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Optimization of the transmission cost of distributed quantum circuits based on merged transfer

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Abstract

The size of quantum circuits is growing as quantum computing develops, yet the devices available today cannot handle the large-scale quantum computing problems. Distributed quantum computing is an effective way to solve this problem. How to efficiently reduce the transmission cost of distributed quantum circuits is crucial because it serves as a fundamental standard of the effectiveness of distributed quantum computing. To this end, this research suggests a distributed storage pattern and a merged transfer model. Based on this distributed storage pattern, the quantum circuit matches the appropriate architecture for distribution, and the circuit is initially partitioned. To determine the most effective partitioning scheme for the circuits, a genetic algorithm is employed to reorder qubits and partition distributed circuits. Based on the merged transfer model, the exchange rules of quantum gates are used to combine a number of discontinuous gates into a single transmission through which these gates can be executed. The merged transfer model completes execution with fewer redundant transmissions, so as to achieve a lower transmission cost overall. The method proposed in this paper takes up fewer quantum resources and has a lower transmission cost than previous research results, with an average transmission cost optimization of 51.3%.

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Data Availability

The data that support the findings of this study are available from https://github.com/cxygiao/DQC.

References

  1. Jaeger, G.: Quantum Information. Springer, Berlin (2007)

    MATH  Google Scholar 

  2. Buhrman, H., Röhrig, H.: Distributed quantum computing. In: International Symposium on Mathematical Foundations of Computer Science, pages 1–20. Springer (2003)

  3. Beals, R., Brierley, S., Gray, O., Harrow, A.W., Kutin, S., Linden, N., Stather, M.: Efficient distributed quantum computing. Proc. Royal Soc. A Math. Phys. Eng. Sci. 469(2153), 20120686 (2013)

    MathSciNet  MATH  ADS  Google Scholar 

  4. Peng, T., Harrow, A.W., Ozols, M., Wu, X.: Simulating large quantum circuits on a small quantum computer. Phys. Rev. Lett. 125(15), 150504 (2020)

    Article  ADS  Google Scholar 

  5. Tang, W., Tomesh, T., Suchara, M., Larson, J., Martonosi, M.: Cutqc: using small quantum computers for large quantum circuit evaluations. In: Proceedings of the 26th ACM International conference on architectural support for programming languages and operating systems, pp. 473-486. (2021)

  6. Chou, K.S., Blumoff, J.Z., Wang, C.S., Reinhold, P.C., Axline, C.J., Gao, Y.Y., Schoelkopf, R.J.: Deterministic teleportation of a quantum gate between two logical qubits. Nature 561(7723), 368–373 (2018)

    Article  ADS  Google Scholar 

  7. Wan, Y., Kienzler, D., Erickson, S.D., Mayer, K.H., Tan, T.R., Wu, J.J., Leibfried, D.: Quantum gate teleportation between separated qubits in a trapped-ion processor. Science 364(6443), 875–878 (2019)

    Article  ADS  Google Scholar 

  8. Pirandola, S., Eisert, J., Weedbrook, C., Furusawa, A., Braunstein, S.L.: Advances in quantum teleportation. Nat. photon. 9(10), 641–652 (2015)

    Article  ADS  Google Scholar 

  9. Langenfeld, Stefan, Welte, Stephan, Hartung, Lukas, Daiss, Severin, Thomas, Philip, Morin, Olivier, Distante, Emanuele, Rempe, Gerhard: Quantum teleportation between remote qubit memories with only a single photon as a resource. Phys. Rev. Lett. 126(13), 130502 (2021)

    Article  ADS  Google Scholar 

  10. Strauch, F.W., Williams, C.J.: Theoretical analysis of perfect quantum state transfer with superconducting qubits. Phys. Rev. B 78(9), 094516 (2008)

    Article  ADS  Google Scholar 

  11. Foxen, B., Mutus, J.Y., Lucero, E., Graff, R., Megrant, A., Yu Chen, C., Quintana, B Burkett, Kelly, J., Jeffrey, E., et al.: Qubit compatible superconducting interconnects. Quant. Sci. Technol. 3(1), 014005 (2017)

    Article  ADS  Google Scholar 

  12. Youssefi, A., Shomroni, I., Joshi, Y.J., Bernier, N.R., Lukashchuk, A., Uhrich, P., Kippenberg, T.J.: A cryogenic electro-optic interconnect for superconducting devices. Nat. Electr. 4(5), 326–332 (2021)

    Article  Google Scholar 

  13. Gold, A., Paquette, J.P., Stockklauser, A., Reagor, M.J., Alam, M.S., Bestwick, A., Rigetti, C.: Entanglement across separate silicon dies in a modular superconducting qubit device. NPJ Quant. Inform. 7(1), 142 (2021)

    Article  ADS  Google Scholar 

  14. Awschalom, D., Berggren, K.K., Bernien, H., Bhave, S., Carr, L.D., Davids, P., Zhang, Z.: Development of quantum interconnects (quics) for next-generation information technologies. PRX Quant. 2(1), 017002 (2021)

    Article  Google Scholar 

  15. Gambetta, J.: Expanding the ibm quantum roadmap to anticipate the future of quantum-centric supercomputing. Website, 2022. https://research.ibm.com/blog/ibm-quantum-roadmap-2025

  16. Moghadam, M.C., Mohammadzadeh, N., Sedighi, M., Zamani, M.S.: A hierarchical layout generation method for quantum circuits. In: The 17th CSI International Symposium on Computer Architecture and Digital Systems (CADS 2013), pp. 51-57. IEEE (2013)

  17. Sargaran, Sahar, Mohammadzadeh, Naser: Saqip: a scalable architecture for quantum information processors. ACM Trans. Archit. Code Optim. (TACO) 16(2), 1–21 (2019)

    Article  Google Scholar 

  18. G Sundaram, R., Gupta, H., Ramakrishnan, C.R.: Efficient distribution of quantum circuits. In: 35th International Symposium on Distributed Computing (DISC 2021). Schloss Dagstuhl-Leibniz-Zentrum fur Informatik. (2021)

  19. Davarzani, Zohreh, Zomorodi-Moghadam, Mariam, Houshmand, Mahboobeh, Nouri-baygi, Mostafa: A dynamic programming approach for distributing quantum circuits by bipartite graphs. Quantum Inf. Process. 19(10), 1–18 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  20. Dadkhah, D., Zomorodi, M., Hosseini, S.E., Plawiak, P., Zhou, X.: Reordering and partitioning of distributed quantum circuits. IEEE Access 10, 70329–70341 (2022)

    Article  Google Scholar 

  21. Davarzani, Zohreh, Zomorodi, Mariam, Houshmand, Mahboobeh: A hierarchical approach for building distributed quantum systems. Sci. Rep. 12(1), 15421 (2022)

    Article  ADS  Google Scholar 

  22. Houshmand, Mahboobeh, Mohammadi, Zahra, Zomorodi-Moghadam, Mariam, Houshmand, Monireh: An evolutionary approach to optimizing teleportation cost in distributed quantum computation. Int. J. Theor. Phys. 59(4), 1315–1329 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  23. Daei, Omid, Navi, Keivan, Zomorodi, Mariam: Improving the teleportation cost in distributed quantum circuits based on commuting of gates. Int. J. Theor. Phys. 60(9), 3494–3513 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ghodsollahee, Ismail, Davarzani, Zohreh, Zomorodi, Mariam, Pławiak, Paweł, Houshmand, Monireh, Houshmand, Mahboobeh: Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization. Quantum Inf. Process. 20(7), 1–21 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  25. Wu, A., Zhang, H., Li, G., Shabani, A., Xie, Y., Ding, Y.: AutoComm: a Framework for Enabling Efficient Communication in Distributed Quantum Programs. In: 2022 55th IEEE/ACM International Symposium on Microarchitecture (MICRO), pp. 1027-1041. IEEE (2022)

  26. Cuomo, D., Caleffi, M., Krsulich, K., Tramonto, F., Agliardi, G., Prati, E., Cacciapuoti, A.S.: Optimized compiler for distributed quantum computing. arXiv preprint arXiv:2112.14139, (2021)

  27. Li, Zhiqiang, Chen, Sai, Song, Xiaoyu, Perkowski, Marek, Chen, Hanwu, Zhu, Wei: Quantum circuit synthesis using a new quantum logic gate library of NCV quantum gates. Int. J. Theor. Phys. 56(4), 1023–1038 (2017)

    Article  MATH  Google Scholar 

  28. Miller, D.M., Soeken, M., Drechsler, R.: Mapping ncv circuits to optimized clifford+t circuits. In: International Conference on Reversible Computation, pages 163–175. Springer (2014)

  29. Zhu, Mingqiang, Cheng, Xueyun, Zhu, Pengcheng, Chen, Liang, Guan, Zhijin: Physical constraint-aware Cnot quantum circuit synthesis and optimization. Quantum Inf. Process. 22(1), 1–19 (2023)

    MathSciNet  MATH  ADS  Google Scholar 

  30. Cheng, Xueyun, Guan, Zhijin, Zhu, Pengcheng: Nearest neighbor transformation of quantum circuits in 2d architecture. IEEE Access 8, 222466–222475 (2020)

    Article  Google Scholar 

  31. Zhu, Pengcheng, Guan, Zhijin, Cheng, Xueyun: A dynamic look-ahead heuristic for the qubit mapping problem of NISG computers. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 39(12), 4721–4735 (2020)

    Article  Google Scholar 

  32. Bao, Xiao-Hui., Xiao-Fan, Xu., Li, Che-Ming., Yuan, Zhen-Sheng., Chao-Yang, Lu., Pan, Jian-Wei.: Quantum teleportation between remote atomic-ensemble quantum memories. Proc. Natl. Acad. Sci. 109(50), 20347–20351 (2012)

    Article  ADS  Google Scholar 

  33. Chatterjee, T., Das, A., Mohtashim, S.I., Saha, A., Chakrabarti, A.: Qurzon: a Prototype for a Divide and Conquer-Based Quantum Compiler for Distributed Quantum Systems. SN Comput. Sci. 3(4), 323 (2022)

    Article  Google Scholar 

  34. Dadkhah, D., Zomorodi, M., Hosseini, S.E.: A new approach for optimization of distributed quantum circuits. Int. J. Theor. Phys. 60, 3271–3285 (2021)

    Article  MATH  Google Scholar 

  35. Sarvaghad-Moghaddam, Moein, Zomorodi, Mariam: A general protocol for distributed quantum gates. Quantum Inf. Process. 20(8), 1–14 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  36. Ferrari, D., Cacciapuoti, A.S., Amoretti, M., Caleffi, M.: Compiler design for distributed quantum computing. arXiv preprint arXiv:2012.09680, 2020

  37. Kurpiers, P., Magnard, P., Walter, T., Royer, B., Pechal, M., Heinsoo, J., Wallraff, A.: Deterministic quantum state transfer and remote entanglement using microwave photons. Nature 558(7709), 264–267 (2018)

    Article  ADS  Google Scholar 

  38. Magnard, P., Storz, S., Kurpiers, P., Schar, J., Marxer, F., Lutolf, J., Wallraff, A.: Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems. Phys. Rev. Lett. 125(26), 260502 (2020)

    Article  ADS  Google Scholar 

  39. Zhong, Y., Chang, H.S., Bienfait, A., Dumur, E., Chou, M.H., Conner, C.R., Cleland, A.N.: Deterministic multi-qubit entanglement in a quantum network. Nature 590(7847), 571–575 (2021)

    Article  ADS  Google Scholar 

  40. Leung, N., Lu, Y., Chakram, S., Naik, R.K., Earnest, N., Ma, R., Schuster, D.I.: Deterministic bidirectional communication and remote entanglement generation between superconducting qubits. NPJ Quantum Inform. 5(1), 18 (2019)

    Article  ADS  Google Scholar 

  41. Qasymeh, Montasir, Eleuch, Hichem: High-fidelity quantum information transmission using a room-temperature nonrefrigerated lossy microwave waveguide. Sci. Rep. 12(1), 1–12 (2022)

    Article  Google Scholar 

  42. Penas, G.F., Puebla, R., Ramos, T., Rabl, P., Garcia-Ripoll, J.J.: Universal deterministic quantum operations in microwave quantum links. Phys. Rev. Appl. 17(5), 054038 (2022)

    Article  ADS  Google Scholar 

  43. Nicholas LaRacuente, Kaitlin N Smith, Poolad Imany, Kevin L Silverman, and Frederic T Chong. Short-range microwave networks to scale superconducting quantum computation. arXiv preprint arXiv:2201.08825, 2022

  44. Smith, K.N., Ravi, G.S., Baker, J.M., Chong, F.T.: Scaling Superconducting Quantum Computers with Chiplet Architectures. In: 2022 55th IEEE/ACM International Symposium on Microarchitecture (MICRO), pp. 1092-1109. IEEE (2022)

  45. Baheri, B., Guan, Q., Xu, S., Chaudhary, V.: SQCC: Smart Quantum Circuit Cutting. In: 2022 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), pp. 614-615. IEEE (2022)

  46. Chitambar, Eric, Gour, Gilad: Quantum resource theories. Rev. Mod. Phys. 91(2), 025001 (2019)

    Article  MathSciNet  ADS  Google Scholar 

  47. IBM Quantum. Ibm quantum compute resources. Website, 2022. https://quantum-computing.ibm.com/services/resources?tab=systems

  48. Andreev, K., Racke, H.: Balanced graph partitioning. In: Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures, pp. 120-124. (2004)

  49. Kumar, M., Husain, D., Upreti, N., Gupta, D.: Genetic algorithm: review and application. Avail. at SSRN 3529843 (2010)

  50. Kumar, Rakesh, Gopal, Girdhar, Kumar, Rajesh: Novel crossover operator for genetic algorithm for permutation problems. Int. J. Soft Comput. Eng. (IJSCE) 3(2), 252–258 (2013)

    Google Scholar 

  51. Jozsa, Richard: Illustrating the concept of quantum information. IBM J. Res. Dev. 48(1), 79–85 (2004)

    Article  Google Scholar 

  52. Hua-Yun, C.H.E.N.G.: Optimized simplification algorithm for reversible MCT circuits. Chin. J. Quantum Electr. 34(6), 713 (2017)

    Google Scholar 

  53. RevLib. An online resource for reversible functions and circuits. Website, 2022. http://www.informatik.uni-bremen.de/rev_lib/

  54. Rahman, M.Z., Rice, J.E.: Templates for positive and negative control toffoli networks. In: International Conference on Reversible Computation, pages 125–136. Springer (2014)

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Correspondence to Zhijin Guan.

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The work was supported by the National Natural Science Foundation of China under Grant number 62072259, in part by the Natural Science Foundation of Jiangsu Province under Grant number BK20221411, in part by the PhD Start-up Fund of Nantong University under Grant number 23B03, and in part by the Postgraduate Research and Practice Innovation Program of Jiangsu Province under Grant number SJCX21-1448.

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Cheng, X., Chen, X., Cao, K. et al. Optimization of the transmission cost of distributed quantum circuits based on merged transfer. Quantum Inf Process 22, 187 (2023). https://doi.org/10.1007/s11128-023-03927-0

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