Skip to main content
Top
Published in: Quantum Information Processing 7/2021

01-07-2021

Implementation of efficient quantum search algorithms on NISQ computers

Authors: Kun Zhang, Pooja Rao, Kwangmin Yu, Hyunkyung Lim, Vladimir Korepin

Published in: Quantum Information Processing | Issue 7/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Despite the advent of Grover’s algorithm for the unstructured search, its successful implementation on near-term quantum devices is still limited. We apply three strategies to reduce the errors associated with implementing quantum search algorithms. Our improved search algorithms have been implemented on the IBM quantum processors. Using them, we demonstrate three- and four-qubit search algorithm with higher average success probabilities compared to previous works. We present the successful execution of the five-qubit search on the IBM quantum processor for the first time. The results have been benchmarked using degraded ratio, which is the ratio between the experimental and the theoretical success probabilities. The fast decay of the degraded ratio supports our divide-and-conquer strategy. Our proposed strategies are also useful for implementation of quantum search algorithms in the post-NISQ era.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference Barends, R., Kelly, J., Megrant, A., Veitia, A., Sank, D., Jeffrey, E., White, T.C., Mutus, J., Fowler, A.G., Campbell, B., et al.: Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508(7497), 500 (2014)ADSCrossRef Barends, R., Kelly, J., Megrant, A., Veitia, A., Sank, D., Jeffrey, E., White, T.C., Mutus, J., Fowler, A.G., Campbell, B., et al.: Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508(7497), 500 (2014)ADSCrossRef
2.
go back to reference Ballance, C.J., Harty, T.P., Linke, N.M., Sepiol, M.A., Lucas, D.M.: High-fidelity quantum logic gates using trapped-ion hyperfine qubits. Phys. Rev. Lett. 117(6), 060504 (2016)ADSCrossRef Ballance, C.J., Harty, T.P., Linke, N.M., Sepiol, M.A., Lucas, D.M.: High-fidelity quantum logic gates using trapped-ion hyperfine qubits. Phys. Rev. Lett. 117(6), 060504 (2016)ADSCrossRef
3.
go back to reference Figgatt, C., Maslov, D., Landsman, K.A., Linke, N.M., Debnath, S., Monroe, C.: Complete 3-qubit grover search on a programmable quantum computer. Nat. Commun. 8(1), 1918 (2017)ADSCrossRef Figgatt, C., Maslov, D., Landsman, K.A., Linke, N.M., Debnath, S., Monroe, C.: Complete 3-qubit grover search on a programmable quantum computer. Nat. Commun. 8(1), 1918 (2017)ADSCrossRef
4.
go back to reference Google AI Quantum, et al.: Hartree-fock on a superconducting qubit quantum computer. Science 369(6507), 1084–1089 (2020) Google AI Quantum, et al.: Hartree-fock on a superconducting qubit quantum computer. Science 369(6507), 1084–1089 (2020)
5.
go back to reference Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Sergio, B., Fernando, G.S.L., Buell, D.A., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)ADSCrossRef Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Sergio, B., Fernando, G.S.L., Buell, D.A., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)ADSCrossRef
6.
go back to reference Zhong, H.-S., Wang, H., Deng, Y.-H., Chen, M.-C., Peng, L.-C., Luo, Y.-H., Qin, J., Wu, D., Ding, X., Hu, Y., et al.: Quantum computational advantage using photons. Science 370(6523), 1460–1463 (2020)ADS Zhong, H.-S., Wang, H., Deng, Y.-H., Chen, M.-C., Peng, L.-C., Luo, Y.-H., Qin, J., Wu, D., Ding, X., Hu, Y., et al.: Quantum computational advantage using photons. Science 370(6523), 1460–1463 (2020)ADS
7.
go back to reference Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information, (2010) Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information, (2010)
8.
go back to reference Preskill, J.: Quantum computing in the nisq era and beyond. Quantum 2, 79 (2018)CrossRef Preskill, J.: Quantum computing in the nisq era and beyond. Quantum 2, 79 (2018)CrossRef
9.
go back to reference Cross, A.W., Bishop, L.S., Sheldon, S., Nation, P.D., Gambetta, J.M.: Validating quantum computers using randomized model circuits. Phys. Rev. A 100(3), 032328 (2019)ADSCrossRef Cross, A.W., Bishop, L.S., Sheldon, S., Nation, P.D., Gambetta, J.M.: Validating quantum computers using randomized model circuits. Phys. Rev. A 100(3), 032328 (2019)ADSCrossRef
10.
go back to reference Bharti, K., Cervera-Lierta, A., Kyaw, T.H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J.S., Menke, T., Mok, W.-K., Sim, S., Kwek, L.-C., Aspuru-Guzik, A.: Noisy intermediate-scale quantum (nisq) algorithms. arXiv preprint arXiv:2101.08448, (2021) Bharti, K., Cervera-Lierta, A., Kyaw, T.H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J.S., Menke, T., Mok, W.-K., Sim, S., Kwek, L.-C., Aspuru-Guzik, A.: Noisy intermediate-scale quantum (nisq) algorithms. arXiv preprint arXiv:​2101.​08448, (2021)
11.
go back to reference Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)ADSCrossRef Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)ADSCrossRef
13.
go back to reference Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26(5), 1510–1523 (1997)MathSciNetCrossRef Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26(5), 1510–1523 (1997)MathSciNetCrossRef
14.
go back to reference Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549(7671), 195–202 (2017)ADSCrossRef Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549(7671), 195–202 (2017)ADSCrossRef
15.
go back to reference Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. Fortschritte der Physik: Prog. Phys. 46(4–5), 493–505 (1998)ADSCrossRef Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. Fortschritte der Physik: Prog. Phys. 46(4–5), 493–505 (1998)ADSCrossRef
16.
go back to reference Zalka, C.: Grover’s quantum searching algorithm is optimal. Phys. Rev. A 60(4), 2746 (1999)ADSCrossRef Zalka, C.: Grover’s quantum searching algorithm is optimal. Phys. Rev. A 60(4), 2746 (1999)ADSCrossRef
17.
go back to reference Grassl, M., Langenberg, B., Roetteler, M., Steinwandt, R.: Applying grover’s algorithm to aes: quantum resource estimates. In: Post-Quantum Cryptography, pp. 29–43. Springer, (2016) Grassl, M., Langenberg, B., Roetteler, M., Steinwandt, R.: Applying grover’s algorithm to aes: quantum resource estimates. In: Post-Quantum Cryptography, pp. 29–43. Springer, (2016)
18.
go back to reference Kim, P., Han, D., Jeong, K.C.: Time-space complexity of quantum search algorithms in symmetric cryptanalysis: applying to aes and sha-2. Quantum Inf. Process. 17(12), 339 (2018)ADSMathSciNetCrossRef Kim, P., Han, D., Jeong, K.C.: Time-space complexity of quantum search algorithms in symmetric cryptanalysis: applying to aes and sha-2. Quantum Inf. Process. 17(12), 339 (2018)ADSMathSciNetCrossRef
19.
go back to reference Jaques, S., Naehrig, M., Roetteler, M., Virdia, F.: Implementing grover oracles for quantum key search on aes and lowmc. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 280–310. Springer, (2020) Jaques, S., Naehrig, M., Roetteler, M., Virdia, F.: Implementing grover oracles for quantum key search on aes and lowmc. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 280–310. Springer, (2020)
20.
go back to reference Wang, Y., Krstic, P.S.: Prospect of using grover’s search in the noisy-intermediate-scale quantum-computer era. Phys. Rev. A 102(4), 042609 (2020)ADSCrossRef Wang, Y., Krstic, P.S.: Prospect of using grover’s search in the noisy-intermediate-scale quantum-computer era. Phys. Rev. A 102(4), 042609 (2020)ADSCrossRef
21.
go back to reference Kato, G.: Grover-algorithm-like operator using only single-qubit gates. Phys. Rev. A 72(3), 032319 (2005)ADSCrossRef Kato, G.: Grover-algorithm-like operator using only single-qubit gates. Phys. Rev. A 72(3), 032319 (2005)ADSCrossRef
22.
go back to reference Tulsi, A.: Faster quantum searching with almost any diffusion operator. Phys. Rev. A 91(5), 052307 (2015)ADSCrossRef Tulsi, A.: Faster quantum searching with almost any diffusion operator. Phys. Rev. A 91(5), 052307 (2015)ADSCrossRef
23.
go back to reference Jiang, Z., Rieffel, E.G., Wang, Z.: Near-optimal quantum circuit for grover’s unstructured search using a transverse field. Phys. Rev. A 95(6), 062317 (2017)ADSCrossRef Jiang, Z., Rieffel, E.G., Wang, Z.: Near-optimal quantum circuit for grover’s unstructured search using a transverse field. Phys. Rev. A 95(6), 062317 (2017)ADSCrossRef
24.
go back to reference Grover, L.K., Radhakrishnan, J.: Is partial quantum search of a database any easier? In: Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures, pp. 186–194. ACM, (2005) Grover, L.K., Radhakrishnan, J.: Is partial quantum search of a database any easier? In: Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures, pp. 186–194. ACM, (2005)
26.
27.
go back to reference Grover, L.K.: Trade-offs in the quantum search algorithm. Phys. Rev. A 66(5), 052314 (2002)ADSCrossRef Grover, L.K.: Trade-offs in the quantum search algorithm. Phys. Rev. A 66(5), 052314 (2002)ADSCrossRef
28.
go back to reference Briański, M., Gwinner, J., Hlembotskyi, V., Jarnicki, W., Pliś, S., Szady, A.: Introducing structure to expedite quantum search. arXiv preprint arXiv:2006.05828, (2020) Briański, M., Gwinner, J., Hlembotskyi, V., Jarnicki, W., Pliś, S., Szady, A.: Introducing structure to expedite quantum search. arXiv preprint arXiv:​2006.​05828, (2020)
29.
go back to reference Zhang, K., Korepin, V.E.: Depth optimization of quantum search algorithms beyond grover’s algorithm. Phys. Rev. A 101(3), 032346 (2020)ADSMathSciNetCrossRef Zhang, K., Korepin, V.E.: Depth optimization of quantum search algorithms beyond grover’s algorithm. Phys. Rev. A 101(3), 032346 (2020)ADSMathSciNetCrossRef
31.
go back to reference Mandviwalla, A., Ohshiro, K., Ji, B.: Implementing grover’s algorithm on the ibm quantum computers. In: 2018 IEEE International Conference on Big Data (Big Data), pp. 2531–2537. IEEE, (2018) Mandviwalla, A., Ohshiro, K., Ji, B.: Implementing grover’s algorithm on the ibm quantum computers. In: 2018 IEEE International Conference on Big Data (Big Data), pp. 2531–2537. IEEE, (2018)
32.
go back to reference Gwinner, J., Briański, M., Burkot, W., Czerwiński, Ł., Hlembotskyi, V.: Benchmarking 16-element quantum search algorithms on ibm quantum processors. arXiv preprint arXiv:2007.06539, (2020) Gwinner, J., Briański, M., Burkot, W., Czerwiński, Ł., Hlembotskyi, V.: Benchmarking 16-element quantum search algorithms on ibm quantum processors. arXiv preprint arXiv:​2007.​06539, (2020)
33.
34.
go back to reference Hlembotskyi, V., Burczyński, R., Jarnicki, W., Szady, A., Tułowiecki, J.: Efficient unstructured search implementation on current ion-trap quantum processors. arXiv preprint arXiv:2010.03841, (2020) Hlembotskyi, V., Burczyński, R., Jarnicki, W., Szady, A., Tułowiecki, J.: Efficient unstructured search implementation on current ion-trap quantum processors. arXiv preprint arXiv:​2010.​03841, (2020)
35.
go back to reference Grover, L.K.: Quantum computers can search rapidly by using almost any transformation. Phys. Rev. Lett. 80(19), 4329 (1998)ADSCrossRef Grover, L.K.: Quantum computers can search rapidly by using almost any transformation. Phys. Rev. Lett. 80(19), 4329 (1998)ADSCrossRef
36.
go back to reference Brassard, G., Hoyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. Contemp. Math. 305, 53–74 (2002)MathSciNetCrossRef Brassard, G., Hoyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. Contemp. Math. 305, 53–74 (2002)MathSciNetCrossRef
37.
go back to reference Almazrooie, M., Samsudin, A., Abdullah, R., Mutter, K.N.: Quantum reversible circuit of aes-128. Quantum Inf. Process. 17(5), 112 (2018)MathSciNetCrossRef Almazrooie, M., Samsudin, A., Abdullah, R., Mutter, K.N.: Quantum reversible circuit of aes-128. Quantum Inf. Process. 17(5), 112 (2018)MathSciNetCrossRef
38.
go back to reference Langenberg, B., Pham, H., Steinwandt, R.: Reducing the cost of implementing aes as a quantum circuit. Technical report, Cryptology ePrint Archive, Report 2019/854, (2019) Langenberg, B., Pham, H., Steinwandt, R.: Reducing the cost of implementing aes as a quantum circuit. Technical report, Cryptology ePrint Archive, Report 2019/854, (2019)
39.
go back to reference Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457 (1995)ADSCrossRef Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457 (1995)ADSCrossRef
40.
41.
go back to reference Korepin, V.E., Vallilo, B.C.: Group theoretical formulation of a quantum partial search algorithm. Prog. Theor. Phys. 116(5), 783–793 (2006)ADSMathSciNetCrossRef Korepin, V.E., Vallilo, B.C.: Group theoretical formulation of a quantum partial search algorithm. Prog. Theor. Phys. 116(5), 783–793 (2006)ADSMathSciNetCrossRef
42.
go back to reference Gingrich, R.M., Williams, C.P., Cerf, N.J.: Generalized quantum search with parallelism. Phys. Rev. A 61(5), 052313 (2000)ADSCrossRef Gingrich, R.M., Williams, C.P., Cerf, N.J.: Generalized quantum search with parallelism. Phys. Rev. A 61(5), 052313 (2000)ADSCrossRef
43.
go back to reference Maslov, D.: Advantages of using relative-phase toffoli gates with an application to multiple control toffoli optimization. Phys. Rev. A 93(2), 022311 (2016)ADSCrossRef Maslov, D.: Advantages of using relative-phase toffoli gates with an application to multiple control toffoli optimization. Phys. Rev. A 93(2), 022311 (2016)ADSCrossRef
44.
go back to reference Song, G., Klappenecker, A.: Optimal realizations of simplified toffoli gates. Quantum Inf. Comput. 4(5), 361–372 (2004)MathSciNetMATH Song, G., Klappenecker, A.: Optimal realizations of simplified toffoli gates. Quantum Inf. Comput. 4(5), 361–372 (2004)MathSciNetMATH
45.
go back to reference Tannu, S.S., Qureshi, M.: Ensemble of diverse mappings: Improving reliability of quantum computers by orchestrating dissimilar mistakes. In: Proceedings of the 52nd Annual IEEE/ACM International Symposium on Microarchitecture, pp. 253–265 (2019) Tannu, S.S., Qureshi, M.: Ensemble of diverse mappings: Improving reliability of quantum computers by orchestrating dissimilar mistakes. In: Proceedings of the 52nd Annual IEEE/ACM International Symposium on Microarchitecture, pp. 253–265 (2019)
Metadata
Title
Implementation of efficient quantum search algorithms on NISQ computers
Authors
Kun Zhang
Pooja Rao
Kwangmin Yu
Hyunkyung Lim
Vladimir Korepin
Publication date
01-07-2021
Publisher
Springer US
Published in
Quantum Information Processing / Issue 7/2021
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-021-03165-2

Other articles of this Issue 7/2021

Quantum Information Processing 7/2021 Go to the issue