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Compiler Management of Communication and Parallelism for Quantum Computation

Published:14 March 2015Publication History
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Abstract

Quantum computing (QC) offers huge promise to accelerate a range of computationally intensive benchmarks. Quantum computing is limited, however, by the challenges of decoherence: i.e., a quantum state can only be maintained for short windows of time before it decoheres. While quantum error correction codes can protect against decoherence, fast execution time is the best defense against decoherence, so efficient architectures and effective scheduling algorithms are necessary. This paper proposes the Multi-SIMD QC architecture and then proposes and evaluates effective schedulers to map benchmark descriptions onto Multi-SIMD architectures. The Multi-SIMD model consists of a small number of SIMD regions, each of which may support operations on up to thousands of qubits per cycle.

Efficient Multi-SIMD operation requires efficient scheduling. This work develops schedulers to reduce communication requirements of qubits between operating regions, while also improving parallelism.We find that communication to global memory is a dominant cost in QC. We also note that many quantum benchmarks have long serial operation paths (although each operation may be data parallel). To exploit this characteristic, we introduce Longest-Path-First Scheduling (LPFS) which pins operations to SIMD regions to keep data in-place and reduce communication to memory. The use of small, local scratchpad memories also further reduces communication. Our results show a 3% to 308% improvement for LPFS over conventional scheduling algorithms, and an additional 3% to 64% improvement using scratchpad memories. Our work is the most comprehensive software-to-quantum toolflow published to date, with efficient and practical scheduling techniques that reduce communication and increase parallelism for full-scale quantum code executing up to a trillion quantum gate operations.

References

  1. P. Aliferis and A. Cross. Subsystem fault tolerance with the Bacon- Shor code. arXiv preprint quant-ph/0610063, 2006.Google ScholarGoogle Scholar
  2. A. Ambainis, A. M. Childs, B. W. Reichardt, R. Spalek, and S. Zhang. Any AND-OR formula of size N can be evaluated in time N1=2+o(1) on a quantum computer. In Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS '07. IEEE Computer Society, 2007. ISBN 0-7695-3010-9. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. B. Blinov, D. Moehring, L.-M. Duan, and C. Monroe. Observation of entanglement between a single trapped atom and a single photon. Nature, 428(6979):153--157, 2004.Google ScholarGoogle ScholarCross RefCross Ref
  4. S. Cavallar, B. Dodson, A. Lenstra, W. Lioen, P. Montgomery, B. Murphy, H. te Riele, K. Aardal, J. Gilchrist, G. Guillerm, P. Leyland, J. Marchand, F. Morain, A. Muffett, C. Putnam, and P. Zimmermann. Factorization of a 512--bit RSA modulus. In B. Preneel, editor, Advances in Cryptology -- EUROCRYPT 2000, volume 1807 of Lecture Notes in Computer Science, pages 1--18. Springer Berlin Heidelberg, 2000. ISBN 978-3-540-67517-4. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. E. Chi, S. A. Lyon, and M. Martonosi. Tailoring quantum architectures to implementation style: a quantum computer for mobile and persistent qubits. In Proceedings of the 34th Annual International Symposium on Computer Architecture, ISCA '07. ACM, 2007. ISBN 978-1-59593-706-3. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. J. Chiaverini, D. Leibfried, T. Schaetz, M. Barrett, R. Blakestad, J. Britton, W. Itano, J. Jost, E. Knill, C. Langer, R. Ozeri, and D. J. Wineland. Realization of quantum error correction. Nature, 432 (7017):602--605, 2004.Google ScholarGoogle ScholarCross RefCross Ref
  7. A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman. Exponential algorithmic speedup by a quantum walk. In Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, STOC '03. ACM, 2003. ISBN 1-58113-674-9. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. I. Chuang. Quantum architectures: qasm2circ. URL http://www.media.mit.edu/quanta/qasm2circ/.Google ScholarGoogle Scholar
  9. J. I. Cirac and P. Zoller. Quantum computations with cold trapped ions. Phys. Rev. Lett., 74:4091--4094, May 1995.Google ScholarGoogle ScholarCross RefCross Ref
  10. D. Copsey, M. Oskin, F. Impens, T. Metodiev, A. Cross, F. T. Chong, I. L. Chuang, and J. Kubiatowicz. Toward a scalable, silicon-based quantum computing architecture. Selected Topics in Quantum Electronics, IEEE Journal of, 9(6):1552--1569, 2003.Google ScholarGoogle Scholar
  11. D. P. L. A. Craik, N. M. Linke, T. P. Harty, C. J. Ballance, D. M. Lucas, A. M. Steane, and D. T. C. Allcock. Microwave control electrodes for scalable, parallel, single-qubit operations in a surface-electrode ion trap, August 2013. URL http://arxiv.org/pdf/1308.2078.pdf.Google ScholarGoogle Scholar
  12. D. P. DiVincenzo. The physical implementation of quantum computation. Fortschritte der Physik, 48(9-11):771--783, 2000. ISSN 1521-3978.Google ScholarGoogle ScholarCross RefCross Ref
  13. J. García-Ripoll, P. Zoller, and J. Cirac. Speed optimized two-qubit gates with laser coherent control techniques for ion trap quantum computing. Phys. Rev. Lett, 91(15):157901, 2003.Google ScholarGoogle ScholarCross RefCross Ref
  14. M. Gebhart, B. A. Maher, K. E. Coons, J. Diamond, P. Gratz, M. Marino, N. Ranganathan, B. Robatmili, A. Smith, J. Burrill, S. W. Keckler, D. Burger, and K. S. McKinley. An evaluation of the TRIPS computer system. In Proceedings of the Fourteenth International Conference on Architectural Support for Programming Languages and Operating Systems. ACM, Mar. 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. L. K. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, STOC '96, 1996. ISBN 0-89791-785-5. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. S. Hallgren. Fast quantum algorithms for computing the unit group and class group of a number field. In H. N. Gabow and R. Fagin, editors, STOC. ACM, 2005. ISBN 1-58113-960-8. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. C. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter. Surface code quantum computing by lattice surgery. New Journal of Physics, 14 (12):123011, 2012.Google ScholarGoogle ScholarCross RefCross Ref
  18. N. Isailovic. An investigation into the realities of a quantum datapath. PhD thesis, University of California, Berkeley, 2010.Google ScholarGoogle Scholar
  19. N. Isailovic, M. Whitney, Y. Patel, and J. Kubiatowicz. Running a quantum circuit at the speed of data. In ACM SIGARCH Computer Architecture News, volume 36, pages 177--188. IEEE Computer Society, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. A. JavadiAbhari, A. Faruque, M. J. Dousti, L. Svec, O. Catu, A. Chakrabati, C.-F. Chiang, S. Vanderwilt, J. Black, F. Chong, M. Martonosi, M. Suchara, K. Brown, M. Pedram, and T. Brun. Scaffold: Quantum programming language. Technical report, Princeton University, 2012.Google ScholarGoogle Scholar
  21. A. JavadiAbhari, S. Patil, D. Kudrow, J. Heckey, A. Lvov, F. Chong, and M. Martonosi. ScaffCC: A framework for compilation and analysis of quantum computing programs. ACM International Conference on Computing Frontiers (CF 2014), May 2014. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. M. Johanning, A. Braun, N. Timoney, V. Elman, W. Neuhauser, and C. Wunderlich. Individual addressing of trapped ions and coupling of motional and spin states using RF radiation. Phys. Rev. Lett., 102: 073004, Feb 2009.Google ScholarGoogle ScholarCross RefCross Ref
  23. N. C. Jones, R. Van Meter, A. G. Fowler, P. L. McMahon, J. Kim, T. D. Ladd, and Y. Yamamoto. Layered architecture for quantum computing. Physical Review X, 2(3):031007, 2012.Google ScholarGoogle ScholarCross RefCross Ref
  24. J. Kim, S. Pau, Z. Ma, H. McLellan, J. Gates, A. Kornblit, R. E. Slusher, R. M. Jopson, I. Kang, and M. Dinu. System design for large- scale ion trap quantum information processor. Quantum Information & Computation, 5(7):515--537, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. V. Kliuchnikov, D. Maslov, and M. Mosca. SQCT: Single qubit circuit toolkit. URL https://code.google.com/p/sqct/.Google ScholarGoogle Scholar
  26. C. Lattner and V. Adve. LLVM: a compilation framework for life-long program analysis and transformation. In Code Generation and Optimization, 2004. CGO 2004. International Symposium on, pages 75--86, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, B. J. WM Itano, C. Langer, and D. T Rosenband. Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature, 422(6930):412--415, 2003.Google ScholarGoogle ScholarCross RefCross Ref
  28. F. Magniez, M. Santha, and M. Szegedy. Quantum algorithms for the triangle problem. In Proceedings of the Sixteenth annual ACM- SIAM Symposium on Discrete Algorithms, SODA '05, pages 1109--1117, 2005. ISBN 0-89871-585-7. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. T. Metodi, D. Thaker, A. Cross, F. T. Chong, and I. L. Chuang. Scheduling physical operations in a quantum information processor. Proceedings for the SPIE Defense & Security symposium, Orlando, FL, April, 2006.Google ScholarGoogle ScholarCross RefCross Ref
  30. T. S. Metodi, D. D. Thaker, and A. W. Cross. A quantum logic array microarchitecture: Scalable quantum data movement and computation. In MICRO, pages 305--318. IEEE Computer Society, 2005. ISBN 0-7695-2440-0. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. C. Monroe, D. Meekhof, B. King, W. Itano, and D. Wineland. Demonstration of a fundamental quantum logic gate. Physical Review Letters, 75(25):4714, 1995.Google ScholarGoogle ScholarCross RefCross Ref
  32. M. Mosca. Quantum algorithms. In R. A. Meyers, editor, Encyclopedia of Complexity and Systems Science, pages 7088--7118. Springer New York, 2009. ISBN 978-0-387-75888-6.Google ScholarGoogle ScholarCross RefCross Ref
  33. M. A. Nielsen and I. L. Chuang. Quantum computation and quantum information. Cambridge university press, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. N. I. of Standards and Technology. FIPS PUB 180-4: Secure Hash Standard (SHS). U.S. Department of Commerce, 2012.Google ScholarGoogle Scholar
  35. M. Oskin, F. Chong, and I. Chuang. A practical architecture for reliable quantum computers. Computer, 35(1):79--87, 2002. ISSN 0018-9162. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. C. Ospelkaus, U. Warring, Y. Colombe, K. R. Brown, J. M. Amini, D. Leibfried, and D. J. Wineland. Microwave quantum logic gates for trapped ions. Nature, 476:181--184, 2011.Google ScholarGoogle ScholarCross RefCross Ref
  37. M. Riebe, H. Haffner, C. Roos, W. Hansel, J. Benhelm, G. Lancaster, T. Korber, C. Becher, F. Schmidt-Kaler, and D. James. Deterministic quantum teleportation with atoms. Nature, 429(6993):734--737, 2004.Google ScholarGoogle ScholarCross RefCross Ref
  38. F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt. Realization of the Cirac--Zoller controlled-NOT quantum gate. Nature, 422 (6930):408--411, 2003.Google ScholarGoogle ScholarCross RefCross Ref
  39. E. Schuchman and T. N. Vijaykumar. A program transformation and architecture support for quantum uncomputation. SIGARCH Comput. Archit. News, 34(5):252--263, Oct. 2006. ISSN 0163-5964. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. C. M. Shappert, J. T. Merrill, K. R. Brown, J. M. Amini, C. Volin, S. C. Doret, H. Hayden, C.-S. Pai, and A. W. Harter. Spatially uniform single-qubit gate operations with near-field microwaves and composite pulse compensation. New Journal of Physics, 15(083053), 2013.Google ScholarGoogle Scholar
  41. P. W. Shor. Algorithms for quantum computation: discrete logarithms and factoring. In Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on, pages 124--134. IEEE, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  42. A. Steane. Error correcting codes in quantum theory. Physical Review Letters, 77(5):793--797, 1996.Google ScholarGoogle ScholarCross RefCross Ref
  43. A. M. Steane. Active stabilization, quantum computation, and quantum state synthesis. Phys. Rev. Lett., 78:2252--2255, Mar 1997.Google ScholarGoogle ScholarCross RefCross Ref
  44. K. Svore, A. Aho, A. Cross, I. Chuang, and I. Markov. A layered software architecture for quantum computing design tools. Computer, 39(1):74--83, 2006. ISSN 0018-9162. Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. S. Swanson, A. Schwerin, M. Mercaldi, A. Petersen, A. Putnam, K. Michelson, M. Oskin, and S. J. Eggers. The WaveScalar architecture. ACM Trans. Comput. Syst., 25(2):4:1--4:54, May 2007. ISSN 0734-2071. Google ScholarGoogle ScholarDigital LibraryDigital Library
  46. M. B. Taylor, W. Lee, J. Miller, D. Wentzlaff, I. Bratt, B. Greenwald, H. Hoffmann, P. Johnson, J. Kim, J. Psota, A. Saraf, N. Shnidman, V. Strumpen, M. Frank, S. Amarasinghe, and A. Agarwal. Evaluation of the Raw Microprocessor: An Exposed-Wire-Delay Architecture for ILP and Streams. In Proceedings of the 31st Annual International Symposium on Computer Architecture, ISCA '04, pages 2--. IEEE Computer Society, 2004. ISBN 0-7695-2143-6. Google ScholarGoogle ScholarDigital LibraryDigital Library
  47. D. D. Thaker, T. S. Metodi, A. W. Cross, I. L. Chuang, and F. T. Chong. Quantum memory hierarchies: Efficient designs to match available parallelism in quantum computing. In ISCA, pages 378--390. IEEE Computer Society, 2006. ISBN 0-7695-2608-X. Google ScholarGoogle ScholarDigital LibraryDigital Library
  48. J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik. Simulation of electronic structure Hamiltonians using quantum computers. Molecular Physics, 109(5):735, 2010.Google ScholarGoogle ScholarCross RefCross Ref
  49. M. G. Whitney, N. Isailovic, Y. Patel, and J. Kubiatowicz. A fault tolerant, area efficient architecture for shor's factoring algorithm. In Proceedings of the 36th annual international symposium on Computer architecture, ISCA '09, pages 383--394, New York, NY, USA, 2009. ACM. ISBN 978-1-60558-526-0. Google ScholarGoogle ScholarDigital LibraryDigital Library
  50. D. Wineland, C. Monroe, W. Itano, B. King, D. Leibfried, D. Meekhof, C. Myatt, and C. Wood. Experimental primer on the trapped ion quantum computer. Spectroscopy, 7:8, 1998.Google ScholarGoogle Scholar
  51. T. Yang and A. Gerasoulis. PYRROS: static task scheduling and code generation for message passing multiprocessors. In Proceedings of the 6th ACM International Conference on Supercomputing, pages 428--437, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  52. T. Yang and A. Gerasoulis. List scheduling with and without communication delays. Parallel Comput., 19(12):1321--1344, Dec. 1993. ISSN 0167-8191. Google ScholarGoogle ScholarDigital LibraryDigital Library

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    • Published in

      cover image ACM SIGPLAN Notices
      ACM SIGPLAN Notices  Volume 50, Issue 4
      ASPLOS '15
      April 2015
      676 pages
      ISSN:0362-1340
      EISSN:1558-1160
      DOI:10.1145/2775054
      • Editor:
      • Andy Gill
      Issue’s Table of Contents
      • cover image ACM Conferences
        ASPLOS '15: Proceedings of the Twentieth International Conference on Architectural Support for Programming Languages and Operating Systems
        March 2015
        720 pages
        ISBN:9781450328357
        DOI:10.1145/2694344

      Copyright © 2015 ACM

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      • Published: 14 March 2015

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