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A brief introduction to quantum algorithms

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Abstract

Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum algorithms for both the academic community and the general public with interest. We start from elucidating quantum parallelism, the basic framework of quantum algorithms and the difficulty of quantum algorithm design. Then we mainly focus on a historical overview of progress in quantum algorithm research over the past three to four decades. Finally, we clarify two common questions about the study of quantum algorithms, hoping to stimulate readers for further exploration.

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References

  • Aaronson, S.: Quantum computing since Democritus. Cambridge University Press, Cambridge (2013)

    MATH  Google Scholar 

  • Abhijith, J., Adetokunbo, A., Ambrosiano, J., Anisimov, P., Bärtschi, A., Casper, W., Chennupati, G., Coffrin, C., Djidjev, H., Gunter, D., Karra, S., Lemons, N., Lin, S., Malyzhenkov, A., Mascarenas, D., Mniszewski, S., Nadiga, B., O'Malley, D., Oyen, D., Pakin, S., Prasad, L., Roberts, R., Romero, P., Santhi, N., Sinitsyn, N., Swart, P. J., Wendelberger, J. G., Yoon, B., Zamora, R., Zhu, W., Eidenbenz, S., Coles, P. J., Vuffray, M., Lokhov, A. Y.: Quantum algorithm implementations for beginners. arXiv: 1804.03719 (2020) https://arxiv.org/abs/1804.03719

  • Allcock, J., Zhang, S.: Quantum machine learning. Nat. Sci. Rev. 6(1), 26–28 (2019)

    Google Scholar 

  • Ambainis, A.: Quantum walks and their algorithmic applications. Int. J. Quantum Inf. 1(04), 507–518 (2003)

    MATH  Google Scholar 

  • Ambainis, A.: Quantum walk algorithm for element distinctness. SIAM J. Comput. 37(1), 210–239 (2007)

    MathSciNet  MATH  Google Scholar 

  • Arrazola, J.M., Delgado, A., Bardhan, B.R., Lloyd, S.: Quantum-inspired algorithms in practice. Quantum 4, 307 (2020)

    Google Scholar 

  • Arunachalam, S., de Wolf, R.: Guest column: a survey of quantum learning theory. ACM SIGACT News 48, 41 (2017)

    MathSciNet  Google Scholar 

  • Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)

    Google Scholar 

  • Bacon, D., van Dam, W.: Recent progress in quantum algorithms. Commun. ACM 53(2), 84–93 (2010)

    Google Scholar 

  • Ban, Y., Chen, X., Torrontegui, E., Solano, E., Casanova, J.: Speeding up quantum perceptron via shortcuts to adiabaticity. Sci. Rep. 11(1), 5783 (2021)

    Google Scholar 

  • Bang, J., Ryu, J., Yoo, S., Pawłowski, M., Lee, J.: A strategy for quantum algorithm design assisted by machine learning. New J. Phys. 16(7), 073017 (2014)

    MATH  Google Scholar 

  • Bauer, B., Bravyi, S., Motta, M., Chan, G.K.-L.: Quantum algorithms for quantum chemistry and quantum materials science. Chem. Rev. 120(22), 12685–12717 (2020)

    Google Scholar 

  • Bell, J.S.: Physics Physique Fizika 1(3), 195–200 (1964)

    MathSciNet  Google Scholar 

  • Benedetti, M., Lloyd, E., Sack, S., Fiorentini, M.: Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4(4), 43001 (2019)

    Google Scholar 

  • Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549(7671), 195–202 (2017)

    Google Scholar 

  • Boneh, D., Lipton, R. J.: Quantum cryptanalysis of hidden linear functions. In: Advances in cryptology—CRYPTO’95, Springer, Berlin, pp. 424–437 (1995)

  • Bravyi, S., Gosset, D.: Improved classical simulation of quantum circuits dominated by Clifford gates. Phys. Rev. Lett. 116(25), 250501 (2016)

    Google Scholar 

  • Bravyi, S., Gosset, D., König, R.: Quantum advantage with shallow circuits. Science 362(6412), 308–311 (2018)

    MathSciNet  MATH  Google Scholar 

  • Chen, Z.-Y., Zhou, Q., Xue, C., Yang, X., Guo, G.-C., Guo, G.-P.: 64-qubit quantum circuit simulation. Science Bulletin 63(15), 964–971 (2018)

    Google Scholar 

  • Chia, N.-H., Gilyén, A., Li, T., Lin, H.-H., Tang, E., Wang, C.: Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning. In: Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, pp. 387–400 (2020)

  • Childs, A.M., van Dam, W.: Quantum algorithms for algebraic problems. Rev. Mod. Phys. 82(1), 1 (2010)

    MathSciNet  MATH  Google Scholar 

  • Childs, A. M., Cleve, R., Deotto, E., Farhi, E., Gutmann, S., Spielman, D. A.: Exponential algorithmic speedup by a quantum walk. In: Proceedings of the thirty-fifth Annual ACM Symposium on Theory of Computing, pp. 59–68 (2003)

  • Chuang, I.L., Yamamoto, Y.: Simple Quantum Computer. Phys. Rev. A 52(5), 3489 (1995)

    Google Scholar 

  • Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23(15), 880 (1969)

    MATH  Google Scholar 

  • Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proceedings of the Royal Society of London. Ser Math Phys Eng Sci 454(19), 339–354 (1998)

    MATH  Google Scholar 

  • Cong, I., Duan, L.: Quantum discriminant analysis for dimensionality reduction and classification. New J. Phys. 18(7), 73011 (2016)

    MATH  Google Scholar 

  • Dallaire-Demers, P.-L., Killoran, N.: Quantum generative adversarial networks. Phys. Rev. A 98(1), 012324 (2018)

    Google Scholar 

  • Deng, W., Liu, H., Xu, J., Zhao, H., Song, Y.: An improved quantum-inspired differential evolution algorithm for deep belief network. IEEE Trans. Instrum. Meas. 69(10), 7319–7327 (2020)

    Google Scholar 

  • Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. A Math. Phys. Sci. 400(18), 97–117 (1985)

    MATH  Google Scholar 

  • Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum.Proceeding computation of the Royal Society of London. Ser. A Math. Phys. Sci. 439(19), 553–558 (1992)

    MATH  Google Scholar 

  • Diao, Z.: Exactness of the original Grover search algorithm. Phys. Rev. A 82(4), 44301 (2010)

    Google Scholar 

  • Ding, C., Bao, T.-Y., Huang, H.-L.: Quantum-inspired support vector machine. IEEE Trans Neural Netw Learn Syst (2021). https://doi.org/10.1109/TNNLS.2021.3084467

    Article  Google Scholar 

  • Du, Y., Hsieh, M.H., Liu, T., et al.: Quantum-inspired algorithm for general minimum conical hull problems. Phys. Rev. Res. 2(3), 33199 (2020)

    Google Scholar 

  • Duan, B., Yuan, J., Liu, Y., Li, D.: Quantum algorithm for support matrix machines. Phys. Rev. A 96(3), 32301 (2017)

    Google Scholar 

  • Duan, B., Yuan, J., Xu, J., Li, D.: Quantum algorithm and quantum circuit for A-optimal projection: dimensionality reduction. Phys. Rev. A 99(3), 32311 (2019)

    Google Scholar 

  • Dunjko, V., Briegel, H.J.: Machine learning and artificial intelligence in the quantum domain: a review of recent progress. Rep. Prog. Phys. 81(7), 74001 (2018)

    MathSciNet  Google Scholar 

  • Endo, S., Cai, Z., Benjamin, S.C., Yuan, X.: Hybrid quantum-classical algorithms and quantum error mitigation. J. Phys. Soc. Jpn 90(3), 32001 (2021)

    Google Scholar 

  • Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv: 1411.4028 (2014) https://arxiv.org/abs/1411.4028

  • Figgatt, C., Maslov, D., Landsman, K., Linke, N.M., Debnath, S., Monroe, C.: Complete 3-qubit Grover search on a programmable quantum computer. Nat. Commun. 8(1), 1–9 (2017)

    Google Scholar 

  • Galindo, A., Martin-Delgado, M.A.: Information and computation: classical and quantum aspects. Rev. Mod. Phys. 74(2), 347 (2002)

    MathSciNet  MATH  Google Scholar 

  • Grover, L. K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the twenty-eighth Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)

  • Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)

    Google Scholar 

  • Gruska, J.: Quantum computing. McGraw-Hill, London (1999)

    MATH  Google Scholar 

  • Guo, C., Liu, Y., Xiong, M., Xue, S., Fu, X., Huang, A., Qiang, X., Xu, P., Liu, J., Zheng, S., Huang, H.-L., Deng, M., Poletti, D., Bao, W.-S., Wu, J.: General-purpose quantum circuit simulator with projected entangled-pair states and the quantum supremacy frontier. Phys. Rev. Lett. 123(19), 190501 (2019)

    Google Scholar 

  • Gyongyosi, L., Imre, S.: A survey on quantum computing technology. Comput. Sci. Rev. 31, 51–71 (2019)

    MathSciNet  Google Scholar 

  • Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103(15), 150502 (2009)

    MathSciNet  Google Scholar 

  • Hu, L., Wu, S.-H., Cai, W., Ma, Y., Mu, X., Xu, Y., Wang, H., Song, Y., Deng, D.-L., Zou, C.-L., Sun, L.: Quantum generative adversarial learning in a superconducting quantum circuit. Sci. Adv. 5(1), 2761 (2019)

    Google Scholar 

  • Huggins, W.J., McClean, J.R., Rubin, N.C., Jiang, Z., Wiebe, N., Whaley, K.B., Babbush, R.: Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers. NPJ Quant. Inf. 7, 23 (2021)

    Google Scholar 

  • Jethwani, D., Gall, F. L., Singh, S. K.: Quantum-inspired classical algorithms for singular value transformation. In: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020), Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2020)

  • Jones, T., Endo, S., McArdle, S., Yuan, X., Benjamin, S.C.: Variational quantum algorithms for discovering Hamiltonian spectra. Phys. Rev. A 99(6), 62304 (2019)

    Google Scholar 

  • Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017)

    Google Scholar 

  • Kaplan, M., Leurent, G., Leverrier, A., Naya-Plasencia, M.: Breaking symmetric cryptosystems using quantum period finding. In: Advances in Cryptology CRYPTO 2016. Berlin: Springer, pp. 207–237 (2016)

  • Kapoor, A., Wiebe, N.: Svore KM (2016) Quantum perceptron models. Adv. Neural Inf. Process. Syst. (NIPS 2016) 29, 3999–4007 (2016)

    Google Scholar 

  • Kerenidis, I., Prakash, A.: Quantum recommendation systems. In: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017), Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik (2017)

  • Kobori, A., Takahashi, R., Nakanishi, M.: A hardware architecture for the Walsh-Hadamard transform toward fast simulation of quantum algorithms. CCF Trans. High Perform. Comput. 2(3), 211–220 (2020)

    Google Scholar 

  • Li, Y., Benjamin, S.C.: Efficient variational quantum simulator incorporating active error minimization. Phys. Rev. X 7(2), 21050 (2017)

    Google Scholar 

  • Li, Y., Zhou, R.-G., Xu, R., Luo, J., Hu, W.: A quantum deep convolutional neural network for image recognition. Quantum Sci. Technol. 5(4), 44003 (2020)

    Google Scholar 

  • Liang, J.-M., Shen, S.-Q., Li, M., Li, L.: Variational quantum algorithms for dimensionality reduction and classification. Phys. Rev. A 101(3), 032323 (2020)

    MathSciNet  Google Scholar 

  • Lin, J., Lai, Z.Y., Li, X.: Quantum adiabatic algorithm design using reinforcement learning. Phys. Rev. A 101(5), 052327 (2020)

    Google Scholar 

  • Linke, N.M., Maslov, D., Roetteler, M., Debnath, S., Figgatt, C., Landsman, K.A., Wright, K., Monroe, C.: Experimental comparison of two quantum computing architectures. Proc. Natl. Acad. Sci. 114(13), 3305–3310 (2017)

    Google Scholar 

  • Liu, Y., Zhang, S.: Fast quantum algorithms for least squares regression and statistic leverage scores. Theoret. Comput. Sci. 657, 38–47 (2017)

    MathSciNet  MATH  Google Scholar 

  • Lloyd, S., Weedbrook, C.: Quantum generative adversarial learning. Phys. Rev. Lett. 121(4), 040502 (2018)

    MathSciNet  Google Scholar 

  • Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10(9), 631–633 (2014)

    Google Scholar 

  • McArdle, S., Yuan, X., Benjamin, S.: Error-mitigated digital quantum simulation. Phys. Rev. Lett. 122(18), 180501 (2019)

    Google Scholar 

  • McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of variational hybrid quantum-classical algorithms. New J. Phys. 18(2), 23023 (2016)

    MATH  Google Scholar 

  • Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Phys. Rev. A 98(3), 32309 (2018)

    Google Scholar 

  • Moll, N., Barkoutsos, P., Bishop, L.S., Chow, J.M., Cross, A., Egger, D.J., Filipp, S., Fuhrer, A., Gambetta, J.M., Ganzhorn, M.: Quantum optimization using variational algorithms on near-term quantum devices. Quantum Sci. Technol. 3(3), 030503 (2018)

    Google Scholar 

  • Montanaro, A.: Quantum algorithms: an overview. NPJ Quantum Inf. 2, 15023 (2016)

    Google Scholar 

  • Mosca, M.: Quantum algorithms. arXiv:0808.0369 (2008) https://arxiv.org/abs/0808.0369

  • Nielsen, M. A., Chuang, I. L.: Quantum Computation and Quantum Information (10th Anniversary Edition). Cambridge University Press, Cambridge, (2010) https://doi.org/10.1017/CBO9780511976667

  • Okamoto, T., Tanaka, K., Uchiyama, S.: Quantum public-key cryptosystems. In: Advances in Cryptology-CRYPTO 2000, Springer, Berlin, pp. 147–165 (2000)

  • Otten, M., Gray, S.K.: Accounting for errors in quantum algorithms via individual error reduction. NPJ Quantum Inf. 5, 11 (2019)

    Google Scholar 

  • Pan, S.J., Wan, L.C., Liu, H.L., Wang, Q.L., Qin, S.J., Wen, Q.Y., Gao, F.: Improved quantum algorithm for A-optimal projection. Phys. Rev. A 102(5), 52402 (2020)

    MathSciNet  Google Scholar 

  • Paredes, B., Verstraete, F., Cirac, J.I.: Exploiting quantum parallelism to simulate quantum random many-body systems. Phys. Rev. Lett. 95(14), 140501 (2005)

    Google Scholar 

  • Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.H., Zhou, X.Q., Love, P.J., Aspuru-Guzik, A., Obrien, J.L.: A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5(1), 1–7 (2014)

    Google Scholar 

  • Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018)

    Google Scholar 

  • Qiang, X., Wang, Y., Xue, S., Ge, R., Chen, L., Liu, Y., Huang, A., Fu, X., Xu, P., Yi, T., Xu, F., Deng, M., Wang, J.B., Meinecke, J.D.A., Matthews, J.C.F., Cai, X., Yang, X., Wu, J.: Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor. Sci. Adv. 7(9), eabb8375 (2021)

    Google Scholar 

  • Rebentrost, P., Mohseni, M., Lloyd, S.: Quantum support vector machine for big data classification. Phys. Rev. Lett. 113(13), 130503 (2014)

    Google Scholar 

  • Schreiber, A., Cassemiro, K.N., Potoček, V., Gábris, A., Mosley, P.J., Andersson, E., Jex, I., Silberhorn, C.: Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104(5), 050502 (2010)

    Google Scholar 

  • Schuld, M., Sinayskiy, I., Petruccione, F.: An introduction to quantum machine learning. Contemp. Phys. 56(2), 172–185 (2015)

    MATH  Google Scholar 

  • Schuld, M., Sweke, R., Meyer, J.J.: Effect of data encoding on the expressive power of variational quantum-machine-learning models. Phys. Rev. A 103(3), 32430 (2021)

    MathSciNet  Google Scholar 

  • Shao, C.: Fast variational quantum algorithms for training neural networks and solving convex optimizations. Phys. Rev. A 99(4), 42325 (2019)

    MathSciNet  Google Scholar 

  • Shao, C., Li, Y., Li, H.: Quantum algorithm design: techniques and applications. J. Syst. Sci. Complexity 32(1), 375–452 (2019)

    MathSciNet  MATH  Google Scholar 

  • Shen, H., Zhang, P., You, Y.-Z., Zhai, H.: Information scrambling in quantum neural networks. Phys. Rev. Lett. 124(20), 200504 (2020)

    Google Scholar 

  • Shor, P. W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, IEEE, pp.124–134 (1994)

  • Shor, P.W.: Why haven’t more quantum algorithms been found? J. ACM (JACM) 50(1), 87–90 (2003)

    MathSciNet  MATH  Google Scholar 

  • Shor, P.W.: Progress in quantum algorithms. Quantum Inf. Process. 3(1), 5–13 (2004)

    MathSciNet  MATH  Google Scholar 

  • Simon, D.: On the power of quantum computation. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, IEEE Computer Society, pp. 116–123 (1994)

  • Situ, H., He, Z., Wang, Y., Li, L., Zheng, S.: Quantum generative adversarial network for generating discrete distribution. Information Sciences 538, 193–208 (2020). Also see arXiv:1807.01235(2018)

  • Svore, K.M., Troyer, M.: The quantum future of computation. Computer 49(9), 21–30 (2016)

    Google Scholar 

  • Tang, E.: A quantum-inspired classical algorithm for recommendation systems. In: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pp. 217–228 (2019)

  • Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc. 2(1), 230–265 (1937)

    MathSciNet  MATH  Google Scholar 

  • Walther, P., Resch, K.J., Rudolph, T., Schenck, E., Weinfurter, H., Vedral, V., Aspelmeyer, M., Zeilinger, A.: Experimental one-way quantum computing. Nature 434(73), 169–176 (2005)

    Google Scholar 

  • Wan, L.C., Yu, C.H., Pan, S.J., Gao, F., Wen, Q.Y.: Asymptotic quantum algorithm for the Toeplitz systems. Phys. Rev. A 97(6), 62322 (2018)

    Google Scholar 

  • Wang, G.: Quantum algorithm for linear regression. Phys. Rev. A 96(1), 12335 (2017)

    MathSciNet  Google Scholar 

  • Wang, X., Song, Z., Wang, Y.: Variational quantum singular value decomposition. Quantum 5, 483 (2021)

    Google Scholar 

  • Watts, A. B., Kothari, R., Schaeffer, L., Tal, A.: Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits. In: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pp. 515–526 (2019)

  • Wiebe, N., Braun, D., Lloyd, S.: Quantum algorithm for data fitting. Phys. Rev. Lett. 109(5), 050505 (2012)

    Google Scholar 

  • Wiebe, N., Kapoor, A., Svore, K.M.: Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning. Quantum Inf. Comput. 15(34), 316–356 (2015)

    MathSciNet  Google Scholar 

  • Wiebe, N., Kapoor, A., Svore, K.M.: Quantum deep learning. Quantum Inf. Comput. 16(7–8), 541–587 (2016)

    MathSciNet  Google Scholar 

  • Williams, C.P.: Explorations in quantum computing. Springer, Berlin (2011)

    MATH  Google Scholar 

  • Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299(5886), 802–803 (1982)

    MATH  Google Scholar 

  • Xu, X., Sun, J., Endo, S., Li, Y., Benjamin, S.C., Yuan, X.: Variational algorithms for linear algebra. Sci. Bull. 66(21), 2181–2188 (2021)

    Google Scholar 

  • Yang, Z., Zhang, X.: Entanglement-based quantum deep learning. New J. Phys. 22(3), 033041 (2020)

    MathSciNet  Google Scholar 

  • Ye, Z., Li, L., Situ, H.W.Y.: Quantum speedup of twin support vector machines. Sci. China Inf. Sci. 63(8), 189501 (2020)

    MathSciNet  Google Scholar 

  • Yu, C.H., Gao, F., Wang, Q.L., Wen, Q.Y.: Quantum algorithm for association rules mining. Phys. Rev. A 94(4), 042311 (2016)

    Google Scholar 

  • Yu, C.H., Gao, F., Liu, C., Huynh, D., Reynolds, M., Wang, J.: Quantum algorithm for visual tracking. Phys. Rev. A 99(2), 022301 (2019)

    Google Scholar 

  • Yu, C.H., Gao, F., Wen, Q.: An improved quantum algorithm for ridge regression. IEEE Trans. Knowl. Data Eng. 33(3), 858–866 (2021). https://doi.org/10.1109/TKDE.2019.2937491

    Article  Google Scholar 

  • Zeng, J., Wu, Y., Liu, J.-G., Wang, L., Hu, J.: Learning and inference on generative adversarial quantum circuits. Phys. Rev. A 99(5), 052306 (2019)

    Google Scholar 

  • Zhang, S., Zhang, Y., Sun, Y., Sun, H., Zhang, X.: Quantum-inspired microwave signal processing for implementing unitary transforms. Opt. Express 27(2), 436–460 (2019)

    Google Scholar 

  • 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., Hu, P., Yang, X.-Y., Zhang, W.-J., Li, H., Li, Y., Jiang, X., Gan, L., Yang, G., You, L., Wang, Z., Li, L., Liu, N.-L., Lu, C.-Y., Pan, J.-W.: Quantum computational advantage using photons. Science 370(6523), 1460–1463 (2020)

    Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62102464, 61772565), and the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020B1515020050), the Key Research and Development project of Guangdong Province (Grant No. 2018B030325001) and the China Postdoctoral Science Foundation (Grant Nos. 2020M683049, 2021T140761). The authors thank Dr. Li Zhang from South China Normal University for help discussions and suggestions on this work.

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62102464, 61772565), and the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020B1515020050), the Key Research and Development project of Guangdong Province (Grant No. 2018B030325001) and the China Postdoctoral Science Foundation (Grant Nos. 2020M683049, 2021T140761).

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  1. Institute of Quantum Computing and Computer Theory, School of Computer Science and Engineering, Sun Yat-Sen University, Guangzhou, 510006, China

    Shihao Zhang & Lvzhou Li

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  1. Shihao Zhang
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All authors contributed to this review article. L. L. had the idea for the article and proposed the framework, S. Z. performed the literature search and drafted the work. Both authors revised the article.

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Zhang, S., Li, L. A brief introduction to quantum algorithms. CCF Trans. HPC 4, 53–62 (2022). https://doi.org/10.1007/s42514-022-00090-3

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