Applications of Finsler Geometry to Speed Limits to Quantum Information Processing

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JournalInternational Journal of Foundations of Computer Science
DatePublished - Jun 2014
Issue number4
Volume25
Pages (from-to)489–505
Original languageEnglish

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.

    Research areas

  • Quantum optimal control, Finsler geometry, quantum speed limit, quantum computing

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