Skip to main content
Erschienen in: The Journal of Supercomputing 8/2021

13.01.2021

On protocols for increasing the uniformity of random bits generated with noisy quantum computers

verfasst von: Elías F. Combarro, Federico Carminati, Sofia Vallecorsa, José Ranilla, Ignacio F. Rúa

Erschienen in: The Journal of Supercomputing | Ausgabe 8/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Generating random numbers is important for many real-world applications, including cryptography, statistical sampling and Monte Carlo simulations. Quantum systems subject to a measurement produce random results via Born’s rule, and thus it is natural to study the possibility of using such systems in order to generate high-quality random numbers. However, current quantum devices are subject to errors and noise, which can make the output bits deviate from the uniform distribution. In this work, we propose and analyse two protocols that can be used to increase the uniformity of the bits obtained when running a circuit with a Hadamard gate and a measurement in a noisy quantum computer. These protocols may be used prior to other standard processes, such as randomness amplification. We conduct experiments on both a quantum simulator and a real quantum computer, obtaining results that suggest that these protocols are useful to improve the probability of the generated bits passing statistical tests for uniformity.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

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+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!

Literatur
1.
Zurück zum Zitat Aleksandrowicz G, Alexander T, Barkoutsos P, Bello L, Ben-Haim Y, Bucher D, Cabrera-Hernández FJ, Carballo-Franquis J, Chen A, Chen C-F, Chow JM, Córcoles-Gonzales AD, Cross AJ, Cross A, Cruz-Benito J, Culver C, De La Puente González S, De La Torre E, Ding D, Dumitrescu E, Duran I, Eendebak P, Everitt M, Sertage IF, Frisch A, Fuhrer A, Gambetta J, Gago BG, Gomez-Mosquera J, Greenberg D, Hamamura I, Havlicek V, Hellmers J, Herok Ł, Horii H, Hu S, Imamichi T, Itoko T, Javadi-Abhari A, Kanazawa N, Karazeev A, Krsulich K, Liu P, Luh Y, Maeng Y, Marques M, Martín-Fernández FJ, McClure DT, McKay D, Meesala S, Mezzacapo A, Moll N, Rodríguez DM, Nannicini G, Nation P, Ollitrault P, O'Riordan LJ, Paik H, Pérez J, Phan A, Pistoia M, Prutyanov V, Reuter M, Rice J, Davila AR, Rudy RHP, Ryu M, Sathaye N, Schnabel C, Schoute E, Setia K, Shi Y, Silva A, Siraichi Y, Sivarajah S, Smolin JA, Soeken M, Takahashi H, Tavernelli I, Taylor C, Taylour P, Trabing K, Treinish M, Turner W, Vogt-Lee D, Vuillot C, Wildstrom JA, Wilson J, Winston E, Wood C, Wood S, Wörner S, Akhalwaya IY, Zoufal C (2019) Qiskit: An open-source framework for quantum computing. Zenodo, 0.7.2. https://doi.org/10.5281/zenodo.2562111 Aleksandrowicz G, Alexander T, Barkoutsos P, Bello L, Ben-Haim Y, Bucher D, Cabrera-Hernández FJ, Carballo-Franquis J, Chen A, Chen C-F, Chow JM, Córcoles-Gonzales AD, Cross AJ, Cross A, Cruz-Benito J, Culver C, De La Puente González S, De La Torre E, Ding D, Dumitrescu E, Duran I, Eendebak P, Everitt M, Sertage IF, Frisch A, Fuhrer A, Gambetta J, Gago BG, Gomez-Mosquera J, Greenberg D, Hamamura I, Havlicek V, Hellmers J, Herok Ł, Horii H, Hu S, Imamichi T, Itoko T, Javadi-Abhari A, Kanazawa N, Karazeev A, Krsulich K, Liu P, Luh Y, Maeng Y, Marques M, Martín-Fernández FJ, McClure DT, McKay D, Meesala S, Mezzacapo A, Moll N, Rodríguez DM, Nannicini G, Nation P, Ollitrault P, O'Riordan LJ, Paik H, Pérez J, Phan A, Pistoia M, Prutyanov V, Reuter M, Rice J, Davila AR, Rudy RHP, Ryu M, Sathaye N, Schnabel C, Schoute E, Setia K, Shi Y, Silva A, Siraichi Y, Sivarajah S, Smolin JA, Soeken M, Takahashi H, Tavernelli I, Taylor C, Taylour P, Trabing K, Treinish M, Turner W, Vogt-Lee D, Vuillot C, Wildstrom JA, Wilson J, Winston E, Wood C, Wood S, Wörner S, Akhalwaya IY, Zoufal C (2019) Qiskit: An open-source framework for quantum computing. Zenodo, 0.7.2. https://​doi.​org/​10.​5281/​zenodo.​2562111
2.
Zurück zum Zitat Acín A, Masanes L (2016) Certified randomness in quantum physics. Nature 540:213–219CrossRef Acín A, Masanes L (2016) Certified randomness in quantum physics. Nature 540:213–219CrossRef
3.
Zurück zum Zitat Asmussen S, Glynn P (2007) Stochastic simulation: algorithms and analysis. Springer, BerlinCrossRef Asmussen S, Glynn P (2007) Stochastic simulation: algorithms and analysis. Springer, BerlinCrossRef
4.
Zurück zum Zitat Bakiri M, Guyeux C, Couchot JF, Oudjida AK (2018) Survey on hardware implementation of random number generators on fpga: theory and experimental analyses. Comput Sci Rev 27:135–153MathSciNetCrossRef Bakiri M, Guyeux C, Couchot JF, Oudjida AK (2018) Survey on hardware implementation of random number generators on fpga: theory and experimental analyses. Comput Sci Rev 27:135–153MathSciNetCrossRef
5.
Zurück zum Zitat Bassham LE, Rukhin AL, Soto J et al (2010) A statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical Report, National Institute of Standards and Technology, Gaithersburg, MD, USA Bassham LE, Rukhin AL, Soto J et al (2010) A statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical Report, National Institute of Standards and Technology, Gaithersburg, MD, USA
6.
Zurück zum Zitat Bera MN, Acín A, Kuś M, Mitchell MW, Lewenstein M (2017) Randomness in quantum mechanics: philosophy, physics and technology. Reports Progress Phys 80(12):124,001MathSciNetCrossRef Bera MN, Acín A, Kuś M, Mitchell MW, Lewenstein M (2017) Randomness in quantum mechanics: philosophy, physics and technology. Reports Progress Phys 80(12):124,001MathSciNetCrossRef
7.
Zurück zum Zitat Born M (1955) Statistical interpretation of quantum mechanics. Science 122(3172):675–679CrossRef Born M (1955) Statistical interpretation of quantum mechanics. Science 122(3172):675–679CrossRef
9.
Zurück zum Zitat Combarro E, Carminati F, Vallecorsa S, Ranilla J, Rúa I (2020) Quantum random numbers generated by the cloud superconducting quantum computer. Bristol Quantum Information Technologies Workshop (BQIT:20) Combarro E, Carminati F, Vallecorsa S, Ranilla J, Rúa I (2020) Quantum random numbers generated by the cloud superconducting quantum computer. Bristol Quantum Information Technologies Workshop (BQIT:20)
10.
Zurück zum Zitat Combarro E, Carminati F, Vallecorsa S, Ranilla J, Rúa I (2020) Two simple protocols for improving the uniformity of quantum random bits in the presence of noise. In 20th Computational and Mathematical Methods in Science and Engineering Conference Combarro E, Carminati F, Vallecorsa S, Ranilla J, Rúa I (2020) Two simple protocols for improving the uniformity of quantum random bits in the presence of noise. In 20th Computational and Mathematical Methods in Science and Engineering Conference
11.
Zurück zum Zitat Combarro EF, Ranilla J, Rúa I (2019) A quantum algorithm for the commutativity of finite dimensional algebras. IEEE Access 7:45554–45562CrossRef Combarro EF, Ranilla J, Rúa I (2019) A quantum algorithm for the commutativity of finite dimensional algebras. IEEE Access 7:45554–45562CrossRef
12.
Zurück zum Zitat Gentle JE (2004) Random number generation and monte carlo methods. Springer, BerlinMATH Gentle JE (2004) Random number generation and monte carlo methods. Springer, BerlinMATH
13.
Zurück zum Zitat Grover LK (1996) A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, STOC ’96, pp. 212–219. ACM, New York, NY, USA Grover LK (1996) A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, STOC ’96, pp. 212–219. ACM, New York, NY, USA
14.
16.
Zurück zum Zitat James F, Moneta L (2020) Review of high-quality random number generators. Comput Softw Big Sci 4:2CrossRef James F, Moneta L (2020) Review of high-quality random number generators. Comput Softw Big Sci 4:2CrossRef
18.
Zurück zum Zitat Kollmitzer C, Schauer S, Rass S, Rainer B (2020) Quantum random number generation theory and practice: theory and practice. Springer, BerlinCrossRef Kollmitzer C, Schauer S, Rass S, Rainer B (2020) Quantum random number generation theory and practice: theory and practice. Springer, BerlinCrossRef
19.
Zurück zum Zitat L’Ecuyer P (2012) Random number generation. In: Gentle JE, Härdle WK, Mori Y (eds) Handbook of computational statistics: concepts and methods. Springer, Berlin Heidelberg, Berlin, Heidelberg L’Ecuyer P (2012) Random number generation. In: Gentle JE, Härdle WK, Mori Y (eds) Handbook of computational statistics: concepts and methods. Springer, Berlin Heidelberg, Berlin, Heidelberg
20.
Zurück zum Zitat Li L, Yu F, Tang Q, Song Y, Xu Q, Cai S (2019) A survey on true random number generators based on Chaos. Discrete Dyn Nature Soc 2019:1–10MathSciNetMATH Li L, Yu F, Tang Q, Song Y, Xu Q, Cai S (2019) A survey on true random number generators based on Chaos. Discrete Dyn Nature Soc 2019:1–10MathSciNetMATH
21.
Zurück zum Zitat Liu Y, Zhao Q, Li MH et al (2018) Device-independent quantum random-number generation. Nature 562(7728):548–551CrossRef Liu Y, Zhao Q, Li MH et al (2018) Device-independent quantum random-number generation. Nature 562(7728):548–551CrossRef
22.
Zurück zum Zitat Luby M (1996) Pseudorandomness and cryptographic applications. Princeton University Press, Princeton, NJCrossRef Luby M (1996) Pseudorandomness and cryptographic applications. Princeton University Press, Princeton, NJCrossRef
23.
Zurück zum Zitat L’Ecuyer P, Simard R (2007) Testu01: A c library for empirical testing of random number generators. ACM Trans Math Softw 33(4):1–40MathSciNetCrossRef L’Ecuyer P, Simard R (2007) Testu01: A c library for empirical testing of random number generators. ACM Trans Math Softw 33(4):1–40MathSciNetCrossRef
24.
Zurück zum Zitat Ma X, Yuan X, Cao Z, Qi B, Zhang Z (2016) Quantum random number generation. npj Quantum Inf 2(1):16,021CrossRef Ma X, Yuan X, Cao Z, Qi B, Zhang Z (2016) Quantum random number generation. npj Quantum Inf 2(1):16,021CrossRef
25.
Zurück zum Zitat Nielsen MA, Chuang IL (2011) Quantum computation and quantum information, 10th edn. Cambridge University Press, CambridgeMATH Nielsen MA, Chuang IL (2011) Quantum computation and quantum information, 10th edn. Cambridge University Press, CambridgeMATH
26.
Zurück zum Zitat Schlosshauer M, Kofler J, Zeilinger A (2013) A snapshot of foundational attitudes toward quantum mechanics. Stud History Philos Sci Part B: Stud History Philos Modern Phys 44(3):222–230CrossRef Schlosshauer M, Kofler J, Zeilinger A (2013) A snapshot of foundational attitudes toward quantum mechanics. Stud History Philos Sci Part B: Stud History Philos Modern Phys 44(3):222–230CrossRef
27.
Zurück zum Zitat Shaltiel R (2011) An introduction to randomness extractors. In: Aceto L, Henzinger M, Sgall J (eds) Automata, languages and programming. Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 21–41CrossRef Shaltiel R (2011) An introduction to randomness extractors. In: Aceto L, Henzinger M, Sgall J (eds) Automata, languages and programming. Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 21–41CrossRef
28.
Zurück zum Zitat Shor P (1994) Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings of FOCS pp. 124–134 Shor P (1994) Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings of FOCS pp. 124–134
29.
Zurück zum Zitat Stipčević M, Koç ÇK (2014) True random number generators. In: Koç ÇK (ed) Open problems in mathematics and computational science. Springer, Cham Stipčević M, Koç ÇK (2014) True random number generators. In: Koç ÇK (ed) Open problems in mathematics and computational science. Springer, Cham
30.
Zurück zum Zitat Tamura K, Shikano Y (2019) Quantum random numbers generated by the cloud superconducting quantum computer. In International Symposium on Mathematics, Quantum Theory, and Cryptography: Proceedings of MQC 2019 Tamura K, Shikano Y (2019) Quantum random numbers generated by the cloud superconducting quantum computer. In International Symposium on Mathematics, Quantum Theory, and Cryptography: Proceedings of MQC 2019
Metadaten
Titel
On protocols for increasing the uniformity of random bits generated with noisy quantum computers
verfasst von
Elías F. Combarro
Federico Carminati
Sofia Vallecorsa
José Ranilla
Ignacio F. Rúa
Publikationsdatum
13.01.2021
Verlag
Springer US
Erschienen in
The Journal of Supercomputing / Ausgabe 8/2021
Print ISSN: 0920-8542
Elektronische ISSN: 1573-0484
DOI
https://doi.org/10.1007/s11227-020-03574-7

Weitere Artikel der Ausgabe 8/2021

The Journal of Supercomputing 8/2021 Zur Ausgabe

Premium Partner