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Nearly Quantum Computing by Simulation

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High Performance Computing (CARLA 2022)

Abstract

Quantum computing has ceased to be an exotic topic for researchers, moving its treatment today from theoretical physicists to computer scientists and engineers. Recently, several real quantum devices have become available through the cloud. On the other hand, different possibilities on-premises allow having quantum computing simulators using High-Performance Computing (HPC) capabilities. Nevertheless, they did not expect to be very limited, in the near term, the number and quality of the fundamental storage element, the qubit. Therefore, software quantum simulators are the only widely available tools to design and test quantum algorithms. However, the representation of quantum computing components in classical computers consumes significant resources. In quantum computing, a state composed of n qubits will be a union of all possible combinations of n 0s and 1s. That is to say, the size of the information is \(2^n\). The amplitude is the magnitude associated with every variety and is composed of a complex number. This paper shows a survey of different implementations to simulate quantum computing supported by classical computing, highlighting important considerations for implementing and developing solutions.

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Notes

  1. 1.

    A quantum computer simulates a quantum system.

  2. 2.

    A list of the recent developments is maintained on several websites [11, 12, 34, 35].

References

  1. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. 27(3), 379–423 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  2. Born, M., Jordan, P.: Zur quantenmechanik. Z. Angew. Phys. 34(1), 858–888 (1925)

    MATH  Google Scholar 

  3. Feynman, R.P.: Feynman and Computation. There’s Plenty of Room at the Bottom, pp. 63–76. Perseus Books, Cambridge (1999)

    Google Scholar 

  4. Holevo, A.S.: Bounds for the quantity of information transmitted by a quantum communication channel. Probl. Inf. Transm. 9(3), 177–183 (1973)

    Google Scholar 

  5. Poplavski, R.P.: Thermodynamic models of information processes. Sov. Phys. Uspekhi 18(3), 222–241 (1975)

    Article  MathSciNet  Google Scholar 

  6. Ingarden, R.S.: Quantum Information Theory. Preprint - Instytut Fizyki Uniwersytetu Mikolaja Kopernika. PWN (1975)

    Google Scholar 

  7. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Benioff, P.: The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computers as represented by turing machines. J. Stat. Phys. 22(5), 563–591 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  9. Deutsch, D.: Quantum theory, the church-turing principle and the universal quantum computer. Proc. R. Soc. Lond. 400, 97–117 (1985)

    MathSciNet  MATH  Google Scholar 

  10. Shaydulin, R., Ushijima-Mwesigwa, H., Negre, C., Safro, I., Mniszewski, S., Alexeev, Y.: A hybrid approach for solving optimization problems on small quantum computers. Computer 52, 18–26 (2019)

    Article  Google Scholar 

  11. Fingerhuth, M.: Open-source quantum software projects (2019). https://github.com/qosf/os_quantum_software

  12. Quantum Computing Report. Qbit count (2019). https://quantumcomputingreport.com/scorecards/qubit-count/

  13. Chen, J., Zhang, F., Huang, C., Newman, M., Shi, Y.: Classical simulation of intermediate-size quantum circuits (2018)

    Google Scholar 

  14. Dang, A., Hill, C.D., Hollenberg, L.C.L.: Optimising matrix product state simulations of Shor’s algorithm. Quantum 3, 116 (2019)

    Article  Google Scholar 

  15. Wu, X., Di, S., Cappello, F., Finkel, H., Alexeev, Y., Chong, F.T.: Memory-efficient quantum circuit simulation by using lossy data compression (2018)

    Google Scholar 

  16. Eleanor, R., Wolfgang, P.: Quantum Computing, A Gentle Introduction. The MIT Press, Cambridge (2011)

    MATH  Google Scholar 

  17. Haner, T., Steiger, D.S.: 0.5 petabyte simulation of a 45-qubit quantum circuit. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2017, NY, USA, pp. 33:1–33:10 (2017)

    Google Scholar 

  18. Imanuel, A.: What is quantum computing? Top 18 quantum computing companies (2018). https://www.predictiveanalyticstoday.com/what-is-quantum-computing/

  19. Planck, M.: Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum. j-VERH- DTSCH-PHYS-GES 2(17), 237–245 (1900)

    Google Scholar 

  20. Einstein, A.: Uber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. j-ANN-PHYS-1900-4 322(6), 132–148 (1905)

    Google Scholar 

  21. Lein, M.: Quantum mechanical systems (2016). https://physics.stackexchange.com/questions/278413/what-exactly-is-a-quantum-mechanical-physical-system

  22. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, New York (2011)

    Google Scholar 

  23. Hartley, R.V.L.: Transmission of information. Bell Syst. Tech. J. 7(3), 535–563 (1928)

    Article  Google Scholar 

  24. Wilde, M.: From Classical to Quantum Shannon Theory. Cambridge University Press, Cambridge (2018)

    Google Scholar 

  25. Barnum, H., Wehner, S., Wilce, A.: Introduction: quantum information theory and quantum foundations. Found. Phys. 48(8), 853–856 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  26. Hayden, P., Ekert, A., Inamori, H.: Basic concepts in quantum computation. In: Kaiser, R., Westbrook, C., David, F. (eds.) Coherent Atomic Matter Waves. Les Houches - Ecole d’Ete de Physique Theorique, vol. 72, pp. 661–701. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45338-5_10

    Chapter  Google Scholar 

  27. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: 1994 Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994)

    Google Scholar 

  28. Humble, T.S., De Benedictis, E.P.: Quantum realism. Computer 52(6), 13–17 (2019)

    Article  Google Scholar 

  29. Jordan, S.: Quantum Algorithm Zoo (2018). https://quantumalgorithmzoo.org

  30. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Boston (1994)

    MATH  Google Scholar 

  31. Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Technical report, University of Bristol, Bristol, UK (1992)

    Google Scholar 

  32. Karafyllidis, I., Sirakoulis, G.Ch., Dimitrakis, P.: Representation of qubit states using 3D memristance spaces: a first step towards a memristive quantum simulator. In: Proceedings of the 14th IEEE/ACM International Symposium on Nanoscale Architectures, NANOARCH 2018, New York, USA, pp. 163–168 (2018)

    Google Scholar 

  33. Haner, T., Steiger, D., Svore, K., Troyer, M.: A software methodology for compiling quantum programs. Quantum Sci. Technol. 3(2), 020501 (2018)

    Article  Google Scholar 

  34. Quantiki. List of qc simulators (2019). https://www.quantiki.org/wiki/list-qc-simulators

  35. Quantum Open Source Foundation Team. Quantum open source foundation (2019). https://qosf.org/

  36. La Rose, R.: Overview and comparison of gate level quantum software platforms. Quantum 3, 130 (2019)

    Article  Google Scholar 

  37. Guzik, V., Gushanskiy, S., Polenov, M., Potapov, V.: Models of a quantum computer, their characteristics and analysis. In: 9th International Conference on Application of Information and Communication Technologies (AICT), pp. 583–587 (2015)

    Google Scholar 

  38. Fingerhuth, M., Babej, T., Wittek, P.: Open source software in quantum computing. PLOS One 13(12), 1–28 (2018)

    Article  Google Scholar 

  39. Gheorghiu, V.: Quantum++: a modern C++ quantum computing library. PLoS One 13(12), 1–27 (2018)

    Article  Google Scholar 

  40. Strano, D.: Qrack (2019). https://vm6502q.readthedocs.io/en/latest/

  41. Strilanc, A drag-and-drop quantum circuit simulator (2019). https://github.com/Strilanc/Quirk

  42. Cliffords.jl (2018). https://github.com/BBN-Q/Cliffords.jl

  43. D Wave (2019). https://www.dwavesys.com/

  44. Qbsolv (2019). https://github.com/dwavesystems/qbsolv

  45. McCaskey, A., Dumitrescu, E., Liakh, D., Chen, M., Feng, W., Humble, T.: A language and hardware independent approach to quantum-classical computing (2017)

    Google Scholar 

  46. Tensor Network QPU Simulator for Eclipse XACC (2019). https://github.com/ornl-qci/tnqvm

  47. Qiskit (2019). https://qiskit.org/

  48. Qiskit aer (2019). https://github.com/Qiskit/qiskit-aer

  49. Projectq (2019). https://github.com/ProjectQ-Framework/ProjectQ

  50. QVM Reference (2019). https://github.com/rigetti/reference-qvm/

  51. De Raedt, K., et al.: Massively parallel quantum computer simulator. Comput. Phys. Commun. 176(2), 121–136 (2007)

    Article  MATH  Google Scholar 

  52. Smelyanskiy, M., Sawaya, N.P.D., Aspuru-Guzik, A.: qHIPSTER: the quantum high performance software testing environment. CoRR, abs/1601.07195 (2016)

    Google Scholar 

  53. Li, R., Wu, B., Ying, M., Sun, X., Yang, G.: Quantum supremacy circuit simulation on Sunway TaihuLight (2018)

    Google Scholar 

  54. Li, R., Wu, B., Ying, M., Sun, X., Yang, G.: Quantum supremacy circuit simulation on Sunway TaihuLight. IEEE Trans. Parallel Distrib. Syst. 31(4), 805–816 (2020)

    Article  Google Scholar 

  55. Boixo, S., et al.: Characterizing quantum supremacy in near-term devices. Nat. Phys. 14(6), 595–600 (2018)

    Article  Google Scholar 

  56. Boixo, S., Isakov, S.V., Smelyanskiy, V.N., Neven, H.: Simulation of low-depth quantum circuits as complex undirected graphical models (2017)

    Google Scholar 

  57. Orus, R.: A practical introduction to tensor networks: matrix product states and projected entangled pair states. Ann. Phys. 349, 117–158 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  58. Vidal, G.: Classical simulation of infinite-size quantum lattice systems in one spatial dimension. Phys. Rev. Lett. 98, 070201 (2007)

    Google Scholar 

  59. Schollwock, U.: The density-matrix renormalization group in the age of matrix product states. Ann. Phys. 326(1), 96–192 (2011). Special Issue

    Article  MathSciNet  MATH  Google Scholar 

  60. Wang, D.S., Hill, C.D., Hollenberg, L.L.C.L.: Simulations of Shor’s algorithm using matrix product states (2015)

    Google Scholar 

  61. Vidal, G.: Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91, 147902 (2003)

    Google Scholar 

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Correspondence to Gilberto J. Díaz T .

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Díaz T, G.J., Barrios H., C.J., Steffenel, L.A., Couturier, J.F. (2022). Nearly Quantum Computing by Simulation. In: Navaux, P., Barrios H., C.J., Osthoff, C., Guerrero, G. (eds) High Performance Computing. CARLA 2022. Communications in Computer and Information Science, vol 1660. Springer, Cham. https://doi.org/10.1007/978-3-031-23821-5_15

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  • DOI: https://doi.org/10.1007/978-3-031-23821-5_15

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