2020

TensorFlow Quantum: A Software Framework for Quantum Machine Learning

Broughton, Michael, Verdon, Guillaume, McCourt, Trevor et al.

Understand

We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data.

This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators.
We provide an overview of the software architecture and building blocks through several examples and review the theory of hybrid quantum-classical neural networks.
We illustrate TFQ functionalities via several basic applications including supervised learning for quantum classification, quantum control, simulating noisy quantum circuits, and quantum approximate optimization.

Built on

G. Verdon, J. M. Arrazola, K. Brádler, and N. Killoran, arXiv preprint arXiv:1902.00409 (2019b)
Original
1902
Earlier work this paper cites.
C. Roberts, A. Milsted, M. Ganahl, A. Zalcman, B. Fontaine, Y. Zou, J. Hidary, G. Vidal, and S. Leichenauer, “TensorNetwork: A Library for Physics and Machine Learning,” (2019), arXiv:1905.01330 [physics.comp-ph]
Original
1905
Earlier work this paper cites.
S. Greydanus, M. Dzamba, and J. Yosinski, “Hamiltonian neural networks,” (2019), arXiv:1906.01563 [cs.NE]
Original
1906
Earlier work this paper cites.
G. Verdon, M. Broughton, J. R. McClean, K. J. Sung, R. Babbush, Z. Jiang, H. Neven, and M. Mohseni, “Learning to learn with quantum neural networks via classical neural networks,” (2019a), arXiv:1907.05415
Original
1907
Earlier work this paper cites.
M. Wilson, S. Stromswold, F. Wudarski, S. Hadfield, N. M. Tubman, and E. Rieffel, “Optimizing quantum heuristics with meta-learning,” (2019), arXiv:1908.03185 [quant-ph]
Original
1908
Earlier work this paper cites.
G. Verdon, T. McCourt, E. Luzhnica, V. Singh, S. Leichenauer, and J. Hidary, “Quantum graph neural networks,” (2019d), arXiv:1909.12264 [quant-ph]
Original
1909
Earlier work this paper cites.
G. Verdon, A. J. Martinez, J. Marks, S. Patel, G. Roeder, F. Sbahi, J. H. Yoo, S. Nanda, S. Leichenauer, and J. Hidary, arXiv preprint arXiv:1910.02071 (2019c)
Original
1910
Earlier work this paper cites.
C. Cirstoiu, Z. Holmes, J. Iosue, L. Cincio, P. J. Coles, and A. Sornborger, “Variational fast forwarding for quantum simulation beyond the coherence time,” (2019), arXiv:1910.04292 [quant-ph]
Original
1910
Earlier work this paper cites.
F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell, et al. , arXiv:1910.11333 (2019b)
Original
1910
Earlier work this paper cites.
C. Berner, G. Brockman, B. Chan, V. Cheung, P. Dębiak, C. Dennison, D. Farhi, Q. Fischer, S. Hashme, C. Hesse, et al. , “Dota 2 with large scale deep reinforcement learning,” (2019), arXiv:1912.06680 [cs.LG]
Original
1912
Earlier work this paper cites.
R. P. Feynman, International Journal of Theoretical Physics 21
1982
Earlier work this paper cites.
D. E. Rumelhart, G. E. Hinton, and R. J. Williams, nature 323
1986
Earlier work this paper cites.
S. Wold, K. Esbensen, and P. Geladi, Chemometrics and intelligent laboratory systems 2
1987
Earlier work this paper cites.
L. S. Pontryagin, Mathematical theory of optimal processes (CRC press, 1987)
1987
Earlier work this paper cites.
Y. LeCun, D. Touresky, G. Hinton, and T. Sejnowski, in Proceedings of the 1988 connectionist models summer school , Vol. 1 (CMU, Pittsburgh, Pa: Morgan Kaufmann, 1988) pp. 21–28
1988
Earlier work this paper cites.
M. Suzuki, Physics Letters A 146
1990
Earlier work this paper cites.
P. W. Shor, in Proceedings 35th annual symposium on foundations of computer science (Ieee, 1994) pp. 124–134
1994
Earlier work this paper cites.
D. Gottesman, Stabilizer codes and quantum error correction , Ph.D. thesis, California Institute of Technology (1997)
1997
Earlier work this paper cites.
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, Proceedings of the IEEE 86
1998
Earlier work this paper cites.
M. S. L. du Croo de Jongh and J. M. J. van Leeuwen, Phys. Rev. B 57
1998
Earlier work this paper cites.
R. S. Sutton, A. G. Barto, et al. , Introduction to reinforcement learning , Vol. 135 (MIT press Cambridge, 1998)
1998
Earlier work this paper cites.
J. A. Suykens and J. Vandewalle, Neural processing letters 9
1999
Earlier work this paper cites.
I. Newton, The Principia: mathematical principles of natural philosophy (Univ of California Press, 1999)
1999
Earlier work this paper cites.
R. S. Sutton, D. A. McAllester, S. P. Singh, Y. Mansour, et al. , in NIPS , Vol. 99 (1999) pp. 1057–1063
1999
Earlier work this paper cites.
G. S. Hartnett and M. Mohseni, “A probability density theory for spin-glass systems,” (2020a), arXiv:2001.00927
Original
2001
Earlier work this paper cites.
G. S. Hartnett and M. Mohseni, “Self-supervised learning of generative spin-glasses with normalizing flows,” (2020b), arXiv:2001.00585
Original
2001
Earlier work this paper cites.
H. W. J. Blöte and Y. Deng, Phys. Rev. E 66
2002
Earlier work this paper cites.
M. Mohseni, A. M. Steinberg, and J. A. Bergou, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434
2005
Earlier work this paper cites.
M. Abramowitz and I. Stegun, Appl. Math. Ser 55
2006
Earlier work this paper cites.
M. A. Nielsen, Reports on Mathematical Physics 57
2006
Earlier work this paper cites.
P. B. M. Sousa and R. V. Ramos, “Universal quantum circuit for n-qubit quantum gate: A programmable quantum gate,” (2006), arXiv:quant-ph/0602174 [quant-ph]
2006
Earlier work this paper cites.
E. Knill, G. Ortiz, and R. D. Somma, Physical Review A 75
2007
Earlier work this paper cites.
V. Giovannetti, S. Lloyd, and L. Maccone, Physical review letters 100
2008
Earlier work this paper cites.
G. Vidal, Physical Review Letters 101
2008
Earlier work this paper cites.
A. Hagberg, P. Swart, and D. S Chult, Exploring network structure, dynamics, and function using NetworkX , Tech. Rep. (Los Alamos National Lab.(LANL), Los Alamos, NM (United States), 2008)
2008
Earlier work this paper cites.
F. Verstraete, V. Murg, and J. Cirac, Advances in Physics 57
2008
Earlier work this paper cites.
A. K. Jain, Pattern recognition letters 31
2010
Earlier work this paper cites.
L. Bottou, in Proceedings of COMPSTAT’2010 (Springer, 2010) pp. 177–186
2010
Earlier work this paper cites.
D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, Physical Review Letters 105
2010
Earlier work this paper cites.
X. Glorot and Y. Bengio, in AISTATS (2010) pp. 249–256
2010
Earlier work this paper cites.
A. W. Sandvik, AIP Conference Proceedings 1297
2010
Earlier work this paper cites.
A. Arrasmith, M. Cerezo, P. Czarnik, L. Cincio, and P. J. Coles, “Effect of barren plateaus on gradient-free optimization,” (2020), arXiv:2011.12245
Original
2011
Earlier work this paper cites.
Mark Buxton, “Haswell New Instruction Descriptions Now Available!” (2011)
2011
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition , 10th ed. (Cambridge University Press, USA, 2011)
2011
Earlier work this paper cites.
K. P. Murphy, Machine learning: a probabilistic perspective (MIT press, 2012)
2012
Earlier work this paper cites.
A. Krizhevsky, I. Sutskever, and G. E. Hinton, in Advances in Neural Information Processing Systems 25 , edited by F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger (Curran Associates, Inc., 2012) pp. 1097–1105
2012
Earlier work this paper cites.
J. R. Johansson, P. D. Nation, and F. Nori, Comput. Phys. Commun. 183
2012
Earlier work this paper cites.
Y. Bengio, in Neural networks: Tricks of the trade (Springer, 2012) pp. 437–478
2012
Earlier work this paper cites.
S. Lloyd, M. Mohseni, and P. Rebentrost, “Quantum algorithms for supervised and unsupervised machine learning,” (2013), arXiv:1307.0411 [quant-ph]
Original
2013
Earlier work this paper cites.
S. Bhatnagar, H. Prasad, and L. Prashanth, Stochastic Recursive Algorithms for Optimization: Simultaneous Perturbation Methods (Springer, 2013)
2013
Earlier work this paper cites.
S. Lloyd, M. Mohseni, and P. Rebentrost, Nature Physics 10
2014
Earlier work this paper cites.
P. Rebentrost, M. Mohseni, and S. Lloyd, Phys. Rev. Lett. 113
2014
Earlier work this paper cites.
A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’brien, Nature communications 5
2014
Earlier work this paper cites.
D. P. Kingma and J. Ba, arXiv preprint arXiv:1412.6980 (2014)
Original
2014
Earlier work this paper cites.
E. Farhi, J. Goldstone, and S. Gutmann, ArXiv e-prints (2014), arXiv:1411.4028 [quant-ph]
Original
2014
Earlier work this paper cites.

Similar

N. Wiebe, C. Granade, C. Ferrie, and D. Cory, Physical Review Letters 112
2014
Cited alongside, same era.
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, in Advances in neural information processing systems (2014) pp. 2672–2680
2014
Cited alongside, same era.
Y. LeCun, Y. Bengio, and G. Hinton, nature 521
2015
Cited alongside, same era.
S. Arunachalam, V. Gheorghiu, T. Jochym-O’Connor, M. Mosca, and P. V. Srinivasan, New Journal of Physics 17
2015
Cited alongside, same era.
D. Wecker, M. B. Hastings, and M. Troyer, Phys. Rev. A 92
2015
Cited alongside, same era.
F. Chollet et al. , “Keras,” https://keras.io (2015)
2015
Cited alongside, same era.
J. Schulman, N. Heess, T. Weber, and P. Abbeel, in Advances in Neural Information Processing Systems (2015) pp. 3528–3536
2015
Cited alongside, same era.
N. Tishby and N. Zaslavsky, “Deep learning and the information bottleneck principle,” (2015), arXiv:1503.02406 [cs.LG]
Original
2015
Cited alongside, same era.
C. P. Robert, “The metropolis-hastings algorithm,” (2015), arXiv:1504.01896 [stat.CO]
Original
2015
Cited alongside, same era.
V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, et al. , nature 518
2015
Cited alongside, same era.
I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep learning , Vol. 1 (MIT press Cambridge, 2016)
2016
Cited alongside, same era.
I. Kerenidis and A. Prakash, “Quantum recommendation systems,” (2016), arXiv:1603.08675
Original
2016
Cited alongside, same era.

Then

E. Tang, in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (2019) pp. 217–228
2019
Later among the works it cites.
S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborger, and P. J. Coles, Quantum 3
2019
Later among the works it cites.
M. Schuld and N. Killoran, Physical review letters 122
2019
Later among the works it cites.
M. Benedetti, E. Grant, L. Wossnig, and S. Severini, New Journal of Physics 21
2019
Later among the works it cites.
B. Nash, V. Gheorghiu, and M. Mosca, arXiv preprint arXiv:1904.01972 (2019)
Original
2019
Later among the works it cites.
H. Situ, Z. Huang, X. Zou, and S. Zheng, Quantum Information Processing 18
2019
Later among the works it cites.
R. Sweke, F. Wilde, J. Meyer, M. Schuld, P. K. Fährmann, B. Meynard-Piganeau, and J. Eisert, arXiv preprint arXiv:1910.01155 (2019)
Original
2019
Later among the works it cites.
Z. Wang, N. C. Rubin, J. M. Dominy, and E. G. Rieffel, arXiv preprint arXiv:1904.09314 (2019)
Original
2019
Later among the works it cites.
I. Cong, S. Choi, and M. D. Lukin, Nature Physics 15
2019
Later among the works it cites.
J. Romero and A. Aspuru-Guzik, arXiv preprint arXiv:1901.00848 (2019)
Original
2019
Later among the works it cites.
M. Y. Niu, S. Boixo, V. N. Smelyanskiy, and H. Neven, npj Quantum Information 5
2019
Later among the works it cites.
C. Roberts and S. Leichenauer, “Introducing TensorNetwork, an Open Source Library for Efficient Tensor Calculations,” (2019)
2019
Later among the works it cites.
The TensorFlow Authors, “Effective TensorFlow 2,” (2019)
2019
Later among the works it cites.
G. E. Crooks, arXiv preprint arXiv:1905.13311 (2019)
Original
2019
Later among the works it cites.
E. Campbell, Physical Review Letters 123
2019
Later among the works it cites.
A. Harrow and J. Napp, arXiv preprint arXiv:1901.05374 (2019)
Original
2019
Later among the works it cites.
V. Havlíček, A. D. Córcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, Nature 567
2019
Later among the works it cites.
W. Huggins, P. Patil, B. Mitchell, K. B. Whaley, and E. M. Stoudenmire, Quantum Science and Technology 4
2019
Later among the works it cites.
E. Grant, L. Wossnig, M. Ostaszewski, and M. Benedetti, Quantum 3
2019
Later among the works it cites.
O. Higgott, D. Wang, and S. Brierley, Quantum 3
2019
Later among the works it cites.
K. M. Nakanishi, K. Mitarai, and K. Fujii, Physical Review Research 1
2019
Later among the works it cites.
H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, Nature communications 10
2019
Later among the works it cites.
N. Yamamoto, arXiv preprint arXiv:1909.05074 (2019)
Original
2019
Later among the works it cites.
A. Smith, M. S. Kim, F. Pollmann, and J. Knolle, npj Quantum Information 5
2019
Later among the works it cites.
W. W. Ho and T. H. Hsieh, SciPost Phys. 6
2019
Later among the works it cites.
O. Vinyals, I. Babuschkin, W. M. Czarnecki, M. Mathieu, A. Dudzik, J. Chung, D. H. Choi, R. Powell, T. Ewalds, P. Georgiev, et al. , Nature 575
2019
Later among the works it cites.
Google AI Quantum and Collaborators, Science 369
2020
Closest in time.
K. K. van Dam, From Long-distance Entanglement to Building a Nationwide Quantum Internet: Report of the DOE Quantum Internet Blueprint Workshop , Tech. Rep. BNL-216179-2020-FORE (Brookhaven National Laboratory, 2020)
2020
Closest in time.
J. Carolan, M. Mohseni, J. P. Olson, M. Prabhu, C. Chen, D. Bunandar, M. Y. Niu, N. C. Harris, F. N. C. Wong, M. Hochberg, S. Lloyd, and D. Englund, Nature Physics (2020)
2020
Closest in time.
Intel®, “Intel® Instruction Set Extensions Technology,” (2020)
2020
Closest in time.
X.-Z. Luo, J.-G. Liu, P. Zhang, and L. Wang, Quantum 4
2020
Closest in time.
M. Y. Niu, L. Li, M. Mohseni, and I. Chuang, to be published (2020)
2020
Closest in time.
M. Streif and M. Leib, Quantum Sci. Technol. 5
2020
Closest in time.
M. Cerezo, A. Sone, T. Volkoff, L. Cincio, and P. J. Coles, arXiv preprint arXiv:2001.00550 (2020)
Original
2020
Closest in time.
S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Reviews of Modern Physics 92
2020
Closest in time.
P. K. Barkoutsos, G. Nannicini, A. Robert, I. Tavernelli, and S. Woerner, Quantum 4
2020
Closest in time.
J. R. McClean, N. C. Rubin, K. J. Sung, I. D. Kivlichan, X. Bonet-Monroig, Y. Cao, C. Dai, E. S. Fried, C. Gidney, B. Gimby, et al. , Quantum Science and Technology 5
2020
Closest in time.
A. V. Uvarov, A. S. Kardashin, and J. D. Biamonte, Phys. Rev. A 102
2020
Closest in time.
D. Wierichs, C. Gogolin, and M. Kastoryano, Phys. Rev. Research 2
2020
Closest in time.
R. Wiersema, C. Zhou, Y. de Sereville, J. F. Carrasquilla, Y. B. Kim, and H. Yuen, PRX Quantum 1
2020
Closest in time.
F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, A. Bengtsson, S. Boixo, M. Broughton, B. B. Buckley, et al. , arXiv preprint arXiv:2010.07965 (2020)
Original
2020
Closest in time.
N. Klco and M. J. Savage, Phys. Rev. A 102
2020
Closest in time.
S. Y.-C. Chen, C.-H. H. Yang, J. Qi, P.-Y. Chen, X. Ma, and H.-S. Goan, IEEE Access 8
2020
Closest in time.
O. Lockwood and M. Si, in Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment , Vol. 16 (2020) pp. 245–251
2020
Closest in time.
A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, Quantum 4
2020
Closest in time.
S. Wu, S. Jin, D. Wen, and X. Wang, arXiv preprint arXiv:2012.10711 (2020)
Original
2020
Closest in time.
J. J. Meyer, J. Borregaard, and J. Eisert, npj Quantum Information 7
2021
Closest in time.
M. Y. Niu, A. Zlokapa, M. Broughton, S. Boixo, M. Mohseni, V. Smelyanskyi, and H. Neven, “Entangling quantum generative adversarial networks,” (2021), arXiv:2105.00080 [quant-ph]
Original
2021
Closest in time.
J. M. Martinis, npj Quantum Inf 7
2021
Closest in time.
M. McEwen, L. Faoro, K. Arya, A. Dunsworth, T. Huang, S. Kim, B. Burkett, A. Fowler, F. Arute, J. C. Bardin, A. Bengtsson, A. Bilmes, B. B. Buckley, N. Bushnell, Z. Chen, R. Collins, S. Demura, A. R. Derk, C. Erickson, M. Giustina, S. D. Harrington, S. Hong, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, P. Laptev, A. Locharla, X. Mi, K. C. Miao, S. Montazeri, J. Mutus, O. Naaman, M. Neeley, C. Neill, A. Opremcak, C. Quintana, N. Redd, P. Roushan, D. Sank, K. J. Satzinger, V. Shvarts, T. White, Z. J. Yao, P. Yeh, J. Yoo, Y. Chen, V. Smelyanskiy, J. M. Martinis, H. Neven, A. Megrant, L. Ioffe, and R. Barends, “Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits,” (2021), arXiv:2104.05219 [quant-ph]
Original
2021
Closest in time.
E. Campos, A. Nasrallah, and J. Biamonte, Physical Review A 103
2021
Closest in time.
M. Ostaszewski, E. Grant, and M. Benedetti, Quantum 5
2021
Closest in time.
S. Jerbi, C. Gyurik, S. Marshall, H. J. Briegel, and V. Dunjko, “Variational quantum policies for reinforcement learning,” (2021), arXiv:2103.05577 [quant-ph]
Original
2021
Closest in time.
O. Lockwood and M. Si, in NeurIPS 2020 Workshop on Pre-registration in Machine Learning (PMLR, 2021) pp. 285–301
2021
Closest in time.
M. Schuld, R. Sweke, and J. J. Meyer, Physical Review A 103
2021
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…