Biamonte, Jacob
(Quantum Complexity Science Initiative, Skolkovo Institute of Science and Technology, Skoltech Building 3, Moscow 143026, Russia)
,
Wittek, Peter
(Institute for Quantum Computing, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada)
,
Pancotti, Nicola
(ICFO—)
,
Rebentrost, Patrick
(The Institute of Photonic Sciences, Castelldefels, Barcelona 08860 Spain)
,
Wiebe, Nathan
(Max Planck Institute of Quantum Optics, 1 Hans-Kopfermannstrasse, D-85748 Garching, Germany)
,
Lloyd, Seth
(Massachusetts Institute of Technology, Research Laboratory of Electronics, Cambridge, Massachusetts 02139, USA)
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum c...
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum computers may outperform classical computers on machine learning tasks. The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Recent work has produced quantum algorithms that could act as the building blocks of machine learning programs, but the hardware and software challenges are still considerable.
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum computers may outperform classical computers on machine learning tasks. The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Recent work has produced quantum algorithms that could act as the building blocks of machine learning programs, but the hardware and software challenges are still considerable.
참고문헌 (109)
Psychol. Rev. F Rosenblatt 65 386 1958 10.1037/h0042519 Rosenblatt, F. The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65, 386 (1958)
QV Le 8595 2013 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP) Le, Q. V. Building high-level features using large scale unsupervised learning. In IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP) 8595-8598 (IEEE, 2013)
Contemp. Phys. M Schuld 56 172 2015 10.1080/00107514.2014.964942 Schuld, M., Sinayskiy, I. & Petruccione, F. An introduction to quantum machine learning. Contemp. Phys. 56, 172-185 (2015)
10.1016/B978-0-12-800953-6.00004-9 Wittek, P. Quantum Machine Learning: What Quantum Computing Means to Data Mining (Academic Press, New York, NY, USA, 2014)
Adcock, J. et al. Advances in quantum machine learning. Preprint at https://arxiv.org/abs/1512.02900 (2015)
Arunachalam, S. & de Wolf, R. A survey of quantum learning theory. Preprint at https://arxiv.org/abs/1701.06806 (2017)
Phys. Rev. Lett. AW Harrow 103 150502 2009 10.1103/PhysRevLett.103.150502 Harrow, A. W., Hassidim, A. & Lloyd, S. Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009)
Phys. Rev. Lett. N Wiebe 109 050505 2012 10.1103/PhysRevLett.109.050505 Wiebe, N., Braun, D. & Lloyd, S. Quantum algorithm for data fitting. Phys. Rev. Lett. 109, 050505 (2012)
Childs, A. M., Kothari, R. & Somma, R. D. Quantum linear systems algorithm with exponentially improved dependence on precision. Preprint at https://arxiv.org/abs/1511.02306 (2015)
Nat. Phys. S Lloyd 10 631 2014 10.1038/nphys3029 Lloyd, S., Mohseni, M. & Rebentrost, P. Quantum principal component analysis. Nat. Phys. 10, 631-633 (2014)
Kimmel, S., Lin, C. Y.-Y., Low, G. H., Ozols, M. & Yoder, T. J. Hamiltonian simulation with optimal sample complexity. Preprint at https://arxiv.org/abs/1608.00281 (2016)
Phys. Rev. Lett. P Rebentrost 113 130503 2014 10.1103/PhysRevLett.113.130503 Rebentrost, P., Mohseni, M. & Lloyd, S. Quantum support vector machine for big data classification. Phys. Rev. Lett. 113, 130503 (2014). This study applies quantum matrix inversion in a supervised discriminative learning algorithm.
Nat. Commun. S Lloyd 7 10138 2016 10.1038/ncomms10138 Lloyd, S., Garnerone, S. & Zanardi, P. Quantum algorithms for topological and geometric analysis of data. Nat. Commun. 7, 10138 (2016)
Dridi, R. & Alghassi, H. Homology computation of large point clouds using quantum annealing. Preprint at https://arxiv.org/abs/1512.09328 (2015)
Rebentrost, P., Steffens, A. & Lloyd, S. Quantum singular value decomposition of non-sparse low-rank matrices. Preprint at https://arxiv.org/abs/1607.05404 (2016)
Phys. Rev. A M Schuld 94 022342 2016 10.1103/PhysRevA.94.022342 Schuld, M., Sinayskiy, I. & Petruccione, F. Prediction by linear regression on a quantum computer. Phys. Rev. A 94, 022342 (2016)
Brandao, F. G. & Svore, K. Quantum speed-ups for semidefinite programming. Preprint at https://arxiv.org/abs/1609.05537 (2016)
Rebentrost, P., Schuld, M., Petruccione, F. & Lloyd, S. Quantum gradient descent and Newton’s method for constrained polynomial optimization. Preprint at https://arxiv.org/abs/1612.01789 (2016)
Wiebe, N., Kapoor, A. & Svore, K. M. Quantum deep learning. Preprint at https://arxiv.org/abs/1412.3489 (2014)
Adachi, S. H. & Henderson, M. P. Application of quantum annealing to training of deep neural networks. Preprint at https://arxiv.org/abs/arXiv:1510.06356 (2015)
Amin, M. H., Andriyash, E., Rolfe, J., Kulchytskyy, B. & Melko, R. Quantum Boltzmann machine. Preprint at https://arxiv.org/abs/arXiv:1601.02036 (2016)
Phys. Rev. A M Sasaki 64 022317 2001 10.1103/PhysRevA.64.022317 Sasaki, M., Carlini, A. & Jozsa, R. Quantum template matching. Phys. Rev. A 64, 022317 (2001)
Phys. Rev. A A Bisio 81 032324 2010 10.1103/PhysRevA.81.032324 Bisio, A., Chiribella, G., D’Ariano, G. M., Facchini, S. & Perinotti, P. Optimal quantum learning of a unitary transformation. Phys. Rev. A 81, 032324 (2010)
Phys. Lett. A A Bisio 375 3425 2011 10.1016/j.physleta.2011.08.002 Bisio, A., D’Ariano, G. M., Perinotti, P. & Sedlák, M. Quantum learning algorithms for quantum measurements. Phys. Lett. A 375, 3425-3434 (2011)
Phys. Rev. X GD Paparo 4 031002 2014 Paparo, G. D., Dunjko, V., Makmal, A., Martin-Delgado, M. A. & Briegel, H. J. Quantum speedup for active learning agents. Phys. Rev. X 4, 031002 (2014)
New J. Phys. V Dunjko 17 023006 2015 10.1088/1367-2630/17/2/023006 Dunjko, V., Friis, N. & Briegel, H. J. Quantum-enhanced deliberation of learning agents using trapped ions. New J. Phys. 17, 023006 (2015)
Phys. Rev. Lett. V Dunjko 117 130501 2016 10.1103/PhysRevLett.117.130501 Dunjko, V., Taylor, J. M. & Briegel, H. J. Quantum-enhanced machine learning. Phys. Rev. Lett. 117, 130501 (2016). This paper investigates the theoretical maximum speedup achievable in reinforcement learning in a closed quantum system, which proves to be Grover-like if we wish to obtain classical verification of the learning process.
Phys. Rev. Lett. G Sentís 117 150502 2016 10.1103/PhysRevLett.117.150502 Sentís, G., Bagan, E., Calsamiglia, J., Chiribella, G. & Muñoz Tapia, R. Quantum change point. Phys. Rev. Lett. 117, 150502 (2016)
Phys. Rev. X M Faccin 4 041012 2014 Faccin, M., Migdał, P., Johnson, T. H., Bergholm, V. & Biamonte, J. D. Community detection in quantum complex networks. Phys. Rev. X 4, 041012 (2014). This paper defines closeness measures and then maximizes modularity with hierarchical clustering to partition quantum data.
Phys. Rev. Lett. BD Clader 110 250504 2013 10.1103/PhysRevLett.110.250504 Clader, B. D., Jacobs, B. C. & Sprouse, C. R. Preconditioned quantum linear system algorithm. Phys. Rev. Lett. 110, 250504 (2013)
Lloyd, S., Mohseni, M. & Rebentrost, P. Quantum algorithms for supervised and unsupervised machine learning. Preprint at https://arxiv.org/abs/1307.0411 (2013)
Quantum Inf. Comput. N Wiebe 15 316 2015 Wiebe, N., Kapoor, A. & Svore, K. M. Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning. Quantum Inf. Comput. 15, 316-356 (2015)
Phys. Rev. Lett. H-K Lau 118 080501 2017 10.1103/PhysRevLett.118.080501 Lau, H.-K., Pooser, R., Siopsis, G. & Weedbrook, C. Quantum machine learning over infinite dimensions. Phys. Rev. Lett. 118, 080501 (2017)
E Aïmeur 431 2006 Machine Learning in a Quantum World Aïmeur, E ., Brassard, G . & Gambs, S. in Machine Learning in a Quantum World 431-442 (Springer, 2006)
SIAM J. Comput. PW Shor 26 1484 1997 10.1137/S0097539795293172 Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484-1509 (1997)
Nielsen, M. A . & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000)
Wossnig, L., Zhao, Z. & Prakash, A. A quantum linear system algorithm for dense matrices. Preprint at https://arxiv.org/abs/1704.06174 (2017)
Phys. Rev. Lett. V Giovannetti 100 160501 2008 10.1103/PhysRevLett.100.160501 Giovannetti, V., Lloyd, S. & Maccone, L. Quantum random access memory. Phys. Rev. Lett. 100, 160501 (2008)
10.1007/978-1-4757-2440-0 Vapnik, V. The Nature of Statistical Learning Theory (Springer, 1995)
Neural Netw. D Anguita 16 763 2003 10.1016/S0893-6080(03)00087-X Anguita, D., Ridella, S., Rivieccio, F. & Zunino, R. Quantum optimization for training support vector machines. Neural Netw. 16, 763-770 (2003)
Dürr, C. & Høyer, P. A quantum algorithm for finding the minimum. Preprint at https://arxiv.org/abs/quant-ph/9607014 (1996)
Chatterjee, R. & Yu, T. Generalized coherent states, reproducing kernels, and quantum support vector machines. Preprint at https://arxiv.org/abs/1612.03713 (2016)
Zhao, Z., Fitzsimons, J. K. & Fitzsimons, J. F. Quantum assisted Gaussian process regression. Preprint at https://arxiv.org/abs/1512.03929 (2015)
Phys. Rev. Lett. Z Li 114 140504 2015 10.1103/PhysRevLett.114.140504 Li, Z., Liu, X., Xu, N. & Du, J. Experimental realization of a quantum support vector machine. Phys. Rev. Lett. 114, 140504 (2015)
Europhys. Lett. JD Whitfield 99 57004 2012 10.1209/0295-5075/99/57004 Whitfield, J. D., Faccin, M. & Biamonte, J. D. Ground-state spin logic. Europhys. Lett. 99, 57004 (2012)
New J. Phys. S Arunachalam 17 123010 2015 10.1088/1367-2630/17/12/123010 Arunachalam, S., Gheorghiu, V., Jochym-O’Connor, T., Mosca, M. & Srinivasan, P. V. On the robustness of bucket brigade quantum RAM. New J. Phys. 17, 123010 (2015)
Scherer, A. et al. Concrete resource analysis of the quantum linear system algorithm used to compute the electromagnetic scattering cross section of a 2D target. Preprint at https://arxiv.org/abs/1505.06552 (2015)
M Denil 2011 Neural Information Processing Systems (NIPS) Conf. on Deep Learning and Unsupervised Feature Learning Workshop Denil, M . & De Freitas, N. Toward the implementation of a quantum RBM. In Neural Information Processing Systems (NIPS) Conf. on Deep Learning and Unsupervised Feature Learning Workshop Vol. 5 (2011)
10.1609/aaai.v28i1.8924 Dumoulin, V., Goodfellow, I. J., Courville, A. & Bengio, Y. On the challenges of physical implementations of RBMs. Preprint at https://arxiv.org/abs/1312.5258 (2013)
Phys. Rev. A M Benedetti 94 022308 2016 10.1103/PhysRevA.94.022308 Benedetti, M., Realpe-Gómez, J., Biswas, R. & Perdomo-Ortiz, A. Estimation of effective temperatures in quantum annealers for sampling applications: a case study with possible applications in deep learning. Phys. Rev. A 94, 022308 (2016)
Phys. Rev. A JD Biamonte 78 012352 2008 10.1103/PhysRevA.78.012352 Biamonte, J. D. & Love, P. J. Realizable Hamiltonians for universal adiabatic quantum computers. Phys. Rev. A 78, 012352 (2008). This study established the contemporary experimental target for non-stoquastic (that is, non-quantum stochastic) D-Wave quantum annealing hardware able to realize universal quantum Boltzmann machines.
Nature K Temme 471 87 2011 10.1038/nature09770 Temme, K., Osborne, T. J., Vollbrecht, K. G., Poulin, D. & Verstraete, F. Quantum metropolis sampling. Nature 471, 87-90 (2011)
Proc. Natl Acad. Sci. USA M-H Yung 109 754 2012 10.1073/pnas.1111758109 Yung, M.-H. & Aspuru-Guzik, A. A quantum-quantum metropolis algorithm. Proc. Natl Acad. Sci. USA 109, 754-759 (2012)
Quant. Inf. Comput. AN Chowdhury 17 41 2017 Chowdhury, A. N. & Somma, R. D. Quantum algorithms for Gibbs sampling and hitting-time estimation. Quant. Inf. Comput. 17, 41-64 (2017)
Kieferova, M. & Wiebe, N. Tomography and generative data modeling via quantum Boltzmann training. Preprint at https://arxiv.org/abs/1612.05204 (2016)
New J. Phys. S Lloyd 18 023042 2016 10.1088/1367-2630/18/2/023042 Lloyd, S. & Terhal, B. Adiabatic and Hamiltonian computing on a 2D lattice with simple 2-qubit interactions. New J. Phys. 18, 023042 (2016)
New J. Phys. CE Granade 14 103013 2012 10.1088/1367-2630/14/10/103013 Granade, C. E., Ferrie, C., Wiebe, N. & Cory, D. G. Robust online Hamiltonian learning. New J. Phys. 14, 103013 (2012)
Phys. Rev. Lett. N Wiebe 112 190501 2014 10.1103/PhysRevLett.112.190501 Wiebe, N., Granade, C., Ferrie, C. & Cory, D. G. Hamiltonian learning and certification using quantum resources. Phys. Rev. Lett. 112, 190501 (2014)
New J. Phys. N Wiebe 17 022005 2015 10.1088/1367-2630/17/2/022005 Wiebe, N., Granade, C. & Cory, D. G. Quantum bootstrapping via compressed quantum Hamiltonian learning. New J. Phys. 17, 022005 (2015)
Phys. Rev. Lett. E Zahedinejad 114 200502 2015 10.1103/PhysRevLett.114.200502 Zahedinejad, E., Ghosh, J. & Sanders, B. C. High-fidelity single-shot Toffoli gate via quantum control. Phys. Rev. Lett. 114, 200502 (2015)
Phys. Rev. A D Zeidler 64 023420 2001 10.1103/PhysRevA.64.023420 Zeidler, D., Frey, S., Kompa, K.-L. & Motzkus, M. Evolutionary algorithms and their application to optimal control studies. Phys. Rev. A 64, 023420 (2001)
Phys. Rev. Lett. U Las Heras 116 230504 2016 10.1103/PhysRevLett.116.230504 Las Heras, U., Alvarez-Rodriguez, U., Solano, E. & Sanz, M. Genetic algorithms for digital quantum simulations. Phys. Rev. Lett. 116, 230504 (2016)
10.1103/PhysRevA.95.012335 August, M. & Ni, X. Using recurrent neural networks to optimize dynamical decoupling for quantum memory. Preprint at https://arxiv.org/abs/1604.00279 (2016)
J. Phys. Chem. B Amstrup 99 5206 1995 10.1021/j100014a048 Amstrup, B., Toth, G. J., Szabo, G., Rabitz, H. & Loerincz, A. Genetic algorithm with migration on topology conserving maps for optimal control of quantum systems. J. Phys. Chem. 99, 5206-5213 (1995)
Phys. Rev. Lett. A Hentschel 104 063603 2010 10.1103/PhysRevLett.104.063603 Hentschel, A. & Sanders, B. C. Machine learning for precise quantum measurement. Phys. Rev. Lett. 104, 063603 (2010)
Phys. Rev. Lett. NB Lovett 110 220501 2013 10.1103/PhysRevLett.110.220501 Lovett, N. B., Crosnier, C., Perarnau-Llobet, M. & Sanders, B. C. Differential evolution for many-particle adaptive quantum metrology. Phys. Rev. Lett. 110, 220501 (2013)
Neurocomputing Pantita Palittapongarnpim 268 116 2017 10.1016/j.neucom.2016.12.087 Palittapongarnpim, P., Wittek, P., Zahedinejad, E., Vedaie, S. & Sanders, B. C. Learning in quantum control: high-dimensional global optimization for noisy quantum dynamics. Neurocomputing https://doi.org/10.1016/j.neucom.2016.12.087 (in the press)
10.1038/s41598-017-09098-0 Broecker, P., Carrasquilla, J., Melko, R. G. & Trebst, S. Machine learning quantum phases of matter beyond the fermion sign problem. Preprint at https://arxiv.org/abs/1608.07848 (2016)
Science G Carleo 355 602 2017 10.1126/science.aag2302 Carleo, G. & Troyer, M. Solving the quantum many-body problem with artificial neural networks. Science 355, 602-606 (2017)
Nat. Commun. D Brunner 4 1364 2013 10.1038/ncomms2368 Brunner, D., Soriano, M. C., Mirasso, C. R. & Fischer, I. Parallel photonic information processing at gigabyte per second data rates using transient states. Nat. Commun. 4, 1364 (2013)
Phys. Rev. Lett. X-D Cai 114 110504 2015 10.1103/PhysRevLett.114.110504 Cai, X.-D. et al. Entanglement-based machine learning on a quantum computer. Phys. Rev. Lett. 114, 110504 (2015)
J. Mach. Learn. Res. M Hermans 16 2081 2015 Hermans, M., Soriano, M. C., Dambre, J., Bienstman, P. & Fischer, I. Photonic delay systems as machine learning implementations. J. Mach. Learn. Res. 16, 2081-2097 (2015)
Phys. Rev. A R Neigovzen 79 042321 2009 10.1103/PhysRevA.79.042321 Neigovzen, R., Neves, J. L., Sollacher, R. & Glaser, S. J. Quantum pattern recognition with liquid-state nuclear magnetic resonance. Phys. Rev. A 79, 042321 (2009)
Phys. Rev. Lett. M Pons 98 023003 2007 10.1103/PhysRevLett.98.023003 Pons, M. et al. Trapped ion chain as a neural network: error resistant quantum computation. Phys. Rev. Lett. 98, 023003 (2007)
H Neven 1 2009 24th Ann. Conf. on Neural Information Processing Systems (NIPS-09) Neven, H . et al. Binary classification using hardware implementation of quantum annealing. In 24th Ann. Conf. on Neural Information Processing Systems (NIPS-09) 1-17 (2009). This paper was among the first experimental demonstrations of machine learning using quantum annealing.
VS Denchev 2012 Proc. 29th Int. Conf. on Machine Learning (ICML-2012) Denchev, V. S ., Ding, N ., Vishwanathan, S . & Neven, H. Robust classification with adiabatic quantum optimization. In Proc. 29th Int. Conf. on Machine Learning (ICML-2012) (2012)
Process. K Karimi 11 77 2012 Karimi, K. et al. Investigating the performance of an adiabatic quantum optimization processor. Quantum Inform. Process. 11, 77-88 (2012)
EPJ Spec. Top. BA O’Gorman 224 163 2015 10.1140/epjst/e2015-02349-9 O’Gorman, B. A. et al. Bayesian network structure learning using quantum annealing. EPJ Spec. Top. 224, 163-188 (2015)
Denchev, V. S., Ding, N., Matsushima, S., Vishwanathan, S. V. N. & Neven, H. Totally corrective boosting with cardinality penalization. Preprint at https://arxiv.org/abs/1504.01446 (2015)
Kerenidis, I. & Prakash, A. Quantum recommendation systems. Preprint at https://arxiv.org/abs/1603.08675 (2016)
10.1038/s41598-017-13378-0 Alvarez-Rodriguez, U., Lamata, L., Escandell-Montero, P., Martín-Guerrero, J. D. & Solano, E. Quantum machine learning without measurements. Preprint at https://arxiv.org/abs/1612.05535 (2016)
10.1209/0295-5075/119/60002 Schuld, M., Fingerhuth, M. & Petruccione, F. Quantum machine learning with small-scale devices: implementing a distance-based classifier with a quantum interference circuit. Preprint at https://arxiv.org/abs/1703.10793 (2017)
Phys. Rev. Lett. A Monràs 118 190503 2017 10.1103/PhysRevLett.118.190503 Monràs, A., Sentís, G. & Wittek, P. Inductive supervised quantum learning. Phys. Rev. Lett. 118, 190503 (2017). This paper proves that supervised learning protocols split into a training and application phase in both the classical and the quantum cases.
Sci. Rep. M Tiersch 5 12874 2015 10.1038/srep12874 Tiersch, M., Ganahl, E. J. & Briegel, H. J. Adaptive quantum computation in changing environments using projective simulation. Sci. Rep. 5, 12874 (2015)
10.1103/PhysRevApplied.6.054005 Zahedinejad, E., Ghosh, J. & Sanders, B. C. Designing high-fidelity single-shot three-qubit gates: a machine learning approach. Preprint at https://arxiv.org/abs/1511.08862 (2015)
P Palittapongarnpim 327 2016 Proc. 24th Eur. Symp. Artificial Neural Networks (ESANN-16) on Computational Intelligence and Machine Learning Palittapongarnpim, P ., Wittek, P . & Sanders, B. C. Controlling adaptive quantum phase estimation with scalable reinforcement learning. In Proc. 24th Eur. Symp. Artificial Neural Networks (ESANN-16) on Computational Intelligence and Machine Learning 327-332 (2016)
10.1038/s41534-017-0032-4 Wan, K. H., Dahlsten, O., Kristjánsson, H., Gardner, R. & Kim, M. S. Quantum generalisation of feedforward neural networks. Preprint at https://arxiv.org/abs/1612.01045 (2016)
Lu, D. et al. Towards quantum supremacy: enhancing quantum control by bootstrapping a quantum processor. Preprint at https://arxiv.org/abs/1701.01198 (2017)
Nat. Commun. S Mavadia 8 14106 2017 10.1038/ncomms14106 Mavadia, S., Frey, V., Sastrawan, J., Dona, S. & Biercuk, M. J. Prediction and real-time compensation of qubit decoherence via machine learning. Nat. Commun. 8, 14106 (2017)
Phys. Rev. A GH Low 89 062315 2014 10.1103/PhysRevA.89.062315 Low, G. H., Yoder, T. J. & Chuang, I. L. Quantum inference on Bayesian networks. Phys. Rev. A 89, 062315 (2014)
Wiebe, N. & Granade, C. Can small quantum systems learn? Preprint at https://arxiv.org/abs/1512.03145 (2015)
Adv. Neural Inform. Process. Syst. N Wiebe 29 3999 2016 Wiebe, N., Kapoor, A. & Svore, K. M. Quantum perceptron models. Adv. Neural Inform. Process. Syst. 29, 3999-4007 (2016)
Quantum Inform. Process. A Scherer 16 60 2017 10.1007/s11128-016-1495-5 Scherer, A. et al. Concrete resource analysis of the quantum linear-system algorithm used to compute the electromagnetic scattering cross section of a 2D target. Quantum Inform. Process. 16, 60 (2017)
※ AI-Helper는 부적절한 답변을 할 수 있습니다.