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Performing fully parallel constraint logic programming on a quantum annealer

Published online by Cambridge University Press:  06 May 2018

SCOTT PAKIN Open the ORCID record for SCOTT PAKIN [Opens in a new window]
SCOTT PAKIN*
Affiliation:
Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, MS B287, Los Alamos, New Mexico, USA (e-mail: [email protected])
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Abstract

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A quantum annealer exploits quantum effects to solve a particular type of optimization problem. The advantage of this specialized hardware is that it effectively considers all possible solutions in parallel, thereby potentially outperforming classical computing systems. However, despite quantum annealers having recently become commercially available, there are relatively few high-level programming models that target these devices. In this article, we show how to compile a subset of Prolog enhanced with support for constraint logic programming into a two-local Ising-model Hamiltonian suitable for execution on a quantum annealer. In particular, we describe the series of transformations one can apply to convert constraint logic programs expressed in Prolog into an executable form that bears virtually no resemblance to a classical machine model yet that evaluates the specified constraints in a fully parallel manner. We evaluate our efforts on a 1,095-qubit D-Wave 2X quantum annealer and describe the approach's associated capabilities and shortcomings.

Keywords

quantum annealingquantum computingconstraint logic programmingPrologD-Wave
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 18 , Special Issue 5-6: Special Issue on Parallel and Distributed Logic Programming , September 2018 , pp. 928 - 949
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

*This work was supported by Laboratory Directed Research and Development (LDRD) funding at Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Los Alamos National Security LLC for the US Department of Energy under contract DE-AC52-06NA25396.

References

Barahona, F. 1982. On the computational complexity of Ising spin glass models. Journal of Physics A: Mathematical and General 15, 10, 3241.Google Scholar
Berkeley Logic Synthesis and Verification Group. 2016. ABC: A system for sequential synthesis and verification. URL: http://www.eecs.berkeley.edu/~alanmi/abc/. [Accessed on April 24, 2018].Google Scholar
Bravyi, S., Bessen, A. J. and Terhal, B. M. 2006. Merlin-Arthur games and stoquastic complexity. arXiv:quant-ph/0611021v2.Google Scholar
Bravyi, S. and Hastings, M. 2017. On complexity of the quantum Ising model. Communications in Mathematical Physics 349, 1, 1–45.Google Scholar
Brayton, R. and Mishchenko, A. 2010. ABC: An academic industrial-strength verification tool. In Proc. 22nd International Conference on Computer Aided Verification, Touili, T., Cook, B., and Jackson, P., Eds. Springer, Berlin, Heidelberg, Edinburgh, UK, 24–40.Google Scholar
Bunyk, P. I., Hoskinson, E. M., Johnson, M. W., Tolkacheva, E., Altomare, F., Berkley, A. J., Harris, R., Hilton, J. P., Lanting, T., Przybysz, A. J. and Whittaker, J. 2014. Architectural considerations in the design of a superconducting quantum annealing processor. IEEE Transactions on Applied Superconductivity 24, 4, 1–10.Google Scholar
Cai, J., Macready, B. and Roy, A. 2014. A practical heuristic for finding graph minors. arXiv:1406.2741 [quant-ph].Google Scholar
Choi, V. 2008. Minor-embedding in adiabatic quantum computation: I. The parameter setting problem. Quantum Information Processing 7, 5, 193–209.Google Scholar
Cormen, T. H., Leiserson, C. E., Rivest, R. L. and Stein, C. 2001. Introduction to Algorithms, 2nd ed. MIT Press.Google Scholar
Cross, A. W., Bishop, L. S., Smolin, J. A. and Gambetta, J. M. 2017. Open quantum assembly language. arXiv:1707.03429 [quant-ph].Google Scholar
D-Wave Systems, Inc. 2017a. Developer Guide for Python. D-Wave Systems, Inc., Burnaby, British Columbia, Canada.Google Scholar
D-Wave Systems, Inc. 2017b. ToQ Overview. D-Wave Systems, Inc., Burnaby, British Columbia, Canada. ToQ documentation, qOp version 2.3.1.Google Scholar
Dahl, E. D. 2014. Deqo: A Direct Embedding Quantum Optimizer. D-Wave Systems, Inc.Google Scholar
Dutra, I. 2010. Constraint logic programming: A short tutorial. URL: https://www.dcc.fc.up.pt/~ines/talks/clp-v1.pdf. [Accessed on April 24, 2018].Google Scholar
Farhi, E. and Gutmann, S. 1998. Analog analogue of a digital quantum computation. Physical Review A 57, 2403–2406.Google Scholar
Feynman, R. P. 1986. Quantum mechanical computers. Foundations of Physics 16, 6, 507–531.Google Scholar
Finnila, A. B., Gomez, M. A., Sebenik, C., Stenson, C. and Doll, J. D. 1994. Quantum annealing: A new method for minimizing multidimensional functions. Chemical Physics Letters 219, 5, 343–348.Google Scholar
Fujitsu Laboratories Ltd. 2017. Fujitsu Laboratories Develops New Architecture that Rivals Quantum Computers in Utility. Press release, 20 October 2016, Kawasaki, Japan. URL: http://www.fujitsu.com/global/about/resources/news/press-releases/2016/1020-02.html [Accessed on April 24, 2018].Google Scholar
Gansner, E. R. and North, S. C. 2000. An open graph visualization system and its applications to software engineering. Software–-Practice and Experience 30, 11, 1203–1233.Google Scholar
Green, A. S., Lumsdaine, P. L., Ross, N. J., Selinger, P. and Valiron, B. 2013. Quipper: A scalable quantum programming language. In Proc. of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation. ACM, New York, USA, 333–342.Google Scholar
Grover, L. K. 1996. A fast quantum mechanical algorithm for database search. In Proc. of the 28th Annual ACM Symposium on Theory of Computing. ACM, New York, NY, USA, 212–219.Google Scholar
Heim, B., Brown, E. W., Wecker, D. and Troyer, M. 2017. Designing adiabatic quantum optimization: A case study for the traveling salesman problem. arXiv:1702.06248v1 [quant-ph].Google Scholar
Hen, I. and Young, A. P. 2011. Exponential complexity of the quantum adiabatic algorithm for certain satisfiability problems. Physical Review E 84, 061152.Google Scholar
James, R. P., Ortiz, G. and Sabry, A. 2011. Quantum computing over finite fields. arXiv:1101.3764 [quant-ph].Google Scholar
JavadiAbhari, A., Patil, S., Kudrow, D., Heckey, J., Lvov, A., Chong, F. T. and Martonosi, M. 2015. ScaffCC: Scalable compilation and analysis of quantum programs. Parallel Computing 45, 2–17.Google Scholar
Johnson, M. W., Amin, M. H. S., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A. J., Johansson, J., Bunyk, P., Chapple, E. M., Enderud, C., Hilton, J. P., Karimi, K., Ladizinsky, E., Ladizinsky, N., Oh, T., Perminov, I., Rich, C., Thom, M. C., Tolkacheva, E., Truncik, C. J. S., Uchaikin, S., Wang, J., Wilson, B. and Rose, G. 2011. Quantum annealing with manufactured spins. Nature 473, 7346, 194–198.Google Scholar
Kadowaki, T. and Nishimori, H. 1998. Quantum annealing in the transverse Ising model. Physical Review E 58, 5355–5363.Google Scholar
Kahn, H., La Fontaine, R. and Lau, R. 2000. Electronic design interchange format (EDIF): Part 2: Version 4 0 0. Standard IEC 61690-2:2000, International Electrotechnical Commission, Manchester, UK.Google Scholar
Kaminsky, W. M., Lloyd, S. and Orlando, T. P. 2004. Scalable superconducting architecture for adiabatic quantum computation. arXiv:quant-ph/0403090v2.Google Scholar
Kirkpatrick, S., Gelatt, C. D. and Vecchi, M. P. 1983. Optimization by simulated annealing. Science 220, 4598, 671–680.Google Scholar
Knight, W. 2017. IBM Raises the Bar with a 50-Qubit Quantum Computer. MIT Technology Review. 10 November 2017. ISSN: 0040-1692. URL: https://www.technologyreview.com/s/609451/ibm-raises-the-bar-with-a-50-qubit-quantum-computer [Accessed on April 24, 2018].Google Scholar
Lucas, A. 2014. Ising formulations of many NP problems. Frontiers in Physics 2, 5, 1–15.Google Scholar
Microsoft Corp. 2017. The Q# progamming language. URL: https://docs.microsoft.com/en-us/quantum/quantum-qr-intro [Accessed on April 24, 2018].Google Scholar
Nethercote, N., Stuckey, P. J., Becket, R., Brand, S., Duck, G. J. and Tack, G. 2007. MiniZinc: Towards a standard CP modelling language. In Proc. of the 13th International Conference on Principles and Practice of Constraint Programming, Bessière, C., Ed. Springer, Berlin, Heidelberg, 529–543.Google Scholar
Pakin, S. 2016. A quantum macro assembler. In Proc. of the 2016 IEEE High Performance Extreme Computing Conference (HPEC).Google Scholar
Robinson, J. A. 1965. A machine-oriented logic based on the resolution principle. Journal of the ACM 12, 1, 23–41.Google Scholar
Shor, P. W. 1999. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Review 41, 2, 303–332.Google Scholar
Smith, R. S., Curtis, M. J. and Zeng, W. J. 2017. A practical quantum instruction set architecture. arXiv:1608.03355 [quant-ph].Google Scholar
Thomas, D. and Moorby, P. 2002. The Verilog Hardware Description Language, 5th ed. Springer.Google Scholar
Triska, M. 2012. The finite domain constraint solver of SWI-Prolog. In Proc. of the 11th International Symposium on Functional and Logic Programming (FLOPS 2012). Lecture Notes in Computer Science, vol. 7294. Kobe, Japan, 307–316.Google Scholar
Wecker, D. and Svore, K. M. 2014. LIQUi|〉: A software design architecture and domain-specific language for quantum computing. arXiv:1402.4467 [quant-ph].Google Scholar
Wielemaker, J., Schrijvers, T., Triska, M. and Lager, T. 2012. SWI-Prolog. Theory and Practice of Logic Programming 12, 1–2, 67–96.Google Scholar
Wolf, C. and Glaser, J. 2013. Yosys–-A free Verilog synthesis suite. In Proc. of the 21st Austrian Workshop on Microelectronics (Austrochip 2013). Linz, Austria.Google Scholar
Yamaoka, M., Yoshimura, C., Hayashi, M., Okuyama, T., Aoki, H. and Mizuno, H. 2016. A 20k-spin Ising chip to solve combinatorial optimization problems with CMOS annealing. IEEE Journal of Solid-State Circuits 51, 1, 303–309.Google Scholar