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International Conference on Reversible Computation

RC 2019: Reversible Computation pp 87–107Cite as

Sized Types for Low-Level Quantum Metaprogramming

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11497))

Abstract

One of the most fundamental aspects of quantum circuit design is the concept of families of circuits parametrized by an instance size. As in classical programming, metaprogramming allows the programmer to write entire families of circuits simultaneously, an ability which is of particular importance in the context of quantum computing as algorithms frequently use arithmetic over non-standard word lengths. In this work, we introduce metaQASM, a typed extension of the openQASM language supporting the metaprogramming of circuit families. Our language and type system, built around a lightweight implementation of sized types, supports subtyping over register sizes and is moreover type-safe. In particular, we prove that our system is strongly normalizing, and as such any well-typed metaQASM program can be statically unrolled into a finite circuit.

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Notes

  1. 1.

    The function inplace_add2 could instead be directly generated by writing the adder as , then specializing qa to the finite type (Qubit, Qubit) using type applications. However, the non-generic serialization functions in Quipper appear to work only for small finite tuple types.

  2. 2.

    Controlled circuits are another desirable metaprogramming feature found in many quantum circuit description languages. While metaQASM gates are in fact closed over qubit controls, they require ancillae to construct [21]. This complicates the inclusion of a control instruction in metaQASM, and further abstracts away from concrete, resource-driven nature of QASM.

References

  1. Aharonov, D., Jones, V., Landau, Z.: A polynomial quantum algorithm for approximating the jones polynomial. In: Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing, STOC, pp. 427–436 (2006). https://doi.org/10.1145/1132516.1132579

  2. Altenkirch, T., Grattage, J.: A functional quantum programming language. In: 20th Annual IEEE Symposium on Logic in Computer Science, LICS, pp. 249–258 (2005). https://doi.org/10.1109/LICS.2005.1

  3. Amy, M.: Feynman. https://github.com/meamy/feynman

  4. Amy, M., Roetteler, M., Svore, K.M.: Verified compilation of space-efficient reversible circuits. In: Proceedings of the 29th International Conference on Computer Aided Verification, CAV, pp. 3–21 (2017). https://doi.org/10.1007/978-3-319-63390-9_1

  5. Bello, L., et al.: Qiskit. https://github.com/Qiskit/qiskit-terra

  6. Cross, A.W., Bishop, L.S., Smolin, J.A., Gambetta, J.M.: Open quantum assembly language. arXiv preprint (2017). http://arxiv.org/abs/1707.03429

  7. Fu, P.: Private communication (2018)

    Google Scholar 

  8. Gay, S.J.: Quantum programming languages: survey and bibliography. Math. Struct. Comput. Sci. 16(4), 581–600 (2006). https://doi.org/10.1017/S0960129506005378

    Article  MathSciNet  MATH  Google Scholar 

  9. Gheorghiu, V.: Quantum++: a modern C++ quantum computing library. PLoS ONE 13(12), 1–27 (2018). https://doi.org/10.1371/journal.pone.0208073

    Article  Google Scholar 

  10. Green, A.S., Lumsdaine, P.L.F., Ross, N.J., Selinger, P., Valiron, B.: An introduction to quantum programming in Quipper. In: Dueck, G.W., Miller, D.M. (eds.) RC 2013. LNCS, vol. 7948, pp. 110–124. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38986-3_10

    Chapter  Google Scholar 

  11. Green, A.S., Lumsdaine, P.L., Ross, N.J., Selinger, P., Valiron, B.: Quipper: a scalable quantum programming language. In: Proceedings of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2013, pp. 333–342 (2013). https://doi.org/10.1145/2491956.2462177

  12. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, STOC, pp. 212–219 (1996). https://doi.org/10.1145/237814.237866

  13. Häner, T., Steiger, D.S.: 0.5 petabyte simulation of a 45-qubit quantum circuit. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC, pp. 33:1–33:10 (2017). https://doi.org/10.1145/3126908.3126947

  14. Häner, T., Steiger, D.S., Svore, K., Troyer, M.: A software methodology for compiling quantum programs. Quantum Sci. Technol. 3(2), 020501 (2018). https://doi.org/10.1088/2058-9565/aaa5cc

    Article  Google Scholar 

  15. Heyfron, L.E., Campbell, E.T.: An efficient quantum compiler that reduces T count. Quantum Sci. Technol. 4(1), 015004 (2018). https://doi.org/10.1088/2058-9565/aad604

    Article  Google Scholar 

  16. JavadiAbhari, A., et al.: ScaffCC: scalable compilation and analysis of quantum programs. Parallel Comput. 45(C), 2–17 (2015). https://doi.org/10.1016/j.parco.2014.12.001

    Article  Google Scholar 

  17. Khammassi, N., Ashraf, I., Fu, X., Almudever, C.G., Bertels, K.: QX: a high-performance quantum computer simulation platform. In: Proceedings of the 20th Design, Automation Test in Europe Conference Exhibition, DATE, pp. 464–469 (2017). https://doi.org/10.23919/DATE.2017.7927034

  18. Khammassi, N., Guerreschi, G., Ashraf, I., Hogaboam, J.W., Almudever, C.G., Bertels, K.: cQASM v1.0: towards a common quantum assembly language. arXiv preprint (2018). http://arxiv.org/abs/1805.09607

  19. Killoran, N., Izaac, J., Quesada, N., Bergholm, V., Amy, M., Weedbrook, C.: Strawberry fields: a software platform for photonic quantum computing. Quantum 3, 129 (2019). https://doi.org/10.22331/q-2019-03-11-129

    Article  Google Scholar 

  20. Kissinger, A., van de Wetering, J.: PyZX: large scale automated diagrammatic reasoning. arXiv preprint (2019). http://arxiv.org/abs/1904.04735

  21. Kliuchnikov, V., Maslov, D., Mosca, M.: Fast and efficient exact synthesis of single-qubit unitaries generated by clifford and T gates. Quantum Inf. Comput. 13(7–8), 607–630 (2013). https://doi.org/10.26421/QIC13.7-8

    Article  MathSciNet  Google Scholar 

  22. Liu, S., et al.: \(Q|SI\rangle \): a quantum programming environment. arXiv preprint (2017). http://arxiv.org/abs/1710.09500

  23. Lloyd, S.: Universal quantum simulators. Science 273(5278), 1073–1078 (1996). https://doi.org/10.1126/science.273.5278.1073

    Article  MathSciNet  MATH  Google Scholar 

  24. Martonosi, M., Roetteler, M.: Next steps in quantum computing: computer science’s role. Computing Community Consortium (CCC) workshop report (2019). http://arxiv.org/abs/1903.10541

  25. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge Series on Information and the Natural Sciences. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  26. Ömer, B.: Quantum programming in QCL. Master’s thesis, Technical University of Vienna (2000). http://tph.tuwien.ac.at/~oemer/qcl.html

  27. Paykin, J., Rand, R., Zdancewic, S.: QWIRE: a core language for quantum circuits. In: Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages, POPL, pp. 846–858 (2017). https://doi.org/10.1145/3009837.3009894

  28. Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018). https://doi.org/10.22331/q-2018-08-06-79

    Article  Google Scholar 

  29. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, SFCS, pp. 124–134 (1994). https://doi.org/10.1109/SFCS.1994.365700

  30. Smith, R.S., Curtis, M.J., Zeng, W.J.: A practical quantum instruction set architecture. arXiv preprint (2016). http://arxiv.org/abs/1608.03355

  31. Soeken, M.: RevKit. https://msoeken.github.io/revkit.html

  32. Steiger, D.S., Häner, T., Troyer, M.: ProjectQ: an open source software framework for quantum computing. Quantum 2, 49 (2018). https://doi.org/10.22331/q-2018-01-31-49

    Article  Google Scholar 

  33. Svore, K., et al.: \(Q\#\): enabling scalable quantum computing and development with a high-level DSL. In: Proceedings of the 3rd ACM International Workshop on Real World Domain Specific Languages, RWDSL, pp. 7:1–7:10 (2018). https://doi.org/10.1145/3183895.3183901

  34. Xi, H.: Dependent types for program termination verification. In: Proceedings 16th Annual IEEE Symposium on Logic in Computer Science, LICS, pp. 231–242 (2001). https://doi.org/10.1109/LICS.2001.932500

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Acknowledgements

The author wishes to thank Gregor Richards for motivating this project and Frank Fu for pointing out alternative ways of typing several examples in this manuscript. The author also wishes to thank the anonymous reviewers for their detailed comments which have vastly improved the presentation of this work.

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Authors and Affiliations

  1. University of Waterloo, Waterloo, Canada

    Matthew Amy

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  1. Matthew Amy
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Correspondence to Matthew Amy .

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Editors and Affiliations

  1. University of Copenhagen, Copenhagen, Denmark

    Michael Kirkedal Thomsen

  2. École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Mathias Soeken

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Amy, M. (2019). Sized Types for Low-Level Quantum Metaprogramming. In: Thomsen, M., Soeken, M. (eds) Reversible Computation. RC 2019. Lecture Notes in Computer Science(), vol 11497. Springer, Cham. https://doi.org/10.1007/978-3-030-21500-2_6

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  • DOI: https://doi.org/10.1007/978-3-030-21500-2_6

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