geometry to Speed Limits to Quantum Information Processing",
journal = "International Journal of Foundations of Computer Science",
volume = 25,
issue = 4,
pages = "489-505",
doi = "10.1142/S0129054114400073",
year = 2014
)