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Published in: Quantum Information Processing 2/2021

01-02-2021

Models in quantum computing: a systematic review

Authors: Peter Nimbe, Benjamin Asubam Weyori, Adebayo Felix Adekoya

Published in: Quantum Information Processing | Issue 2/2021

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Abstract

Quantum computing is computing beyond classical computing based on quantum phenomena such as superposition and entanglement. While quantum computing is still seeking its shape, its effect is seen in making magnificent strides in the field of computing bringing into bare a new dimension of computing. Nevertheless, just like any other concept or field, it has some challenges, and a lot of research and work need to be done to realize its capabilities and benefits. This review provides an insight into quantum computing models coupled with the identification of some pros and cons. The main contribution of this systematic review is that it summarizes the current state-of-the-art models of quantum computing in various domains. It provides new classifications of quantum models based on the literature reviewed and links results to that of the four major categories of quantum computing models. Assessment reveals that most of the models reviewed are either mathematical or algorithmic even though they are based on quantum operations and circuits.

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Appendix
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Literature
1.
go back to reference Gamble, S.: Quantum Computing: What It Is, Why We Want It, and How We’re Trying to Get It. Frontiers of Engineering: Reports on Leading-Edge Engineering from the 2018 Symposium. National Academies Press (US), Washington, DC (2019) Gamble, S.: Quantum Computing: What It Is, Why We Want It, and How We’re Trying to Get It. Frontiers of Engineering: Reports on Leading-Edge Engineering from the 2018 Symposium. National Academies Press (US), Washington, DC (2019)
2.
go back to reference Coles, P.J., Eidenbenz, S., Pakin, S., Adedoyin, A., Ambrosiano, J., Anisimov, P., Casper, W., Chennupati, G., Coffrin, C., Djidjev, H., Gunter, D., Karra, S., Lemons, N., Lin, S., Lokhov, A., Malyzhenkov, A., Mascarenas, D., Mniszewski, S., Nadiga, B., O’Malley, D., Oyen, D., Prasad, L., Roberts, R., Romero, P., Santhi, N., Sinitsyn, N., Swart, P., Vuffray, M., Wendelberger, J., Yoon, B., Zamora, R., Zhu, W.: Quantum Algorithm Implementations for Beginners. Los Alamos National Laboratory, Los Alamos (2018) Coles, P.J., Eidenbenz, S., Pakin, S., Adedoyin, A., Ambrosiano, J., Anisimov, P., Casper, W., Chennupati, G., Coffrin, C., Djidjev, H., Gunter, D., Karra, S., Lemons, N., Lin, S., Lokhov, A., Malyzhenkov, A., Mascarenas, D., Mniszewski, S., Nadiga, B., O’Malley, D., Oyen, D., Prasad, L., Roberts, R., Romero, P., Santhi, N., Sinitsyn, N., Swart, P., Vuffray, M., Wendelberger, J., Yoon, B., Zamora, R., Zhu, W.: Quantum Algorithm Implementations for Beginners. Los Alamos National Laboratory, Los Alamos (2018)
3.
go back to reference Riedel, M.F.: The European quantum technologies flagship. Quantum Sci. Technol. 2, 030501 (2017)ADSCrossRef Riedel, M.F.: The European quantum technologies flagship. Quantum Sci. Technol. 2, 030501 (2017)ADSCrossRef
6.
go back to reference Chen, G., Church, D.A., Englert B.G., Zubairy M.S.: Mathematical Models of Contemporary Elementary Quantum Computing Devices. Centre de Recherches Mathematiques. CRM Proceedings and Lecture Notes. volume 33 (2003) Chen, G., Church, D.A., Englert B.G., Zubairy M.S.: Mathematical Models of Contemporary Elementary Quantum Computing Devices. Centre de Recherches Mathematiques. CRM Proceedings and Lecture Notes. volume 33 (2003)
8.
go back to reference Mavroeidis, V., Vishi, K., Zych, M.D., Josang, A.: The impact of quantum computing on present crytography. Int. J. Adv. Comput. Sci. Appl. 9(3), 1–2 (2018)CrossRef Mavroeidis, V., Vishi, K., Zych, M.D., Josang, A.: The impact of quantum computing on present crytography. Int. J. Adv. Comput. Sci. Appl. 9(3), 1–2 (2018)CrossRef
9.
10.
go back to reference Claude C.S., Casti, J., Dinneen M.J.: Unconventional Models of Computation. Springer, Singapore, ISBN 981-3083-69-7 (1998) Claude C.S., Casti, J., Dinneen M.J.: Unconventional Models of Computation. Springer, Singapore, ISBN 981-3083-69-7 (1998)
11.
go back to reference Raychev, N.: Multi-functional formalized quantum circuits. Int. J. Sci. Eng. Res. 6(9), 1302–1309 (2015) Raychev, N.: Multi-functional formalized quantum circuits. Int. J. Sci. Eng. Res. 6(9), 1302–1309 (2015)
12.
go back to reference Raychev, N.: Formalized quantum model for solving the eigenfunctions. J. Quantum Inf. Sci. 6, 16–30 (2016)CrossRef Raychev, N.: Formalized quantum model for solving the eigenfunctions. J. Quantum Inf. Sci. 6, 16–30 (2016)CrossRef
17.
go back to reference Svore, K.M., Cross, A.W., Chuang, I.L., Aho, A.V.: A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing. Quantum Information and Computation. arXiv:quant-ph/0508176v2. 6(9) (2006) Svore, K.M., Cross, A.W., Chuang, I.L., Aho, A.V.: A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing. Quantum Information and Computation. arXiv:​quant-ph/​0508176v2. 6(9) (2006)
20.
go back to reference Gallego, M.B.: The bohm-penrose-hameroff model for consciousness and free will theoretical foundations and empirical evidences. Pensamiento 67(254), 661–674 (2011) Gallego, M.B.: The bohm-penrose-hameroff model for consciousness and free will theoretical foundations and empirical evidences. Pensamiento 67(254), 661–674 (2011)
21.
go back to reference Platel, M.D., Schliebs, S., Kasabov N.: Quantum-Inspired Evolutionary Algorithm: A Multimodel EDA. IEEE Transactions on Evolutionary Computation, vol 13, No. 6 (2009) Platel, M.D., Schliebs, S., Kasabov N.: Quantum-Inspired Evolutionary Algorithm: A Multimodel EDA. IEEE Transactions on Evolutionary Computation, vol 13, No. 6 (2009)
22.
go back to reference Hahanov, V., Hahanova, I., Guz, O., Abbas, M.A.: Quantum models for data structures and computing. In: Proceedings of International Conference on Modern Problem of Radio Engineering, Telecommunications and Computer Science, Lviv-Slavske, 2012, pp. 291–291 (2012). Hahanov, V., Hahanova, I., Guz, O., Abbas, M.A.: Quantum models for data structures and computing. In: Proceedings of International Conference on Modern Problem of Radio Engineering, Telecommunications and Computer Science, Lviv-Slavske, 2012, pp. 291–291 (2012).
23.
go back to reference Araujo de Resendea, M.F., Ibieta Jimeneza, J.P., Lorca Espiroa, J.: Cyclic Abelian Quantum Double Models coupled with matter: remarks about the presence of non-Abelian fusion rules, and algebraic and topological orders. arXiv:1808.09537v1 (2018) Araujo de Resendea, M.F., Ibieta Jimeneza, J.P., Lorca Espiroa, J.: Cyclic Abelian Quantum Double Models coupled with matter: remarks about the presence of non-Abelian fusion rules, and algebraic and topological orders. arXiv:​1808.​09537v1 (2018)
24.
go back to reference Andrist, R.S., Wootton, J.R., Katzgraber, H.G.: Error thresholds for Abelian quantum double models: Increasing the bit-flip stability of topological quantum memory. Phys. Rev. A 91, 042331 (2015)ADSCrossRef Andrist, R.S., Wootton, J.R., Katzgraber, H.G.: Error thresholds for Abelian quantum double models: Increasing the bit-flip stability of topological quantum memory. Phys. Rev. A 91, 042331 (2015)ADSCrossRef
25.
go back to reference Perus, M., Loo, C.K.: Biological and Quantum Computing for Human Vision: Holonomic Models and Applications. IGI Global Disseminator of Knowledge (2010) Perus, M., Loo, C.K.: Biological and Quantum Computing for Human Vision: Holonomic Models and Applications. IGI Global Disseminator of Knowledge (2010)
26.
27.
go back to reference Raychev, N.: Quantum computing models for algebraic applications. Int. J. Sci. Eng. Res. 6(8), 1281–1288 (2015) Raychev, N.: Quantum computing models for algebraic applications. Int. J. Sci. Eng. Res. 6(8), 1281–1288 (2015)
28.
go back to reference Wecker, D., Svore, K.M.: LIQUi|>: A Software Design Architecture and Domain-Specific Language for Quantum Computing. Microsoft Research. arXiv:1402.4467v1 [quant-ph] (2014) Wecker, D., Svore, K.M.: LIQUi|>: A Software Design Architecture and Domain-Specific Language for Quantum Computing. Microsoft Research. arXiv:​1402.​4467v1 [quant-ph] (2014)
29.
go back to reference Steiger, D.S., Haner, T., Troyer, M.: ProjectQ: An Open Source Software Framework for Quantum Computing. Quantum. arXiv:1612.08091v2 [quant-ph] (2018) Steiger, D.S., Haner, T., Troyer, M.: ProjectQ: An Open Source Software Framework for Quantum Computing. Quantum. arXiv:​1612.​08091v2 [quant-ph] (2018)
32.
go back to reference Marcello, B.: Quantum-classical generative models for machine learning. Doctoral thesis (Ph.D), UCL (University College London) (2019) Marcello, B.: Quantum-classical generative models for machine learning. Doctoral thesis (Ph.D), UCL (University College London) (2019)
33.
go back to reference Sels, D., Demle, E.: Quantum generative model for sampling many-body spectral functions. arXiv: 1910.14213v1 [quant-ph] (2019) Sels, D., Demle, E.: Quantum generative model for sampling many-body spectral functions. arXiv: 1910.14213v1 [quant-ph] (2019)
34.
go back to reference Sadowski, P.: Machine Learning Kernel Method from a Quantum Generative Model. arXiv: 1907.05103v1 [quant-ph]. (2019) Sadowski, P.: Machine Learning Kernel Method from a Quantum Generative Model. arXiv: 1907.05103v1 [quant-ph]. (2019)
38.
go back to reference Aaronson, S., Arkhipov, A.: The computational complexity of linear optics. In: Proceedings of the forty-third annual ACM symposium on Theory of computing, ACM, 2011, 333–42 (2011) Aaronson, S., Arkhipov, A.: The computational complexity of linear optics. In: Proceedings of the forty-third annual ACM symposium on Theory of computing, ACM, 2011, 333–42 (2011)
54.
go back to reference Glover, F., Kochenberger, G., Du, Y.: Quantum Bridge Analytics I: A Tutorial on Formulating and Using QUBO Models. (2018). arXiv:1811.11538 Glover, F., Kochenberger, G., Du, Y.: Quantum Bridge Analytics I: A Tutorial on Formulating and Using QUBO Models. (2018). arXiv:​1811.​11538
62.
go back to reference Yang, G., Ping, J., Segovia, J.: Double-heavy tetraquarks. Phys. Rev. D 101, 014001 (2020)ADSCrossRef Yang, G., Ping, J., Segovia, J.: Double-heavy tetraquarks. Phys. Rev. D 101, 014001 (2020)ADSCrossRef
65.
go back to reference Yang, G., Ping, J., Ortega, P.G., Segovia, J.: Triply heavy baryons in the constituent quark model. Chinese Physics C (2020) Vol. 44, No. 2 Yang, G., Ping, J., Ortega, P.G., Segovia, J.: Triply heavy baryons in the constituent quark model. Chinese Physics C (2020) Vol. 44, No. 2
68.
go back to reference Nielsen, M.A., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH Nielsen, M.A., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH
80.
go back to reference Lipton, R.J., Regan, K.W.: Grover's algorithm. In: Quantum Algorithms via Linear Algebra: A Primer, MITP, pp. 115–128 (2014) Lipton, R.J., Regan, K.W.: Grover's algorithm. In: Quantum Algorithms via Linear Algebra: A Primer, MITP, pp. 115–128 (2014)
84.
go back to reference Lipton, R.J., Regan, K.W.: Simon's algorithm. In: Quantum Algorithms via Linear Algebra: A Primer, MITP, pp. 93–96 (2014) Lipton, R.J., Regan, K.W.: Simon's algorithm. In: Quantum Algorithms via Linear Algebra: A Primer, MITP, pp. 93–96 (2014)
86.
87.
go back to reference Lipton, R.J., Regan, K.W.: Shor's algorithm. In: Quantum Algorithms via Linear Algebra: A Primer, MITP, pp. 97–108 (2014) Lipton, R.J., Regan, K.W.: Shor's algorithm. In: Quantum Algorithms via Linear Algebra: A Primer, MITP, pp. 97–108 (2014)
92.
go back to reference Clifford, P., Clifford, R.: The classical complexity of boson sampling, SODA '18: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 146–155 (2018) Clifford, P., Clifford, R.: The classical complexity of boson sampling, SODA '18: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 146–155 (2018)
103.
go back to reference Magniez, F., Nayak, A.: Quantum complexity of testing group commutativity. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) Automata, Languages and Programming, ICALP 2005. Lecture Notes in Computer Science, vol. 3580. Springer, Berlin (2005) Magniez, F., Nayak, A.: Quantum complexity of testing group commutativity. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) Automata, Languages and Programming, ICALP 2005. Lecture Notes in Computer Science, vol. 3580. Springer, Berlin (2005)
107.
go back to reference Marathe, K.: Knot and link invariants. In: Topics in Physical Mathematics. Springer, London (2010) Marathe, K.: Knot and link invariants. In: Topics in Physical Mathematics. Springer, London (2010)
109.
go back to reference Sansoni, L.: Introduction to quantum simulation. In: Integrated Devices for Quantum Information with Polarization Encoded Qubits. Springer Theses (Recognizing Outstanding Ph.D. Research). Springer, Cham (2014) Sansoni, L.: Introduction to quantum simulation. In: Integrated Devices for Quantum Information with Polarization Encoded Qubits. Springer Theses (Recognizing Outstanding Ph.D. Research). Springer, Cham (2014)
113.
go back to reference Choi, J., Kim, J.: A tutorial on quantum approximate optimization algorithm (QAOA): fundamentals and applications. In: 2019 International Conference on Information and Communication Technology Convergence (ICTC), Jeju Island, Korea (South), pp. 138–142 (2019) Choi, J., Kim, J.: A tutorial on quantum approximate optimization algorithm (QAOA): fundamentals and applications. In: 2019 International Conference on Information and Communication Technology Convergence (ICTC), Jeju Island, Korea (South), pp. 138–142 (2019)
123.
go back to reference Boixo, S., Smelyanskiy, V.N., Shabani, A., Isakov, S.V., Dykman, M., Denchev, V.S., Neven, H.: Computational multiqubit tunnelling in programmable quantum annealers. Nat. Commun. 7, 10327 (2016)ADSCrossRef Boixo, S., Smelyanskiy, V.N., Shabani, A., Isakov, S.V., Dykman, M., Denchev, V.S., Neven, H.: Computational multiqubit tunnelling in programmable quantum annealers. Nat. Commun. 7, 10327 (2016)ADSCrossRef
127.
go back to reference Winci, W., Buffoni, L., Sadeghi, H., Khoshaman, A., Andriyash, E., Amin, M.H. (2020). A path towards quantum advantage in training deep generative models with quantum annealers. Machine Learning: Science and Technology, Vol. 1 No. 4 Winci, W., Buffoni, L., Sadeghi, H., Khoshaman, A., Andriyash, E., Amin, M.H. (2020). A path towards quantum advantage in training deep generative models with quantum annealers. Machine Learning: Science and Technology, Vol. 1 No. 4
131.
go back to reference Mandra, S., Katzgraber, H.G., Thomas, C. (2017). The pitfalls of planar spin-glass benchmarks: raising the bar for quantum annealers (again). Quantum Science and Technology Vol. 2 No. 3 Mandra, S., Katzgraber, H.G., Thomas, C. (2017). The pitfalls of planar spin-glass benchmarks: raising the bar for quantum annealers (again). Quantum Science and Technology Vol. 2 No. 3
132.
go back to reference Zhu, Z., Ochoa, A.J., Schnabel, S., Hamze, F., Katzgraber, H.G.: Best-case performance of quantum annealers on native spin-glass benchmarks: how chaos can affect success probabilities. Phys. Rev. A 93, 012317 (2016)ADSCrossRef Zhu, Z., Ochoa, A.J., Schnabel, S., Hamze, F., Katzgraber, H.G.: Best-case performance of quantum annealers on native spin-glass benchmarks: how chaos can affect success probabilities. Phys. Rev. A 93, 012317 (2016)ADSCrossRef
134.
go back to reference Adame, J.I. McMahon, P.L.: Inhomogeneous driving in quantum annealers can result in orders-of-magnitude improvements in performance. Quantum Sci. Technol. 5(3), 035011 (2020) Adame, J.I. McMahon, P.L.: Inhomogeneous driving in quantum annealers can result in orders-of-magnitude improvements in performance. Quantum Sci. Technol. 5(3), 035011 (2020)
135.
go back to reference Ayanzadeh, R., Dorband, J., Halem, M., Finin, T.: Post-Quantum Error-Correction for Quantum Annealers. Quantum Physics (quant-ph); Emerging Technologies (cs.ET) (2020). arXiv:2010.00115 [quant-ph] Ayanzadeh, R., Dorband, J., Halem, M., Finin, T.: Post-Quantum Error-Correction for Quantum Annealers. Quantum Physics (quant-ph); Emerging Technologies (cs.ET) (2020). arXiv:​2010.​00115 [quant-ph]
136.
go back to reference Marshall, J., Rieffel, E.G., Hen, I.: Thermalization, freeze-out, and noise: deciphering experimental quantum annealers. Phys. Rev. Appl. 8, 064025 (2017)ADSCrossRef Marshall, J., Rieffel, E.G., Hen, I.: Thermalization, freeze-out, and noise: deciphering experimental quantum annealers. Phys. Rev. Appl. 8, 064025 (2017)ADSCrossRef
139.
go back to reference Vinci, W., Lidar, D.A.: Scalable effective-temperature reduction for quantum annealers via nested quantum annealing correction. Phys. Rev. A 97, 022308 (2018)ADSCrossRef Vinci, W., Lidar, D.A.: Scalable effective-temperature reduction for quantum annealers via nested quantum annealing correction. Phys. Rev. A 97, 022308 (2018)ADSCrossRef
140.
go back to reference Marshall, J., Venturelli, D., Hen, I., Rieffel, E.G.: Power of pausing: advancing understanding of thermalization in experimental quantum annealers. Phys. Rev. Appl. 11, 044083 (2019)ADSCrossRef Marshall, J., Venturelli, D., Hen, I., Rieffel, E.G.: Power of pausing: advancing understanding of thermalization in experimental quantum annealers. Phys. Rev. Appl. 11, 044083 (2019)ADSCrossRef
142.
go back to reference Więckowski, A., Deffner, S., Gardas, B.: Disorder-assisted graph coloring on quantum annealers. Phys. Rev. A 100, 062304 (2019)ADSCrossRef Więckowski, A., Deffner, S., Gardas, B.: Disorder-assisted graph coloring on quantum annealers. Phys. Rev. A 100, 062304 (2019)ADSCrossRef
149.
go back to reference Hen, I.: How fast can quantum annealers count? J. Phys. A: Math. Theor. 47(23), 235304 (2014) Hen, I.: How fast can quantum annealers count? J. Phys. A: Math. Theor. 47(23), 235304 (2014)
150.
go back to reference Copenhaver, J., Wasserman, A., Wehefritz-Kaufmann, B.: Using quantum annealers to calculate ground state properties of molecules. Quantum Physics (2020). arXiv:2009.10779 [quant-ph] Copenhaver, J., Wasserman, A., Wehefritz-Kaufmann, B.: Using quantum annealers to calculate ground state properties of molecules. Quantum Physics (2020). arXiv:​2009.​10779 [quant-ph]
151.
go back to reference Albash, T., Martin-Mayor, V., Hen, I.: Temperature scaling law for quantum annealing optimizers. Phys. Rev. Lett. 119, 110502 (2017)ADSCrossRef Albash, T., Martin-Mayor, V., Hen, I.: Temperature scaling law for quantum annealing optimizers. Phys. Rev. Lett. 119, 110502 (2017)ADSCrossRef
152.
go back to reference Hamerly, R., Inagaki, T., McMahon, P.L., Venturelli, D., Marandi, A., Onodera, T., Ng, E., Langrock, C., Inaba, K., Honjo, T., Enbutsu, K., Umeki, T., Kasahara, R., Utsunomiya, S., Kako, S., Kawarabayashi, K.I., Byer, R.L., Fejer, M.M., Mabuchi, H., Englund, D., Rieffe, E., Takesue, H., Yamamoto, Y.: Experimental investigation of performance differences between coherent Ising machines and a quantum annealer. Sci. Adv. (2019). https://doi.org/10.1126/sciadv.aau0823CrossRef Hamerly, R., Inagaki, T., McMahon, P.L., Venturelli, D., Marandi, A., Onodera, T., Ng, E., Langrock, C., Inaba, K., Honjo, T., Enbutsu, K., Umeki, T., Kasahara, R., Utsunomiya, S., Kako, S., Kawarabayashi, K.I., Byer, R.L., Fejer, M.M., Mabuchi, H., Englund, D., Rieffe, E., Takesue, H., Yamamoto, Y.: Experimental investigation of performance differences between coherent Ising machines and a quantum annealer. Sci. Adv. (2019). https://​doi.​org/​10.​1126/​sciadv.​aau0823CrossRef
154.
go back to reference Pelofske, E., Hahn, G., Djidjev, H. (2020). Inferring the Dynamics of the State Evolution During Quantum Annealing. Quantum Physics, arXiv:2009.06387 [quant-ph] Pelofske, E., Hahn, G., Djidjev, H. (2020). Inferring the Dynamics of the State Evolution During Quantum Annealing. Quantum Physics, arXiv:​2009.​06387 [quant-ph]
155.
go back to reference Hen, I., Spedalieri, F.M.: Quantum annealing for constrained optimization. Phys. Rev. Appl. 5, 034007 (2016)ADSCrossRef Hen, I., Spedalieri, F.M.: Quantum annealing for constrained optimization. Phys. Rev. Appl. 5, 034007 (2016)ADSCrossRef
156.
go back to reference Hu, F., Lamata, L., Wang, C., Chen, X., Solano, E., Sanz, M.: Quantum advantage in cryptography with a low-connectivity quantum annealer. Phys. Rev. Appl. 13, 054062 (2020)ADSCrossRef Hu, F., Lamata, L., Wang, C., Chen, X., Solano, E., Sanz, M.: Quantum advantage in cryptography with a low-connectivity quantum annealer. Phys. Rev. Appl. 13, 054062 (2020)ADSCrossRef
158.
go back to reference Ayanzadeh, R., Mousavi, S., Halem, M., Finin, T. (2019). Quantum Annealing Based Binary Compressive Sensing with Matrix Uncertainty. Quantum Physics, arXiv:1901.00088 [cs.IT] Ayanzadeh, R., Mousavi, S., Halem, M., Finin, T. (2019). Quantum Annealing Based Binary Compressive Sensing with Matrix Uncertainty. Quantum Physics, arXiv:​1901.​00088 [cs.IT]
159.
go back to reference Genin, S.N., Ryabinkin, I.G., Izmaylov, A.F. (2019). Quantum chemistry on quantum annealers. Quantum Physics, arXiv:1901.04715 [physics.chem-ph] Genin, S.N., Ryabinkin, I.G., Izmaylov, A.F. (2019). Quantum chemistry on quantum annealers. Quantum Physics, arXiv:​1901.​04715 [physics.chem-ph]
161.
go back to reference Weber, S.J., Samach, G.O., Hover, D., Gustavsson, S., Kim, D.K., Melville, A., Rosenberg, D., Sears, A.P., Yan, F., Joder, J.L., Oliver, W.D., Kerman, A.J.: Coherent coupled qubits for quantum annealing. Phys. Rev. Appl. 8, 014004 (2017)ADSCrossRef Weber, S.J., Samach, G.O., Hover, D., Gustavsson, S., Kim, D.K., Melville, A., Rosenberg, D., Sears, A.P., Yan, F., Joder, J.L., Oliver, W.D., Kerman, A.J.: Coherent coupled qubits for quantum annealing. Phys. Rev. Appl. 8, 014004 (2017)ADSCrossRef
164.
go back to reference Denchev, V.S., Boixo, S., Isakov, S.V., Ding, N., Babbush, R., Smelyanskiy, V., Martinis, J., Neven, H.: What is the computational value of finite-range tunneling? Phys. Rev. X 6, 031015 (2016) Denchev, V.S., Boixo, S., Isakov, S.V., Ding, N., Babbush, R., Smelyanskiy, V., Martinis, J., Neven, H.: What is the computational value of finite-range tunneling? Phys. Rev. X 6, 031015 (2016)
168.
go back to reference Rosenberg, G., Haghnegahdar, P., Goddard, P., Carr, P., Wu, K., de Prado, M.L.: Solving the optimal trading trajectory problem using a quantum annealer. IEEE J. Sel. Top. Signal Process. 10(6), 1053–1060 (2016)ADSCrossRef Rosenberg, G., Haghnegahdar, P., Goddard, P., Carr, P., Wu, K., de Prado, M.L.: Solving the optimal trading trajectory problem using a quantum annealer. IEEE J. Sel. Top. Signal Process. 10(6), 1053–1060 (2016)ADSCrossRef
170.
go back to reference Yarkoni, S., Wang, H., Plaat, A., Bäck, T.: Boosting quantum annealing performance using evolution strategies for annealing offsets tuning. In: Feld, S., Linnhoff-Popien, C. (eds.) Quantum Technology and Optimization Problems, QTOP 2019. Lecture Notes in Computer Science, vol. 11413. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14082-3_14CrossRef Yarkoni, S., Wang, H., Plaat, A., Bäck, T.: Boosting quantum annealing performance using evolution strategies for annealing offsets tuning. In: Feld, S., Linnhoff-Popien, C. (eds.) Quantum Technology and Optimization Problems, QTOP 2019. Lecture Notes in Computer Science, vol. 11413. Springer, Cham (2019). https://​doi.​org/​10.​1007/​978-3-030-14082-3_​14CrossRef
173.
go back to reference Mandal, A.K., Panday, M., Biswas, A., Goswami, S., Chakrabarti, A., Chakraborty, B.: An approach of feature subset selection using simulated quantum annealing. In: Sharma, N., Chakrabarti, A., Balas, V., Martinovic, J. (eds.) Data Management, Analytics and Innovation. Advances in Intelligent Systems and Computing, vol. 1174. Springer, Singapore (2021). https://doi.org/10.1007/978-981-15-5616-6_10CrossRef Mandal, A.K., Panday, M., Biswas, A., Goswami, S., Chakrabarti, A., Chakraborty, B.: An approach of feature subset selection using simulated quantum annealing. In: Sharma, N., Chakrabarti, A., Balas, V., Martinovic, J. (eds.) Data Management, Analytics and Innovation. Advances in Intelligent Systems and Computing, vol. 1174. Springer, Singapore (2021). https://​doi.​org/​10.​1007/​978-981-15-5616-6_​10CrossRef
175.
go back to reference Kurowski, K., Wȩglarz, J., Subocz, M., Różycki, R., Waligóra, G.: Hybrid quantum annealing heuristic method for solving job shop scheduling problem. In: Krzhizhanovskaya, V. (ed.) Computational Science—ICCS 2020. Lecture Notes in Computer Science, vol. 12142. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-50433-5_39CrossRef Kurowski, K., Wȩglarz, J., Subocz, M., Różycki, R., Waligóra, G.: Hybrid quantum annealing heuristic method for solving job shop scheduling problem. In: Krzhizhanovskaya, V. (ed.) Computational Science—ICCS 2020. Lecture Notes in Computer Science, vol. 12142. Springer, Cham (2020). https://​doi.​org/​10.​1007/​978-3-030-50433-5_​39CrossRef
177.
go back to reference Borle, A., Lomonaco, S.J.: Analyzing the quantum annealing approach for solving linear least squares problems. In: Das G., Mandal P., Mukhopadhyaya K., Nakano S. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science, vol. 11355. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10564-8_23 Borle, A., Lomonaco, S.J.: Analyzing the quantum annealing approach for solving linear least squares problems. In: Das G., Mandal P., Mukhopadhyaya K., Nakano S. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science, vol. 11355. Springer, Cham (2019). https://​doi.​org/​10.​1007/​978-3-030-10564-8_​23
180.
go back to reference Vyskočil, T., Pakin, S., Djidjev, H.N.: Embedding inequality constraints for quantum annealing optimization. In: Feld S., Linnhoff-Popien C. (eds) Quantum Technology and Optimization Problems. QTOP 2019. Lecture Notes in Computer Science, vol 11413. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14082-3_2 Vyskočil, T., Pakin, S., Djidjev, H.N.: Embedding inequality constraints for quantum annealing optimization. In: Feld S., Linnhoff-Popien C. (eds) Quantum Technology and Optimization Problems. QTOP 2019. Lecture Notes in Computer Science, vol 11413. Springer, Cham (2019). https://​doi.​org/​10.​1007/​978-3-030-14082-3_​2
182.
go back to reference Leon, F., Lupu, A.Ş., Bădică, C.: Multiagent coalition structure optimization by quantum annealing. In: Nguyen N., Papadopoulos G., Jędrzejowicz P., Trawiński B., Vossen G. (eds) Computational Collective Intelligence. ICCCI 2017. Lecture Notes in Computer Science, vol. 10448. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67074-4_32 Leon, F., Lupu, A.Ş., Bădică, C.: Multiagent coalition structure optimization by quantum annealing. In: Nguyen N., Papadopoulos G., Jędrzejowicz P., Trawiński B., Vossen G. (eds) Computational Collective Intelligence. ICCCI 2017. Lecture Notes in Computer Science, vol. 10448. Springer, Cham (2017). https://​doi.​org/​10.​1007/​978-3-319-67074-4_​32
183.
go back to reference Bottarelli, L., Bicego, M., Denitto, M., Di Pierro, A., Farinelli, A.: A quantum annealing approach to biclustering. In: Martín-Vide C., Mizuki T., Vega-Rodríguez M. (eds) Theory and Practice of Natural Computing. TPNC 2016. Lecture Notes in Computer Science, vol. 10071. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49001-4_14 Bottarelli, L., Bicego, M., Denitto, M., Di Pierro, A., Farinelli, A.: A quantum annealing approach to biclustering. In: Martín-Vide C., Mizuki T., Vega-Rodríguez M. (eds) Theory and Practice of Natural Computing. TPNC 2016. Lecture Notes in Computer Science, vol. 10071. Springer, Cham (2016). https://​doi.​org/​10.​1007/​978-3-319-49001-4_​14
185.
go back to reference Killoran, N., Bromley, T.R., Arrazola, J.M., Schuld, M., Quesada, N., Lloyd, S.: Continuous-variable quantum neural networks. Phys. Rev. Res. 1, 033063 (2019)CrossRef Killoran, N., Bromley, T.R., Arrazola, J.M., Schuld, M., Quesada, N., Lloyd, S.: Continuous-variable quantum neural networks. Phys. Rev. Res. 1, 033063 (2019)CrossRef
186.
go back to reference Bausch, J.: Recurrent Quantum Neural Networks. Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020) (2020) Bausch, J.: Recurrent Quantum Neural Networks. Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020) (2020)
190.
go back to reference Verdon, G., Broughton, M., McClean, J.R., Sung, K.J., Babbush, R., Jiang, Z., Neven, H., Mohseni, M.: Learning to learn with quantum neural networks via classical neural networks. Quantum Physics (2019). arXiv:1907.05415 [quant-ph] Verdon, G., Broughton, M., McClean, J.R., Sung, K.J., Babbush, R., Jiang, Z., Neven, H., Mohseni, M.: Learning to learn with quantum neural networks via classical neural networks. Quantum Physics (2019). arXiv:​1907.​05415 [quant-ph]
191.
go back to reference Farhi, E., Neven, H.: Classification with Quantum Neural Networks on Near Term Processors. Quantum Physics (2018). arXiv:1802.06002 [quant-ph] Farhi, E., Neven, H.: Classification with Quantum Neural Networks on Near Term Processors. Quantum Physics (2018). arXiv:​1802.​06002 [quant-ph]
193.
go back to reference Niu, X.F., Ma, W.P.: Design of a novel quantum neural network. Laser. Phys. Lett. 17, 105208 (2020)ADSCrossRef Niu, X.F., Ma, W.P.: Design of a novel quantum neural network. Laser. Phys. Lett. 17, 105208 (2020)ADSCrossRef
195.
go back to reference Du, Y., Hsieh, M.H., Liu, T., You, S., Tao, D.: On the learnability of quantum neural networks. Quantum Physics (2020). arXiv:2007.12369 [quant-ph] Du, Y., Hsieh, M.H., Liu, T., You, S., Tao, D.: On the learnability of quantum neural networks. Quantum Physics (2020). arXiv:​2007.​12369 [quant-ph]
196.
go back to reference Beer, K., Bondarenko, D., Farrelly, T., Osborne, T.J., Robert Salzmann, R., Wolf, R.: Efficient Learning for Deep Quantum Neural Networks. Quantum Physics (2019). arXiv:1902.10445 [quant-ph] Beer, K., Bondarenko, D., Farrelly, T., Osborne, T.J., Robert Salzmann, R., Wolf, R.: Efficient Learning for Deep Quantum Neural Networks. Quantum Physics (2019). arXiv:​1902.​10445 [quant-ph]
198.
go back to reference Dlaska, C., Sieberer, L.M., Lechner, W.: Designing ground states of Hopfield networks for quantum state preparation. Phys. Rev. A 99, 032342 (2019)ADSCrossRef Dlaska, C., Sieberer, L.M., Lechner, W.: Designing ground states of Hopfield networks for quantum state preparation. Phys. Rev. A 99, 032342 (2019)ADSCrossRef
199.
go back to reference Seki, Y., Nishimori, H.: Quantum annealing with antiferromagnetic transverse interactions for the Hopfield model. J. Phys. A: Math. Theor. 48, 335301 (2015)MathSciNetCrossRef Seki, Y., Nishimori, H.: Quantum annealing with antiferromagnetic transverse interactions for the Hopfield model. J. Phys. A: Math. Theor. 48, 335301 (2015)MathSciNetCrossRef
200.
go back to reference Rotondo, P., Marcuzzi, M., Garrahan, J.P., Lesanovsky, I., Müller, M.: Open quantum generalisation of Hopfield neural networks. J. Phys. A: Math. Theor. 51, 115301 (2018)ADSMathSciNetCrossRef Rotondo, P., Marcuzzi, M., Garrahan, J.P., Lesanovsky, I., Müller, M.: Open quantum generalisation of Hopfield neural networks. J. Phys. A: Math. Theor. 51, 115301 (2018)ADSMathSciNetCrossRef
201.
go back to reference Inoue, J.I.: Pattern-recalling processes in quantum Hopfield networks far from saturation. J. Phys.: Conf. Ser. 297, 012012 (2011) Inoue, J.I.: Pattern-recalling processes in quantum Hopfield networks far from saturation. J. Phys.: Conf. Ser. 297, 012012 (2011)
206.
go back to reference Inoue, J.I.: Application of the quantum spin glass theory to image restoration. Phys. Rev. E 63, 046114 (2001)ADSCrossRef Inoue, J.I.: Application of the quantum spin glass theory to image restoration. Phys. Rev. E 63, 046114 (2001)ADSCrossRef
207.
go back to reference Mukherjee, S.S., Chowdhury, R., Bhattacharyya, S.: Image restoration using a multilayered quantum backpropagation neural network. In: 2011 International Conference on Computational Intelligence and Communication Networks (2011). https://doi.org/10.1109/cicn.2011.89 Mukherjee, S.S., Chowdhury, R., Bhattacharyya, S.: Image restoration using a multilayered quantum backpropagation neural network. In: 2011 International Conference on Computational Intelligence and Communication Networks (2011). https://​doi.​org/​10.​1109/​cicn.​2011.​89
209.
210.
go back to reference Johal, R.S.: Universal efficiency at optimal work with Bayesian statistics. Phys. Rev. E 82, 061113 (2010)ADSCrossRef Johal, R.S.: Universal efficiency at optimal work with Bayesian statistics. Phys. Rev. E 82, 061113 (2010)ADSCrossRef
211.
go back to reference Jordan, A.N., Korotkov, A.N.: Qubit feedback and control with kicked quantum nondemolition measurements: a quantum Bayesian analysis. Phys. Rev. B 74, 085307 (2006)ADSCrossRef Jordan, A.N., Korotkov, A.N.: Qubit feedback and control with kicked quantum nondemolition measurements: a quantum Bayesian analysis. Phys. Rev. B 74, 085307 (2006)ADSCrossRef
216.
go back to reference Lemm, J.C., Uhlig, J., Weiguny, A.: Bayesian approach to inverse quantum statistics. Phys. Rev. Lett. 84, 2068 (2000)ADSCrossRef Lemm, J.C., Uhlig, J., Weiguny, A.: Bayesian approach to inverse quantum statistics. Phys. Rev. Lett. 84, 2068 (2000)ADSCrossRef
223.
Metadata
Title
Models in quantum computing: a systematic review
Authors
Peter Nimbe
Benjamin Asubam Weyori
Adebayo Felix Adekoya
Publication date
01-02-2021
Publisher
Springer US
Published in
Quantum Information Processing / Issue 2/2021
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-021-03021-3

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