Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

Arithmetic on a distributed-memory quantum multicomputer

Published: 28 January 2008 Publication History

Abstract

We evaluate the performance of quantum arithmetic algorithms run on a distributed quantum computer (a quantum multicomputer). We vary the node capacity and I/O capabilities, and the network topology. The tradeoff of choosing between gates executed remotely, through “teleported gates” on entangled pairs of qubits (telegate), versus exchanging the relevant qubits via quantum teleportation, then executing the algorithm using local gates (teledata), is examined. We show that the teledata approach performs better, and that carry-ripple adders perform well when the teleportation block is decomposed so that the key quantum operations can be parallelized. A node size of only a few logical qubits performs adequately provided that the nodes have two transceiver qubits. A linear network topology performs acceptably for a broad range of system sizes and performance parameters. We therefore recommend pursuing small, high-I/O bandwidth nodes and a simple network. Such a machine will run Shor's algorithm for factoring large numbers efficiently.

References

[1]
ACM. 2006. Computer architecture news. In Proceedings of the 33rd Annual International Symposium on Computer Architecture.
[2]
ARDA. 2004. A Quantum Information Science and Technology Roadmap, v2.0 Ed. ARDA.
[3]
Armen, M. A., Au, J. K., Stockton, J. K., Doherty, A. C., and Mabuchi, H. 2002. Adaptive homodyne measurement of optical phase. Phys. Rev. Lett. 89, 133602.
[4]
Athas, W. C. and Seitz, C. L. 1988. Multicomputers: message-passing concurrent computers. IEEE Comput. 21, 9--24.
[5]
Balensiefer, S., Kregor-Stickles, L., and Oskin, M. 2005. An evaluation framework and instruction set architecture for ion-trap based quantum micro-architectures. In Proceedings of the 32nd Annual International Symposium on Computer Architecture.
[6]
Beauregard, S. 2003. Circuit for Shor's algorithm using 2n + 3 qubits. Quantum Inform. Computa. 3, 2, 175--185. http://arXiv.org/quant-ph/0205095.
[7]
Beckman, D., Chari, A. N., Devabhaktuni, S., and Preskill, J. 1996. Efficient networks for quantum factoring. Phys. Rev. A 54, 1034--1063. http://arXiv.org/quant-ph/9602016.
[8]
Bennett, C. H., Brassard, G., Crépeau, C., Josza, R., Peres, A., and Wootters, W. 1993. Teleporting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett. 70, 1895--1899.
[9]
Bouwmeester, D., Pan, J.-W., Mattle, K., Eibl, M., Weinfurter, H., and Zeilinger, A. 1997. Experimental quantum teleportation. Nature 390, 575--579.
[10]
Calderbank, A. R. and Shor, P. W. 1996. Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098--1105.
[11]
Childress, L., Taylor, J., Sørensen, A., and Lukin, M. 2005. Fault-tolerant quantum repeaters with minimal physical resources and implementations based on single-photon emitters. Phys. Rev. A 72, 5, 52330.
[12]
Cirac, J., Ekert, A., Huelga, S., and Macchiavello, C. 1999. Distributed quantum computation over noisy channels. Phys. Rev. A 59, 4249.
[13]
Cleve, R. and Watrous, J. 2000. Fast parallel circuits for the quantum Fourier transform. In Proceedings of the 41st Annual Symposium on Foundations of Computer Science. ACM, 526--536.
[14]
Copsey, D., Oskin, M., Metodiev, T., Chong, F. T., Chuang, I., and Kubiatowicz, J. 2003. The effect of communication costs in solid-state quantum computing architectures. In Proceedings of the 15th Annual ACM Symposium on Parallel Algorithms and Architectures. 65--74.
[15]
Cuccaro, S. A., Draper, T. G., Kutin, S. A., and Moulton, D. P. 2004. A new quantum ripple-carry addition circuit. http://arXiv.org/quant-ph/0410184.
[16]
Dally, W. J. and Towles, B. 2004. Principles and Practices of Interconnection Networks. Elsevier.
[17]
Deutsch, D. and Jozsa, R. 1992. Rapid solution of problems by quantum computation. In Proceedings of the Royal Society London Series A, 439, 553.
[18]
DiVincenzo, D. P. 1998. Quantum gates and circuits. In Proceedings of the Royal Society London Series A.
[19]
Draper, T. G. 2000. Addition on a quantum computer. http://arXiv.org/quant-ph/0008033.
[20]
Draper, T. G., Kutin, S. A., Rains, E. M., and Svore, K. M. 2006. A logarithmic-depth quantum carry-lookahead adder. Quantum Inform. Computa. 6, 4&5, 351--369.
[21]
Ercegovac, M. D. and Lang, T. 2004. Digital Arithmetic. Morgan Kaufmann, San Francisco, CA.
[22]
Fujisawa, T., Oosterkamp, T. H., van der Wiel, W. G., Broer, B. W., Aguado, R., Tarucha, S., and Kouwenhoven, L. P. 1998. Spontaneous emission spectrum in double quantum dot devices. Science 282, 932--935.
[23]
Furusawa, A., Sørensen, J. L., Braunstein, S. L., Fuchs, C. A., Kimble, H. J., and Polzik, E. S. 1998. Unconditional quantum teleportation. Science 282, 5389, 706--709.
[24]
Gossett, P. 1998. Quantum carry-save arithmetic. http://arXiv.org/quant-ph/9808061.
[25]
Gottesman, D. and Chuang, I. L. 1999. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390--393.
[26]
Grover, L. 1996. A fast quantum-mechanical algorithm for database search. In Proceedings of the 28th Annual ACM Symposium on the Theory of Computation. 212--219. http://arXiv.org/quant-ph/9605043.
[27]
Grover, L. K. 1997. Quantum telecomputation. http://arXiv.org/quant-ph/9704012.
[28]
Gulde, S., Riebe, M., Lancaster, G. P. T., Becher, C., Eschner, J., Haffner, H., Schmidt-Kaler, F., Chuang, I. L., and Blatt, R. 2003. Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer. Nature 421, 48--50.
[29]
Jelezko, F., Gaebel, T., Popa, I., Domhan, M., Gruber, A., and Wratchtrup, J. 2004. Observation of coherence oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Phys. Rev. Lett. 93, 130501.
[30]
Johansson, J. et al. 2005. Vacuum Rabi oscillations in a macroscopic superconducting qubit LC oscillator system. http://arXiv.org/cond-mat/0510457.
[31]
Jozsa, R. and Linden, N. 2003. On the role of entanglement in quantum computational speedup. In Proceedings of the Royal Society London Series A 459, 2011--2032. http://arXiv.org/quant-ph/0201143.
[32]
Kielpinski, D., Monroe, C., and Wineland, D. J. 2002. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709--711.
[33]
Kim, J. et al. 2003. 1100 × 1100 port MEMS-based optical crossconnect with 4-dB maximum loss. IEEE Photonics Techn. Lett. 15, 11, 1537--1539.
[34]
Kim, J. et al. 2005. System design for large-scale ion trap quantum information processor. Quantum Inform. Computa. 5, 7, 515--537.
[35]
Knuth, D. E. 1998. The Art of Computer Programming, Seminumerical Algorithms, vol 2, 3rd Ed. Addison-Wesley, Reading, MA.
[36]
Lim, Y. L., Barrett, S. D., Beige, A., Kok, P., and Kwek, L. C. 2005. Repeat-Until-Success quantum computing using stationary and flying qubits. http://arXiv.org/quant-ph/0508218.
[37]
Love, P. and Boghosian, B. 2006. Type II quantum algorithms. Physica A: Statist. Mechan. Appl. 362, 1, 210--214.
[38]
Marchand, P. J., Krishnamoorthy, A. V., Yayla, G. I., Esener, S. C., and Efron, U. 1997. Optically augmented 3-d computer: System technology and architecture. J. Parall. Distrib. Comput. 41, 1, 20--35.
[39]
Martinis, J. M., Nam, S., Aumentado, J., and Urbina, C. 2002. Rabi oscillations in a large Josephson-junction qubit. Phys. Rev. Lett. 89, 117901.
[40]
Matsukevich, D. N. and Kuzmich, A. 2004. Quantum state transfer between matter and light. Science 306, 5696, 663--666.
[41]
Mehring, M., Mende, J., and Scherer, W. 2003. Entanglement between and electron and a nuclear spin 1/2. Phys. Rev. Lett. 90, 153001.
[42]
Miquel, C., Paz, J., and Perazzo, R. 1996. Factoring in a dissipative quantum computer. Phys. Rev. A 54, 4, 2605--2613.
[43]
Munro, W., Nemoto, K., and Spiller, T. 2005. Weak nonlinearities: A new route to optical quantum computation. New J. Physics 7, 137.
[44]
Nakamura, Y., Pashkin, Y. A., and Tsai, J. S. 1999. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786--788.
[45]
Nemoto, K. and Munro, W. J. 2004. Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502.
[46]
Nielsen, M. A. and Chuang, I. L. 2000. Quantum Computation and Quantum Information. Cambridge University Press.
[47]
Oi, D. K. L., Devitt, S. J., and Hollenberg, L. C. L. 2006. Scalable error correction in distributed ion trap computers. Phys. Rev. A 74, 052313.
[48]
Oskin, M., Chong, F. T., Chuang, I. L., and Kubiatowicz, J. 2003. Building quantum wires: The long and short of it. Computer Architecture News. In Proceedings of the 30th Annual International Symposium on Computer Architecture. ACM.
[49]
Shor, P. W. 1994. Algorithms for quantum computation: Discrete logarithms and factoring. In Proceedings of the 35th Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 124--134.
[50]
Shor, P. W. 1996. Fault-tolerant quantum computation. In Proceedings of the 37th Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 56--65.
[51]
Spiller, T. P., Munro, W. J., Barrett, S. D., and Kok, P. 2005. An introduction to quantum information processing: applications and realisations. Contemp. Phys. 46, 406.
[52]
Spiller, T. P., Nemoto, K., Braunstein, S. L., Munro, W. J., van Loock, P., and Milburn, G. J. 2006. Quantum computation by communication. New J. Physics 8, 30.
[53]
Steane, A. M. 2003. Overhead and noise threshold of fault-tolerant quantum error correction. Phys. Rev. A 68, 042322.
[54]
Steane, A. M. 2004. How to build a 300 bit, 1 Gop quantum computer. http://arxiv.org/abs/quant-ph/0412165.
[55]
Steane, A. M. and Lucas, D. M. 2000. Quantum computing with trapped ions, atoms, and light. Fortschritte der Physik. http://arXiv.org/quant-ph/0004053.
[56]
Stockton, J., Armen, M., and Mabuchi, H. 2002. Programmable logic devices in experimental quantum optics. J. Opt. Soc. Am. B 19, 3019.
[57]
Szymanski, T. and Hinton, H. 1995. Design of a terabit free-space photonic backplane for parallel computing. In Proceedings of the 2nd Workshop on Massively Parallel Processing Using Optical Interconnections. IEEE.
[58]
Takahashi, Y. and Kunihiro, N. 2005. A linear-size quantum circuit for addition with no ancillary qubits. Quantum Inform. Computa. 5, 6, 440--448.
[59]
Thaker, D. D., Metodi, T., Cross, A., Chuang, I., and Chong, F. T. 2006. CQLA: Matching density to exploitable parallelism in quantum computing. Computer Architecture News. In Proceedings of the 33rd Annual International Symposium on Computer Architecture.
[60]
van Loock, P., Ladd, T. D., Sanaka, K., Yamaguchi, F., Nemoto, K., Munro, W. J., and Yamamoto, Y. 2006. Hybrid quantum repeater using bright coherent light. Phys. Rev. Lett. 96, 240501.
[61]
Van Meter, R. and Itoh, K. M. 2005. Fast quantum modular exponentiation. Phys. Rev. A 71, 5, 052320.
[62]
Van Meter, R., Munro, W. J., Nemoto, K., and Itoh, K. M. 2006. Distributed arithmetic on a quantum multicomputer. Computer Architecture News. In Proceedings of the 33rd Annual International Symposium on Computer Architecture. 354--365.
[63]
Van Meter, R., Nemoto, K., and Munro, W. J. 2007. Communication links for distributed quantum computation. http://arxiv.org/quant-ph/0701043.
[64]
Van Meter, R. and Oskin, M. 2006. Architectural implications of quantum computing technologies. ACM J. Emerg. Technol. Comput. Syst. 2, 1 (Jan.), 31--63.
[65]
Van Meter III, R. D. 2006. Architecture of a quantum multicomputer optimized for Shor's factoring algorithm. Ph.D. thesis, Keio University.
[66]
Vandersypen, L. M. K., Steffen, M., Breyta, G., Yannoni, C. S., Sherwood, M. H., and Chuang, I. L. 2001. Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883--887.
[67]
Vedral, V., Barenco, A., and Ekert, A. 1996. Quantum networks for elementary arithmetic operations. Phys. Rev. A 54, 147--153. http://arXiv.org/quant-ph/9511018.
[68]
Wallraff, A., Schuster, D. I., Blais, A., Frunzio, L., Huang, R.-S., Majer, J., Kumar, S., Girvin, S. M., and Schoelkopf, R. J. 2004. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162--167.
[69]
Williams, C. P. and Clearwater, S. H. 1999. Ultimate Zero and One: Computing at the Quantum Frontier. Copernicus Books.
[70]
Yepez, J. 2001. Type-II quantum computers. Int. J. Modern Phys. C 12, 9, 1273--1284.
[71]
Yimsiriwattana, A. and Lomonaco Jr., S. J. 2004. Distributed quantum computing: A distributed Shor algorithm. http://arxiv.org/quant-ph/0403146.
[72]
Zalka, C. 1998. Fast versions of Shor's quantum factoring algorithm. http://arXiv.org/quant-ph/9806084. http://arXiv.org/quant-ph/9806084.

Cited By

View all
  • (2024)The Complexity of Being EntangledQuantum10.22331/q-2024-09-12-14728(1472)Online publication date: 12-Sep-2024
  • (2024)ARQUIN: Architectures for Multinode Superconducting Quantum ComputersACM Transactions on Quantum Computing10.1145/36741515:3(1-59)Online publication date: 19-Sep-2024
  • (2024)High-Rate and High-Fidelity Modular Interconnects between Neutral Atom Quantum ProcessorsPRX Quantum10.1103/PRXQuantum.5.0203635:2Online publication date: 20-Jun-2024
  • Show More Cited By

Index Terms

  1. Arithmetic on a distributed-memory quantum multicomputer

      Recommendations

      Comments

      Information & Contributors

      Information

      Published In

      cover image ACM Journal on Emerging Technologies in Computing Systems
      ACM Journal on Emerging Technologies in Computing Systems  Volume 3, Issue 4
      January 2008
      104 pages
      ISSN:1550-4832
      EISSN:1550-4840
      DOI:10.1145/1324177
      Issue’s Table of Contents
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Journal Family

      Publication History

      Published: 28 January 2008
      Accepted: 01 May 2007
      Revised: 01 March 2007
      Received: 01 July 2006
      Published in JETC Volume 3, Issue 4

      Permissions

      Request permissions for this article.

      Check for updates

      Author Tags

      1. Quantum computing
      2. quantum computer architecture

      Qualifiers

      • Research-article
      • Research
      • Refereed

      Contributors

      Other Metrics

      Bibliometrics & Citations

      Bibliometrics

      Article Metrics

      • Downloads (Last 12 months)57
      • Downloads (Last 6 weeks)7
      Reflects downloads up to 25 Dec 2024

      Other Metrics

      Citations

      Cited By

      View all
      • (2024)The Complexity of Being EntangledQuantum10.22331/q-2024-09-12-14728(1472)Online publication date: 12-Sep-2024
      • (2024)ARQUIN: Architectures for Multinode Superconducting Quantum ComputersACM Transactions on Quantum Computing10.1145/36741515:3(1-59)Online publication date: 19-Sep-2024
      • (2024)High-Rate and High-Fidelity Modular Interconnects between Neutral Atom Quantum ProcessorsPRX Quantum10.1103/PRXQuantum.5.0203635:2Online publication date: 20-Jun-2024
      • (2024)Quantum-centric high performance computing for quantum chemistryPhysical Chemistry Chemical Physics10.1039/D4CP00436AOnline publication date: 2024
      • (2024)Long-range data transmission in a fault-tolerant quantum bus architecturenpj Quantum Information10.1038/s41534-024-00928-410:1Online publication date: 26-Dec-2024
      • (2023)Entanglement-efficient bipartite-distributed quantum computingQuantum10.22331/q-2023-12-05-11967(1196)Online publication date: 5-Dec-2023
      • (2023)Simulating quantum key distribution in fiber-based quantum networksThe Journal of Defense Modeling and Simulation: Applications, Methodology, Technology10.1177/1548512923115492921:4(463-486)Online publication date: 7-Apr-2023
      • (2023)QuComm: Optimizing Collective Communication for Distributed Quantum ComputingProceedings of the 56th Annual IEEE/ACM International Symposium on Microarchitecture10.1145/3613424.3614253(479-493)Online publication date: 28-Oct-2023
      • (2023)A Modular Quantum Compilation Framework for Distributed Quantum ComputingIEEE Transactions on Quantum Engineering10.1109/TQE.2023.33039354(1-13)Online publication date: 2023
      • (2023)Fuzzy-Based Balanced Partitioning Under Capacity and Size-Tolerance Constraints in Distributed Quantum CircuitsIEEE Transactions on Quantum Engineering10.1109/TQE.2023.32720234(1-15)Online publication date: 2023
      • Show More Cited By

      View Options

      Login options

      Full Access

      View options

      PDF

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader

      Media

      Figures

      Other

      Tables

      Share

      Share

      Share this Publication link

      Share on social media