Abstract
Grover’s quantum search algorithm is a highly studied quantum algorithm that has potential applications in unstructured data search, achieving quadratic speedup over existing classical search algorithms. In this work, we propose a modified quantum circuit for multi-pattern quantum Grover’s search algorithm. Our proposed modification simplifies the conventional Grover’s algorithm circuit and makes it capable of processing dynamically changing input patterns. The proposed techniques are demonstrated using reconfigurable hardware architectures that are designed for cost-effective, scalable, high-precision and high-throughput emulation of quantum algorithms. We experimentally evaluate the modified algorithm using Field Programmable Gate Array (FPGA) hardware and provide analysis of experimental results in terms of hardware resource utilization and emulation time. Our results demonstrate successful emulation of multi-pattern Grover’s algorithm using up to 22 quantum bits on a single FPGA, which is the highest and most efficient among existing work. Hardware implementations were performed for up to 32 qubits, and emulation time results of up to 32 qubits were projected using a performance estimation model.
Similar content being viewed by others
References
Deutsch, D., Penrose, R.: Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A Math. Phys. Sci. 400(1818), 97–117 (1985)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)
Grover, L.K.: A fast quantum mechanical algorithm for database search. Preprint arXiv:quant-ph/9605043 (1996)
Bernstein, D.J., Buchmann, J., Dahmen, E.: Post-quantum Cryptography, 1st edn. Springer, Berlin (2009)
Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474–1483 (1997)
Williams, C.P.: Explorations in Quantum Computing, 2nd edn. Springer, Berlin (2011)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge (2010)
Boixo, S., Isakov, S.V., Smelyanskiy, V.N., Babbush, R., Ding, N., Jiang, Z., Bremner, M.J., Martinis, J.M., Neven, H.: Characterizing quantum supremacy in near-term devices. Nat. Phys. 14(6), 595 (2018)
The D-Wave 2000Q Quantum Computer Technology Overview. https://www.dwavesys.com/sites/default/files/D-Wave%202000Q%20Tech%20Collateral_0117F.pdf. Last Accessed: March 2020
IBMQ: IBM Q Experience. https://quantumexperience.ng.bluemix.net/qx/devices. Last Accessed: March 2020
Google: Google AI Blog. https://ai.googleblog.com/2018/03/a-preview-of-bristlecone-googles-new.html. Last Accessed: March 2020
Rigetti: Rigetti Computing. https://rigetti.com/. Last Accessed: March 2020
Wang, B.: IonQ has the most powerful quantum computers with 79 trapped ion qubits and 160 stored qubits. https://www.nextbigfuture.com/2018/12/ionq-has-the-most-powerful-quantum-computers-with-79-trapped-ion-qubits-and-160-stored-qubits.html. Last Accessed: March 2020
Preskill, J.: Quantum computing in the nisq era and beyond. Quantum 2, 79 (2018)
Zalka, C.: Using Grover’s quantum algorithm for searching actual databases. Phys. Rev. A 62(5), 052305 (2000)
Bernstein, D.J.: Grover vs. McEliece. In: International Workshop on Post-quantum Cryptography, pp. 73–80. Springer, Berlin (2010)
Cheng, S.-T., Tao, M.-H.: Quantum cooperative search algorithm for 3-sat. J. Comput. Syst. Sci. 73(1), 123–136 (2007)
Bang, J., Ryu, J., Lee, C., Yoo, S., Lim, J., Lee, J.: A quantum heuristic algorithm for the traveling salesman problem. J. Korean Phys. Soc. 61(12), 1944–1949 (2012)
Brassard, G., Høyer, P., Tapp, A.: Quantum cryptanalysis of hash and claw-free functions. ACM Sigact News 28(2), 14–19 (1997)
Viamontes, G.F., Markov, I.L., Hayes, J.P.: Is quantum search practical? Comput. Sci. Eng. 7(3), 62–70 (2005)
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, New York (2018)
Brickman, K.-A., Haljan, P.C., Lee, P.J., Acton, M., Deslauriers, L., Monroe, C.: Implementation of Grover’s quantum search algorithm in a scalable system. Phys. Rev. A 72(5), 050306 (2005)
Das, R., Mahesh, T.S., Kumar, A.: Experimental implementation of Grover’s search algorithm using efficient quantum state tomography. Chem. Phys. Lett. 369(1–2), 8–15 (2003)
Zhou, R., Ding, Q.: Quantum pattern recognition with probability of 100%. Int. J. Theor. Phys. 47(5), 1278–1285 (2008)
DirectStream: DirectStream. https://directstream.com. Last Accessed: March 2020
Harbaum, T., Seboui, M., Balzer, M., Becker, J., Weber, M.: A content adapted FPGA memory architecture with pattern recognition capability for L1 track triggering in the LHC environment. In: 2016 IEEE 24th Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM), pp. 184–191. IEEE, New York (2016)
Zwiebac, B.: Dirac’s Bra and Ket notation, October 2013. https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_04.pdf. Last Accessed: March 2020
Jozsa, R., Linden, N.: On the role of entanglement in quantum-computational speed-up. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 459(2036), 2011–2032 (2003)
Yanofsky, N.S., Mannucci, M.A.: Quantum Computing for Computer Scientists. Cambridge University Press, Cambridge (2008)
Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. Fortsch. Phys. Prog. Phys. 46(4–5), 493–505 (1998)
Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52(4), R2493 (1995)
Hsu, J.: How much power will quantum computing need? October 2015. https://spectrum.ieee.org/tech-talk/computing/hardware/how-much-power-will-quantum-computing-need. Last Accessed: March 2020
Quantiki: Quantiki (2019). https://quantiki.org/wiki/list-qc-simulators. Last Accessed: March 2020
Avila, A., Reiser, R.H.S., Yamin, A.C., Pilla, M.L.: Parallel simulation of Shor’s and Grover’s algorithms in the distributed geometric machine. In: 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), pp. 412–419. IEEE, New York (2017)
Gutiérrez, E., Romero, S., Trenas, M.A., Zapata, E.L.: Quantum computer simulation using the cuda programming model. Comput. Phys. Commun. 181(2), 283–300 (2010)
Chen, J., Zhang, F., Huang, C., Newman, M., Shi, Y.: Classical simulation of intermediate-size quantum circuits. Preprint arXiv:1805.01450 (2018)
Villalonga, B., Lyakh, D., Boixo, S., Neven, H., Humble, T.S., Biswas, R., Rieffel, E.G., Ho, A., Mandrà, S.: Establishing the quantum supremacy frontier with a 281 pflop/s simulation. Preprint arXiv:1905.00444 (2019)
De Raedt, H., Jin, F., Willsch, D., Willsch, M., Yoshioka, N., Ito, N., Yuan, S., Michielsen, K.: Massively parallel quantum computer simulator, eleven years later. Comput. Phys. Commun. 237, 47–61 (2019)
Pednault, E., Gunnels, J.A., Nannicini, G., Horesh, L., Magerlein, T., Solomonik, E., Draeger, E.W., Holland, E.T., Wisnieff, R.: Breaking the 49-qubit barrier in the simulation of quantum circuits. Preprint arXiv:1710.05867 (2017)
Lee, Y.H., Khalil-Hani, M., Marsono, M.N.: An FPGA-based quantum computing emulation framework based on serial-parallel architecture. Int. J. Reconfig. Comput. 2016, 18 (2016)
Suchara, M., Alexeev, Y., Chong, F., Finkel, H., Hoffmann, H., Larson, J., Osborn, J., Smith, G.: Hybrid quantum-classical computing architectures. In: Proceedings of the 3rd International Workshop on Post-Moore Era Supercomputing, 2018 (2018)
Pilch, J., Długopolski, J.: An FPGA-based real quantum computer emulator. J. Comput. Electron. 18(1), 329–342 (2019)
Frank, M.P., Oniciuc, L., Meyer-Baese, U.H., Chiorescu, I.: A space-efficient quantum computer simulator suitable for high-speed FPGA implementation. In: Quantum Information and Computation VII, Volume 7342, pp. 734203. International Society for Optics and Photonics (2009)
Khalid, A.U., Zilic, Z., Radecka, K.: FPGA emulation of quantum circuits. In: IEEE International Conference on Computer Design: VLSI in Computers and Processors, 2004. ICCD 2004. Proceedings, pp. 310–315. IEEE, New York (2004)
Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. Preprint arXiv:1411.4028 (2014)
El-Araby, E., Merchant, S.G., El-Ghazawi, T.: Assessing productivity of high-level design methodologies for high-performance reconfigurable computers. In: High-Performance Computing using FPGAs, pp. 719–745. Springer, Berlin (2013)
Mahmud, N., El-Araby, E.: Towards higher scalability of quantum hardware emulation using efficient resource scheduling. In: 2018 IEEE International Conference on Rebooting Computing (ICRC), pp. 1–10. IEEE, New York (2018)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mahmud, N., Haase-Divine, B., MacGillivray, A. et al. Modifying quantum Grover’s algorithm for dynamic multi-pattern search on reconfigurable hardware. J Comput Electron 19, 1215–1231 (2020). https://doi.org/10.1007/s10825-020-01489-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10825-020-01489-3