- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Noise-tolerant Grover's algorithm via success-probability prediction

Jian Leng1, Fan Yang1, and Xiang-Bin Wang1,2,3,4,*

  • *Contact author: xbwang@mail.tsinghua.edu.cn
PDF

Phys. Rev. Research 7, L012017 – Published 21 January, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012017

Abstract

We present theoretical and experimental studies on efficient quantum search with noise. We propose a noise-tolerant method that significantly reduces the running time and exponentially improves the error threshold with number of qubits for Grover's search. Experiments are implemented on different quantum computing setups, with all results clearly confirming the advantage of our noise-tolerant method to the original Grover's search. In one setup, our method produces quantum advantages while the original Grover's search does not. In another setup with smaller noise, our method produces a larger quantum advantage than the original Grover's search does.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (45)

  1. D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation, Proc. R. Soc. A 439, 553 (1992).
  2. P. W. Shor, Algorithms for quantum computation: Discrete logarithms and factoring, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science (IEEE, Piscataway, NJ, 1994), pp. 124–134.
  3. L. K. Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing (ACM, New York, 1996), pp. 212–219.
  4. S. Aaronson and A. Arkhipov, The computational complexity of linear optics, in Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing (ACM, New York, 2011), pp. 333–342.
  5. D. Anguita, S. Ridella, F. Rivieccio, and R. Zunino, Quantum optimization for training support vector machines, Neural Netw. 16, 763 (2003).
  6. G. Anikeeva, O. Marković, V. Borish, J. A. Hines, S. V. Rajagopal, E. S. Cooper, A. Periwal, A. Safavi-Naeini, E. J. Davis, and M. Schleier-Smith, Number partitioning with Grover's algorithm in central spin systems, PRX Quantum 2, 020319 (2021).
  7. Y. Bejerano, S.-J. Han, and A. Kumar, Efficient load-balancing routing for wireless mesh networks, Comput. Netw. 51, 2450 (2007).
  8. P. Botsinis, D. Alanis, Z. Babar, H. V. Nguyen, D. Chandra, S. X. Ng, and L. Hanzo, Quantum search algorithms for wireless communications, IEEE Commun. Surv. Tutor. 21, 1209 (2018).
  9. G. Brassard, P. Hoyer, and A. Tapp, in Quantum cryptanalysis of hash and claw-free functions, LATIN'98: Theoretical Informatics, Lecture Notes in Computer Science (Springer, Berlin, Heidelberg, 1998), Vol. 1380, pp. 163–169.
  10. S. Ramos-Calderer, E. Bellini, J. I. Latorre, M. Manzano, and V. Mateu, Quantum search for scaled hash function preimages, Quantum Inf. Process. 20, 180 (2021).
  11. M. Grassl, B. Langenberg, M. Roetteler, and R. Steinwandt, Applying Grover's algorithm to AES: Quantum resource estimates, in International Workshop on Post-Quantum Cryptography (Springer, Berlin, 2016), pp. 29–43.
  12. S. Jaques, M. Naehrig, M. Roetteler, and F. Virdia, Implementing Grover oracles for quantum key search on AES and LowMC, in Advances in Cryptology–EUROCRYPT 2020: 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings, Part II (Springer, Berlin, 2020), pp. 280–310.
  13. B. Pablo-Norman and M. Ruiz-Altaba, Robustness of the quantum search algorithm, in The Eighth Mexican School on Particles and Fields, 20–28 November 1998, Oaxaca de Juarez, Mexico, AIP Conference Proceedings (AIP, New York, 1999), Vol. 490, pp. 405–408.
  14. D. Shapira, S. Mozes, and O. Biham, Effect of unitary noise on Grover's quantum search algorithm, Phys. Rev. A 67, 042301 (2003).
  15. N. Shenvi, K. R. Brown, and K. B. Whaley, Effects of a random noisy oracle on search algorithm complexity, Phys. Rev. A 68, 052313 (2003).
  16. P. J. Salas, Noise effect on Grover algorithm, Eur. Phys. J. D 46, 365 (2008).
  17. I. Cohn, A. L. F. De Oliveira, E. Buksman, and J. G. L. De Lacalle, Grover's search with local and total depolarizing channel errors: Complexity analysis, Int. J. Quantum Inf. 14, 1650009 (2016).
  18. D. Reitzner and M. Hillery, Grover search under localized dephasing, Phys. Rev. A 99, 012339 (2019).
  19. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell et al., Quantum supremacy using a programmable superconducting processor, Nature (London) 574, 505 (2019).
  20. H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu et al., Quantum computational advantage using photons, Science 370, 1460 (2020).
  21. Y. Wu, W.-S. Bao, S. Cao, F. Chen, M.-C. Chen, X. Chen, T.-H. Chung, H. Deng, Y. Du, D. Fan et al., Strong quantum computational advantage using a superconducting quantum processor, Phys. Rev. Lett. 127, 180501 (2021).
  22. H.-S. Zhong, Y.-H. Deng, J. Qin, H. Wang, M.-C. Chen, L.-C. Peng, Y.-H. Luo, D. Wu, S.-Q. Gong, H. Su et al., Phase-programmable Gaussian boson sampling using stimulated squeezed light, Phys. Rev. Lett. 127, 180502 (2021).
  23. Y. Zhao, Y. Ye, H.-L. Huang, Y. Zhang, D. Wu, H. Guan, Q. Zhu, Z. Wei, T. He, S. Cao et al., Realization of an error-correcting surface code with superconducting qubits, Phys. Rev. Lett. 129, 030501 (2022).
  24. R. Acharya, I. Aleiner, R. Allen, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, R. Babbush et al., Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  25. Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. Van Den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme et al., Evidence for the utility of quantum computing before fault tolerance, Nature (London) 618, 500 (2023).
  26. S. Cao, B. Wu, F. Chen, M. Gong, Y. Wu, Y. Ye, C. Zha, H. Qian, C. Ying, S. Guo et al., Generation of genuine entanglement up to 51 superconducting qubits, Nature (London) 619, 738 (2023).
  27. P. Zhao, R. Wang, M.-J. Hu, T. Ma, P. Xu, Y. Jin, and H. Yu, Baseband control of superconducting qubits with shared microwave drives, Phys. Rev. Appl. 19, 054050 (2023).
  28. B. Pokharel and D. A. Lidar, Demonstration of algorithmic quantum speedup, Phys. Rev. Lett. 130, 210602 (2023).
  29. T. Roy, L. Jiang, and D. I. Schuster, Deterministic grover search with a restricted oracle, Phys. Rev. Res. 4, L022013 (2022).
  30. P. W. Shor, Fault-tolerant quantum computation, in Proceedings of 37th Conference on Foundations of Computer Science (IEEE, Piscataway, NJ, 1996), pp. 56–65.
  31. D. Gottesman, Class of quantum error-correcting codes saturating the quantum hamming bound, Phys. Rev. A 54, 1862 (1996).
  32. D. Poulin, Stabilizer formalism for operator quantum error correction, Phys. Rev. Lett. 95, 230504 (2005).
  33. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  34. T. Roy, S. Hazra, S. Kundu, M. Chand, M. P. Patankar, and R. Vijay, Programmable superconducting processor with native three-qubit gates, Phys. Rev. Appl. 14, 014072 (2020).
  35. C. Figgatt, D. Maslov, K. A. Landsman, N. M. Linke, S. Debnath, and C. Monroe, Complete 3-qubit grover search on a programmable quantum computer, Nat. Commun. 8, 1918 (2017).
  36. K. Zhang, P. Rao, K. Yu, H. Lim, and V. Korepin, Implementation of efficient quantum search algorithms on NISQ computers, Quantum Inf. Process. 20, 233 (2021).
  37. K. Zhang, K. Yu, and V. Korepin, Quantum search on noisy intermediate-scale quantum devices, Europhys. Lett. 140, 18002 (2022).
  38. B. Pokharel and D. A. Lidar, Better-than-classical grover search via quantum error detection and suppression, npj Quantum Inf. 10, 23 (2024).
  39. M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (AAPT, College Park, MD, 2002).
  40. J. Leng, F. Yang, and X.-B. Wang, Improving D2p Grover's algorithm to reach performance upper bound under phase noise, Phys. Rev. Res. 5, 023202 (2023).
  41. P. O. Boykin, T. Mor, M. Pulver, V. Roychowdhury, and F. Vatan, On universal and fault-tolerant quantum computing: A novel basis and a new constructive proof of universality for Shor's basis, in 40th Annual Symposium on Foundations of Computer Science (IEEE, Piscataway, NJ, 1999), pp. 486–494.
  42. J. Leng, F. Yang, and X.-B. Wang, Decomposing (n+1)-qubit Toffoli gate with shallow circuit depth and no ancilla, Adv. Quantum Technol. 7, 2300370 (2024).
  43. D. Maslov, Advantages of using relative-phase toffoli gates with an application to multiple control Toffoli optimization, Phys. Rev. A 93, 022311 (2016).
  44. https://quafu.baqis.ac.cn
  45. P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer's guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019).

Outline

Information

Phys. Rev. Research 7, L012017– Published 21 January, 2025
  • Received 5 October 2023
  • Revised 4 December 2023
  • Accepted 25 December 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation