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symQV: Automated Symbolic Verification of Quantum Programs

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Formal Methods (FM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14000))

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Abstract

We present symQV, a symbolic execution framework for writing and verifying quantum computations in the quantum circuit model. symQV can automatically verify that a quantum program complies with a first-order specification. We formally introduce a symbolic quantum program model. This allows to encode the verification problem in an SMT formula, which can then be checked with a \(\mathbf \delta \)-complete decision procedure. We also propose an abstraction technique to speed up the verification process. Experimental results show that the abstraction improves symQV ’s scalability by an order of magnitude to quantum programs with 24 qubits (a \( 2^{24}\)-dimensional state space).

F. Bauer-Marquart—The work was done while the first author was employed at the University of Konstanz.

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Notes

  1. 1.

    We choose \(\alpha \) to be real because the global phase [31] has no observable consequences.

  2. 2.

    Available at https://github.com/dreal/dreal4.

  3. 3.

    Available for download at https://doi.org/10.5281/zenodo.7400321.

References

  1. Abraham, F.N., et al.: Qiskit: an open-source framework for quantum computing (2017). https://github.com/Qiskit

  2. Ajagekar, A., Humble, T., You, F.: Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems. Comput. Chem. Eng. 132 (2020). https://doi.org/10.1016/j.compchemeng.2019.106630

  3. Amy, M.: Towards large-scale functional verification of universal quantum circuits. In: QPL. EPTCS, vol. 287, pp. 1–21 (2018). https://doi.org/10.4204/EPTCS.287.1

  4. Bauer-Marquart, F., Leue, S., Schilling, C.: symQV: automated symbolic verification of quantum programs. CoRR, abs/2212.02267 (2022). https://doi.org/10.48550/arXiv.2212.02267

  5. Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development - Coq’Art: The Calculus of Inductive Constructions. TTCS. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-662-07964-5

  6. Beyer, D., Keremoglu, M.E.: CPAchecker: a tool for configurable software verification. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 184–190. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_16

    Chapter  Google Scholar 

  7. Cadar, C., Dunbar, D., Engler, D.R.: KLEE: unassisted and automatic generation of high-coverage tests for complex systems programs. In: OSDI, vol. 8, pp. 209–224. USENIX Association (2008). http://www.usenix.org/events/osdi08/tech/full_papers/cadar/cadar.pdf

  8. Centrone, F., Kumar, N., Diamanti, E., Kerenidis, I.: Experimental demonstration of quantum advantage for NP verification with limited information. Nat. Commun. 12(1), 850 (2021). https://doi.org/10.1038/s41467-021-21119-1

    Article  Google Scholar 

  9. Chareton, C., Bardin, S., Bobot, F., Perrelle, V., Valiron, B.: An automated deductive verification framework for circuit-building quantum programs. In: Yoshida, N. (ed.) ESOP 2021. LNCS, vol. 12648, pp. 148–177. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-72019-3_6

    Chapter  Google Scholar 

  10. Childs, A.M., Maslov, D., Nam, Y.S., Ross, N.J., Su, Y.: Toward the first quantum simulation with quantum speedup. Proc. Natl. Acad. Sci. U.S.A. 115(38), 9456–9461 (2018). https://doi.org/10.1073/pnas.1801723115

    Article  MathSciNet  MATH  Google Scholar 

  11. Cirq Developers. Cirq (2021). See full list of authors on Github: https://github.com/quantumlib/Cirq/graphs/contributors

  12. Clarke, E.M., Henzinger, T.A., Veith, H., Bloem, R. (eds.): Handbook of Model Checking. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-319-10575-8

    Book  MATH  Google Scholar 

  13. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252. ACM (1977). https://doi.org/10.1145/512950.512973

  14. de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78800-3_24

    Chapter  Google Scholar 

  15. Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv preprint (2014). https://doi.org/10.48550/arXiv.1411.4028

  16. Gao, S., Avigad, J., Clarke, E.M.: \(\delta \)-complete decision procedures for satisfiability over the reals. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 286–300. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31365-3_23

    Chapter  Google Scholar 

  17. Gao, S., Kong, S., Clarke, E.M.: dReal: an SMT solver for nonlinear theories over the reals. In: Bonacina, M.P. (ed.) CADE 2013. LNCS (LNAI), vol. 7898, pp. 208–214. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38574-2_14

    Chapter  Google Scholar 

  18. Goddard, P., Mniszewski, S., Neukart, F., Pakin, S., Reinhardt, S.: How will early quantum computing benefit computational methods? In: Proceedings of the SIAM Annual Meeting (2017). https://sinews.siam.org/Details-Page/how-will-early-quantum-computing-benefit-computational-methods

  19. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: STOC, pp. 212–219. ACM (1996). https://doi.org/10.1145/237814.237866

  20. Hietala, K., Rand, R., Hung, S., Li, L., Hicks, M.: Proving quantum programs correct. In: ITP, Dagstuhl, Germany. LIPIcs, vol. 193, pp. 21:1–21:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.ITP.2021.21

  21. Houssein, E.H., Abohashima, Z., Elhoseny, M., Mohamed, W.M.: Hybrid quantum convolutional neural networks model for COVID-19 prediction using chest X-ray images. CoRR (2021). https://arxiv.org/abs/2102.06535

  22. IBM. IBM’s roadmap for scaling quantum technology (2020). https://research.ibm.com/blog/ibm-quantum-roadmap

  23. Jerbi, S., Fiderer, L.J., Nautrup, H.P., Kübler, J.M., Briegel, H.J., Dunjko, V.: Quantum machine learning beyond kernel methods. CoRR (2021). https://arxiv.org/abs/2110.13162

  24. Jordan, S.: Quantum algorithm zoo (2021). https://quantumalgorithmzoo.org

  25. Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse Ising model. Phys. Rev. E 58(5) (1998). https://doi.org/10.1103/PhysRevE.58.5355

  26. Krinner, S., et al.: Realizing repeated quantum error correction in a distance-three surface code. Nature 605(7911), 669–674 (2022). https://doi.org/10.1038/s41586-022-04566-8

    Article  Google Scholar 

  27. Kroening, D., Tautschnig, M.: CBMC – C bounded model checker. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 389–391. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54862-8_26

    Chapter  Google Scholar 

  28. Li, G., Zhou, L., Yu, N., Ding, Y., Ying, M., Xie, Y.: Projection-based runtime assertions for testing and debugging quantum programs. Proc. ACM Program. Lang. 4(OOPSLA), 150:1–150:29 (2020). https://doi.org/10.1145/3428218

  29. Liu, J., et al.: Formal verification of quantum algorithms using quantum Hoare logic. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11562, pp. 187–207. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25543-5_12

    Chapter  Google Scholar 

  30. Liu, S., et al.: \(Q|SI\rangle \): a quantum programming environment. In: Jones, C., Wang, J., Zhan, N. (eds.) Symposium on Real-Time and Hybrid Systems. LNCS, vol. 11180, pp. 133–164. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01461-2_8

    Chapter  Google Scholar 

  31. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information (10th Anniversary edition). Cambridge University Press (2016). https://doi.org/10.1017/CBO9780511976667. ISBN 978-1-10-700217-3

  32. Nipkow, T., Wenzel, M., Paulson, L.C. (eds.): Isabelle/HOL - A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45949-9

    Book  MATH  Google Scholar 

  33. Rand, R., Paykin, J., Zdancewic, S.: QWIRE practice: formal verification of quantum circuits in Coq. In: QPL. EPTCS, vol. 266, pp. 119–132 (2017). https://doi.org/10.4204/EPTCS.266.8

  34. Richardson, D.: Some undecidable problems involving elementary functions of a real variable. J. Symb. Log. 33(4), 514–520 (1968). https://doi.org/10.2307/2271358

    Article  MathSciNet  MATH  Google Scholar 

  35. Shi, Y., et al.: CertiQ: a mostly-automated verification of a realistic quantum compiler. arXiv preprint (2019). https://doi.org/10.48550/arXiv.1908.08963

  36. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997). https://doi.org/10.1137/S0097539795293172

    Article  MathSciNet  MATH  Google Scholar 

  37. Svore, K.M., et al.: Q#: enabling scalable quantum computing and development with a high-level DSL. In: RWDSL, pp. 7:1–7:10. ACM (2018). https://doi.org/10.1145/3183895.3183901

  38. Traversa, F.L.: Aircraft loading optimization: MemComputing the 5th Airbus problem. CoRR, abs/1903.08189 (2019). http://arxiv.org/abs/1903.08189

  39. Yu, N., Palsberg, J.: Quantum abstract interpretation. In: PLDI, pp. 542–558. ACM (2021). https://doi.org/10.1145/3453483.3454061

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Acknowledgments

This research was partly supported by DIREC - Digital Research Centre Denmark and the Villum Investigator Grant S4OS.

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Authors and Affiliations

  1. University of Konstanz, Konstanz, Germany

    Fabian Bauer-Marquart & Stefan Leue

  2. Aalborg University, Aalborg, Denmark

    Christian Schilling

Authors
  1. Fabian Bauer-Marquart
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  2. Stefan Leue
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  3. Christian Schilling
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Correspondence to Fabian Bauer-Marquart .

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Editors and Affiliations

  1. University of Toronto, Toronto, ON, Canada

    Marsha Chechik

  2. RWTH Aachen University, Aachen, Germany

    Joost-Pieter Katoen

  3. University of Lübeck, Lübeck, Germany

    Martin Leucker

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Bauer-Marquart, F., Leue, S., Schilling, C. (2023). symQV: Automated Symbolic Verification of Quantum Programs. In: Chechik, M., Katoen, JP., Leucker, M. (eds) Formal Methods. FM 2023. Lecture Notes in Computer Science, vol 14000. Springer, Cham. https://doi.org/10.1007/978-3-031-27481-7_12

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