ICFP 2022
Sun 11 - Fri 16 September 2022 Ljubljana, Slovenia
Thu 15 Sep 2022 11:00 - 11:25 at E3 - Hardware-aware quantum programming Chair(s): Kartik Singhal

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 it 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 $\mathfrak{su}(2)$-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.

Not only should this emulation of anyonic topological hardware functionality via TED-K implemented in cohesive HoTT make advanced formal software verification tools available for hardware-aware topological quantum programming, but the constructive nature of type-checking a TED-K quantum program in cohesive HoTT on a classical computer using existing software (such as Agda-flat), has the potential to amount at once to classically simulating the intended quantum computation at the deep level of physical topological q-bits.

This would make `TED-K in cohesive HoTT an ideal software laboratory for topological quantum computation on technologically viable types of topological q-bits, complete with ready compilation to topological quantum circuits as soon as the hardware becomes available.

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. Further details are available at: https://ncatlab.org/schreiber/show/TQCinTEDK#FurtherDetails

abstract (TQCinTEDK-220917.pdf)572KiB

Thu 15 Sep

Displayed time zone: Belgrade, Bratislava, Budapest, Ljubljana, Prague change

11:00 - 12:30
Hardware-aware quantum programmingPLanQC at E3
Chair(s): Kartik Singhal University of Chicago
Topological Quantum Programming in TED-KVirtual
Hisham Sati New York University, Abu Dhabi, Urs Schreiber New York University, Abu Dhabi
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Qrisp: A Framework for Compilable High-Level Programming of Gate-Based Quantum Computers
Raphael Seidel Fraunhofer Institute for Open Communication Systems, Sebastian Bock Fraunhofer Institute for Open Communication Systems, Nikolay Tcholtchev Fraunhofer Institute for Open Communication Systems, Manfred Hauswirth Fraunhofer Institute for Open Communication Systems, TU Berlin
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Poster session

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