Topological Quantum Programming in TED-K

• URL: http://arxiv.org/abs/2209.08331v1
• Date: Sat, 17 Sep 2022 14:00:37 GMT
• Title: Topological Quantum Programming in TED-K
• Authors: Hisham Sati and Urs Schreiber
• Abstract summary: We describe a fundamental and natural scheme that we are developing, for typed functional (hence verifiable) topological quantum programming. It reflects the universal fine technical detail of topological q-bits, namely of symmetry-protected (or enhanced) topologically ordered Laughlin-type anyon ground states. The language system is under development at the "Center for Quantum and Topological Systems" at the Research Institute of NYU, Abu Dhabi.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While the realization of scalable quantum computation will arguably require topological stabilization and, with it, topological-hardware-aware quantum programming and topological-quantum circuit verification, the proper combination of these strategies into dedicated topological quantum programming languages has not yet received attention. Here we describe a fundamental and natural scheme that we are developing, for typed functional (hence verifiable) topological quantum programming which is topological-hardware aware -- in that it natively reflects the universal fine technical detail of topological q-bits, namely of symmetry-protected (or enhanced) topologically ordered Laughlin-type anyon ground states in topological phases of quantum materials. What makes this work is: (1) our recent result that wavefunctions of realistic and technologically viable anyon species -- namely of su(2)-anyons such as the popular Majorana/Ising anyons but also of computationally universal Fibonacci anyons -- are reflected in the twisted equivariant differential (TED) K-cohomology of configuration spaces of codimension=2 nodal defects in the host material's crystallographic orbifold; (2) combined with our earlier observation that such TED generalized cohomology theories on orbifolds interpret intuitionistically-dependent linear data types in cohesive homotopy type theory (HoTT), supporting a powerful modern form of modal quantum logic. In this short note we give an exposition of the basic ideas, a quick review of the underlying results and a brief indication of the basic language constructs for anyon braiding via TED-K in cohesive HoTT. The language system is under development at the "Center for Quantum and Topological Systems" at the Research Institute of NYU, Abu Dhabi.

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