Simulated versus reduced noise quantum annealing in maximum independent set solution to wireless network scheduling

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Abstract

With the introduction of adiabatic quantum computation (AQC) and its implementation on D-Wave annealers, there has been a constant quest for benchmark problems that would allow for a fair comparison between such classical combinatorial optimization techniques as simulated annealing (SA) and AQC-based optimization. Such a benchmark case study has been the scheduling problem to avoid interference in the very specific Dirichlet protocol in wireless networking, where it was shown that the gap expansion to retain noninterference solutions benefits AQC better than SA. Here, we show that the same gap expansion allows for significant improvement in the D-Wave 2X solution compared with that of its predecessor, the D-Wave II.

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References

  1. 1.

    Deutsch, D.: Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97–117 (1985)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. 2.

    Albash, T., Lidar, D.A.: Adiabatic quantum computation. Rev. Mod. Phys. 90, 015002 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  3. 3.

    Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. SIAM J. Comput. 26(5), 1484–1509 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. 4.

    Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, Philadelphia, PA, pp. 212–219 (1996)

  5. 5.

    Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. arXiv:quant-ph/0001106 (2000)

  6. 6.

    Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. 7.

    Boixo, S., Rnnow, T.F., Isakov, S.V., Wang, Z., Wecker, D., Lidar, D.A., Martinis, J.M., Troyer, M.: Evidence of quantum annealing with more than one hundred qubits. Nat. Phys. 10(3), 218–224 (2014)

    Article  Google Scholar 

  8. 8.

    Rnnow, T.F., Wang, Z., Job, J., Boixo, S., Isakov, S.V., Wecker, D., Martinis, J.M., Lidar, D.A., Troyer, M.: Defining and detecting quantum speedup. Science 345(6195), 420–424 (2014)

    Article  ADS  Google Scholar 

  9. 9.

    Lanting, T.: Entanglement in a quantum annealing processor. Phys. Rev. X 4, 021041 (2014)

    Google Scholar 

  10. 10.

    Boixo, S., et al.: Computational multiqubit tunnelling in programmable quantum annealers. Nat. Commun. 7, 10327 (2016)

    Article  ADS  Google Scholar 

  11. 11.

    Hen, I., Job, J., Albash, T., Rnnow, T.F., Troyer, M., Lidar, D.A.: Probing for quantum speedup in spin glass problems with planted solutions. Phys. Rev. A 92(4), 042325 (2015)

    Article  ADS  Google Scholar 

  12. 12.

    Katzgraber, H., Hamze, F., Andrist, R.: Glassy chimeras could be blind to quantum speedup: designing better benchmarks for quantum annealing machines. Phys. Rev. X 4, 021008 (2014)

    Google Scholar 

  13. 13.

    King, J., et al.: Benchmarking a quantum annealing processor with the time-to-target metric. arXiv:1508.05087 (2015)

  14. 14.

    Denchev, V., et al.: What is the computational value of finite range tunneling. Phys. Rev. X 6, 031015 (2016)

    Google Scholar 

  15. 15.

    Childs, A.M., Maslov, D., Nam, Y., Ross, N.J., Su, Y.: Towards the first quantum simulation with quantum speedup. arXiv:1711.10980v1 [quant-ph] 29 Nov 2017]

  16. 16.

    Pudenz, K., Albash, T., Lidar, D.A.: Error corrected quantum annealing with hundreds of qubits. Nat. Commun. 5, 3243 (2014)

    Article  ADS  Google Scholar 

  17. 17.

    Boxio, S., et al.: Characterizing quantum supremacy in near-term devices. Nat. Phys. 14, 595 (2018). https://doi.org/10.1038/s41567-018-0124-x

    Article  Google Scholar 

  18. 18.

    Wu, K.J.: Solving practical problems with quantum computing hardware. ASCR Work-shop on Quantum Computing for Science (2015). https://doi.org/10.13140/RG.2.1.3656.5200

  19. 19.

    King, A.D., McGeoch, C.C.: Algorithm engineering for a quantum annealing platform. arXiv:1410.2628 (2014)

  20. 20.

    Perdomo-Ortiz, A., Benedetti, M., Realpe-Gomez, J., Biswas, R.: Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers. arXiv:1708.09757v2 [quant-ph] 19 Mar (2018)

  21. 21.

    Banirazi, R., Jonckheere, E., Krishnamachari, B.: Heat diffusion algorithm for resource allocation and routing in multihop wireless networks. In: GLOBECOM, Anaheim, California, USA, pp. 5915–5920 (2012)

  22. 22.

    Banirazi, R., Jonckheere, E., Krishnamachari, B.: Dirichlet’s principle on multiclass multihop wireless networks: minimum cost routing subject to stability. Analysis and Simulation of Wireless and Mobile Systems, Montreal, Canada, pp. 31–40 (2014)

  23. 23.

    Banirazi, R., Jonckheere, E., Krishnamachari, B.: Heat diffusion optimal dynamic routing for multiclass multihop wireless networks. In: INFOCOM, Toronto, Canada, pp. 325–333 (2014)

  24. 24.

    Ghosh, P., Ren, He, Banirazi, R., Krishnamachari, B., Jonckheere, E.: Empirical evaluation of the heat-diffusion collection protocol for wireless sensor networks. Comput. Netw. (COMNET) 127, 217–232 (2017)

    Article  Google Scholar 

  25. 25.

    Banirazi, R., Jonckheere, E., Krishnamachari, B., Minimum delay in class of throughput-optimal control policies on wireless networks. In: American Control Conference (ACC), Portland, OR, pp. 2668–2675 (2014)

  26. 26.

    Tassiulas, L., Ephremides, A.: Stability properties of constrained queueing systems and scheduling policies for maximal throughput in multihop radio networks. IEEE Trans. Autom. Control 37(12), 1936–1948 (1992)

    Article  MATH  Google Scholar 

  27. 27.

    Wang, C., Chen, H., Jonckheere, E.: Quantum versus simulated annealing in wireless interference network optimization. Sci. Rep. 6, 25797 (2016)

    Article  ADS  Google Scholar 

  28. 28.

    Jonckheere, E.A., Rezakhani, A.T., Ahmad, F.: Differential topology of adiabatically controlled quantum processes. Quantum Inf. Process. 12(3), 1515–1538 (2013). Special Issue on Quantum Control

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. 29.

    Jonckheere, E.A., Ahmad, F., Gutkin, E.: Differential topology of numerical range. Linear Algebra Appl. 279(1–3), 227–254 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  30. 30.

    Wang, C., Jonckheere, E., Brun, T.: Ollivier–Ricci curvature and fast approximation to tree-width in embeddability of QUBO problems. In: ISCCSP, Athens, Greece, pp. 639–642 (2014)

  31. 31.

    Wang, C., Jonckheere, E., Brun, T.: Differential geometric treewidth estimation in adiabatic quantum computation. Quantum Inf. Process. 15(10), 3951–3966 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. 32.

    Wang, C., Jonckheere, E., Banirazi, R.: Wireless network capacity versus Ollivier–Ricci curvature under heat diffusion (HD) protocol. In: American Control Conference (ACC 2014), Portland, OR, pp. 3536–3541 (2014)

  33. 33.

    Wang, C., Jonckheere, E., Banirazi, R.: Interference constrained network performance control based on curvature control. In: 2016 American Control Conference, Boston, USA, pp. 6036–6041 (2016)

  34. 34.

    Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: A survey on sensor network. IEEE Commun. Mag. 40(8), 102–114 (2002)

    Article  Google Scholar 

  35. 35.

    Karp, B., Kung, H.T.: GPSR: Greedy perimeter stateless routing for wireless networks. In: Proceedings ACM MobiCom’00, Boston, MA, pp. 243–254 (2000)

  36. 36.

    Official homepage of the IEEE 802.11 working group. http://www.ieee802.org/11. Accessed 2016

  37. 37.

    Bianchi, G.: Performance analysis of the IEEE 802.11 distributed coordination function. IEEE J. Sel. Areas Commun. 18, 535–547 (2000)

    Article  Google Scholar 

  38. 38.

    Cali, F.: Dynamic tuning of the IEEE 802.11 protocol to achieve a theoretical throughput limit. IEEE/ACM Trans. Netw. 8, 785–799 (2000)

    Article  Google Scholar 

  39. 39.

    Jain, K., Padhey, J., Padmanabhan, V.N., Qiu, L.: Impact of interference on multi-hop wireless network performance. In: MobiCom ’03, San Diego, California, USA, pp. 66–80 (2003)

  40. 40.

    Alicherry, A., Bhatia, R., Li, L.E.: Joint channel assignment and routing for throughput optimization in multiradio wireless mesh networks. IEEE J. Sel. Areas Commun. 24(11), 1960–1971 (2006)

    Article  Google Scholar 

  41. 41.

    Kodialam, M., Nandagopal, T.: Characterizing the capacity region in multi-radio multi-channel wireless mesh networks. In: MobiCom’05, ACM, Cologne, Germany, pp. 73–87 (2005)

  42. 42.

    Sanghavi, S.S., Bui, L., Srikant, R.: Distributed link scheduling with constant overhead. ACM SIGMETRICS 35(1), 313–324 (2007)

    Article  Google Scholar 

  43. 43.

    Wan, P.J.: Multiflows in multihop wireless networks. In: MobiHoc’09, New Orleans, LA, USA, pp. 85–94 (2009)

  44. 44.

    Blough, D.M., Resta, G., Sant, P.: Approximation algorithms for wireless link scheduling with SINR-based interference. IEEE Trans. Netw. 18(6), 1701–1712 (2010)

    Article  Google Scholar 

  45. 45.

    Chafekar, D., Anil Kumar, V.S., Marathe, M.V., Parthasarathy, S., Srinivasan, A.: Capacity of wireless networks under SINR interference constraints. Wirel. Netw. 17, 1605–1624 (2011)

    Article  Google Scholar 

  46. 46.

    Moscibroda, T., Wattenhofer, R., Zollinger, A.: Topology control meets SINR: the scheduling complexity of arbitrary topologies. In: MobiHoc’06, ACM, Florence, Italy, pp. 310–321 (2006)

  47. 47.

    Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Trans. Inf. Theory 46(2), 388–404 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  48. 48.

    Andrews, M., Dinitz, M.: Maximizing capacity in arbitrary wireless networks in the SINR model: complexity and game theory. In: INFOCOM’09, Rio de Janeiro, pp. 1332–1340 (2009)

  49. 49.

    Sharma, G., Mazumdar, R., Shroff, N.: On the complexity of scheduling in wireless networks. In: MobiCom’06, Proceedings of the 12th Annual International Conference on Mobile Computing and Networking, Los Angeles, CA, pp. 227–238 (2006)

  50. 50.

    Edmonds, J.: Paths, trees, and flowers. Can. J. Math. 17, 449–467 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  51. 51.

    Dimakis, A., Walrand, J.: Sufficient conditions for stability of longest-queue-first scheduling: second-order properties using fluid limits. Adv. Appl. Probab. 38(2), 505–521 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  52. 52.

    Joo, C., Lin, X., Shroff, N.: Understanding the capacity region of the greedy maximal scheduling algorithm in multi-hop wireless networks. IEEE/ACM Trans. Netw. 17(4), 1132–1145 (2009)

    Article  Google Scholar 

  53. 53.

    Zussman, G., Brzezinski, A., Modiano, E.: Multihop local pooling for distributed throughput maximization in wireless networks. In: INFOCOM’08, Phoenix, Arizona (2008)

  54. 54.

    Leconte, M., Ni, J., Srikant, R.: Improved bounds on the throughput efficiency of greedy maximal scheduling in wireless networks. In: MOBIHOC’09, pp. 165–174 (2009)

  55. 55.

    Li, B., Boyaci, C., Xia, Y.: A refined performance characterization of longest-queue-first policy in wireless networks. In: ACM MOBIHOC, New York, NY, USA, pp. 65–74 (2009)

  56. 56.

    Brzezinski, A., Zussman, G., Modiano, E.: Distributed throughput maximization in wireless mesh networks via pre-partitioning. IEEE/ACM Trans. Netw. 16(6), 1406–1419 (2008)

    Article  Google Scholar 

  57. 57.

    Proutiere, A., Yi Y., Chiang, M.: Throughput of random access without message passing. In: 42nd Annual Conference on Information Sciences and Systems, Princeton, NJ, USA, pp. 509–514 (2008)

  58. 58.

    Jonckheere, E., Lou, M., Bonahon, F., Baryshnikov, Y.: Euclidean versus hyperbolic congestion in idealized versus experimental networks. Internet Math. 7(1), 1–27 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  59. 59.

    Homer, S., Peinado, M.: Experiments with polynomial-time clique approximation algorithms on very large graphs. Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, volume 26 of DIMACS Series. American Mathematical Society, Providence, RI (1996)

  60. 60.

    Xu, X., Ma, J., An, H.W.: Improved simulated annealing algorithm for the maximum independent set problem. Intelligent Computing, Volume 4113 of the series Lecture Notes in Computer Science, pp. 822–831 (2006)

  61. 61.

    Kim, Y.G., Lee, M.G.: Scheduling multi-channel and multi-timeslot in time constrained wireless sensor networks via simulated annealing and particle swarm optimization. IEEE Commun. Mag. 52(1), 122–129 (2014)

    Article  Google Scholar 

  62. 62.

    Mappar, M., Rahmani, A.M., Ashtari, A.H.: A new approach for sensor scheduling in wireless sensor networks using simulated annealing. In: ICCIT ’09. Fourth International Conference on Computer Sciences and Convergence Information Technology, Seoul, Korea, pp. 746–750 (2009)

  63. 63.

    Grossman, T.: Applying the INN model to the max clique problem. Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, volume 26 of DIMACS Series. American Mathematical Society, Providence, RI (1996)

  64. 64.

    Jagota, A.: Approximating maximum clique with a Hopfield network. IEEE Trans. Neural Netw. 6, 724–735 (1995)

    Article  Google Scholar 

  65. 65.

    Jagota, A., Sanchis, L., Ganesan, R.: Approximately solving maximum clique using neural networks and related heuristics. Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, volume 26 of DIMACS Series. American Mathematical Society, Providence, RI (1996)

  66. 66.

    Bui, T.N., Eppley, P.H.: A hybrid genetic algorithm for the maximum clique problem. In: Proceedings of the 6th International Conference on Genetic Algorithms, Pittsburgh, PA, pp. 478–484 (1995)

  67. 67.

    Hifi, M.: A genetic algorithm-based heuristic for solving the weighted maximum independent set and some equivalent problems. J. Oper. Res. Soc. 48, 612–622 (1997)

    Article  MATH  Google Scholar 

  68. 68.

    Marchiori, E.: Genetic, iterated and multistart local search for the maximum clique problem. Applications of Evolutionary Computing. volume 2279 of Lecture Notes in Computer Science, pp. 112–121. Springer, Berlin (2002)

  69. 69.

    Feo, T.A., Resende, M.: A greedy randomized adaptive search procedure for maximum independent set. Oper. Res. 42, 860–878 (1994)

    Article  MATH  Google Scholar 

  70. 70.

    Battiti, R., Protasi, M.: Reactive local search for the maximum clique problem. Algorithmica 29, 610–637 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  71. 71.

    Friden, C., Hertz, A., de Werra, D.: Stabulus: a technique for finding stable sets in large graphs with tabu search. Computing 42, 35–44 (1989)

    Article  MATH  Google Scholar 

  72. 72.

    Mannino, C., Stefanutti, E.: An augmentation algorithm for the maximum weighted stable set problem. Comput. Optim. Appl. 14, 367–381 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  73. 73.

    Soriano, P., Gendreau, M.: Tabu search algorithms for the maximum clique problem. Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, volume 26 of DIMACS Series. American Mathematical Society, Providence, RI (1996)

  74. 74.

    Reichardt, B.W.: The quantum adiabatic optimization algorithm and local minima. In: STOC ’04, Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing, Chicago, IL, pp. 502–510 (2004)

  75. 75.

    Felzenszwalb, P.F.: Dynamic programming and graph algorithms in computer vision. IEEE Trans. Pattern Anal. Mach. Intell. 33(4), 721–740 (2011)

    Article  Google Scholar 

  76. 76.

    Trummer, I., Koch, C.: Multiple query optimization on the D-Wave 2X adiabatic quantum computer. Proc. VLDB Endow. 9(9), 648–659 (2016)

    Article  Google Scholar 

  77. 77.

    O’Gorman, B., Babbush, R., Perdomo-Ortiz, A., Aspuru-Guzik, A., Smelyanskiy, V.: Bayesian network structure learning using quantum annealing. Eur. Phys. J. Spec. Top. 224(1), 163–188 (2015)

    Article  Google Scholar 

  78. 78.

    Rieffel, E.G., Venturelli, D., O’Gorman, B., Do, M.B., Prystay, E., Smelyanskiy, V.N.: A case study in programming a quantum annealer for hard operational planning problems. Quantum Inf. Process. 14(1), 1–36 (2015)

    Article  ADS  MATH  Google Scholar 

  79. 79.

    Perdomo-Ortiz, A., Fluegemann, J., Narasimhan, S., Biswas, R., Smelyanskiy, V.N.: A quantum annealing approach for fault detection and diagnosis of graph-based systems. Eur. Phys. J. Spec. Top. 224(1), 131–148 (2015)

    Article  Google Scholar 

  80. 80.

    Zick, K.M., Shehab, O., French, M.: Experimental quantum annealing: case study involving the graph isomorphism problem. Sci. Rep. 5, 1168 (2015). https://doi.org/10.1038/srep11168

    Article  Google Scholar 

  81. 81.

    Benedetti, M., Realpe-Gmez, J., Biswas, R., Perdomo-Ortiz, A.: Estimation of effective temperatures in a quantum annealer and its impact in sampling applications: a case study towards deep learning applications. Phys. Rev. A 94(2), 022308 (2016)

    Article  ADS  Google Scholar 

  82. 82.

    Choi, V.: Minor-embedding in adiabatic quantum computation: I. The parameter setting problem. Quantum Inf. Process. 7, 193–209 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  83. 83.

    Bian, Z., Chudak, F., Macready, W.G., Clark, L., Gaitan, F.: Experimental determination of Ramsey numbers. Phys. Rev. Lett. 111, 130505 (2013)

    Article  ADS  Google Scholar 

  84. 84.

    Choi, V.: Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design. Quantum Inf. Process. 10(3), 343–353 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  85. 85.

    Vinci, W., et al.: Quantum annealing correction with minor embedding. Phys. Rev. A 92, 042310 (2015)

    Article  ADS  Google Scholar 

  86. 86.

    Vinci, W., Albash, T., Lidar, D.A.: Nested quantum annealing correction. npj Quantum Inf. 2, 16017 (2016)

    Article  ADS  Google Scholar 

  87. 87.

    Mishra, A., Albash, T., Lidar, D.A.: Performance of two different quantum annealing correction codes. Quantum Inf. Process. 15(2), 609–636 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  88. 88.

    Isakov, S.V., Zintchenko, I.N., Rnnow, T.F., Troyer, M.: Optimized simulated annealing for Ising spin glasses. Comput. Phys. Commun. 192, 265–271 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  89. 89.

    Ollivier, Y.: Ricci curvature on Markov chains on metric spaces. J. Funct. Anal. 256(3), 810–864 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  90. 90.

    Bauer, F., Jost, J., Liu, S.: Ollivier–Ricci curvature and the spectrum of the normalized graph Laplace operator. Math. Res. Lett. 19(6), 1185–1205 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Edmond Jonckheere.

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This research was supported by NSF Grant CCF-1423624.

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Wang, C., Jonckheere, E. Simulated versus reduced noise quantum annealing in maximum independent set solution to wireless network scheduling. Quantum Inf Process 18, 6 (2019). https://doi.org/10.1007/s11128-018-2117-1

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Keywords

  • Quantum computing
  • Graph theory
  • Machine learning algorithms
  • Optimal scheduling
  • Simulated annealing
  • Wireless application protocol