Machine learning in physics source:

Applying classical methods of machine learning to the study of quantum systems (sometimes called quantum machine learning) is the focus of an emergent area of physics research. A basic example of this is quantum state tomography, where a quantum state is learned from measurement.[1] Other examples include learning Hamiltonians,[2] learning quantum phase transitions,[3][4] and automatically generating new quantum experiments.[5][6][7][8] Classical machine learning is effective at processing large amounts of experimental or calculated data in order to characterize an unknown quantum system, making its application useful in contexts including quantum information theory, quantum technologies development, and computational materials design. In this context, it can be used for example as a tool to interpolate pre-calculated interatomic potentials[9] or directly solving the Schrödinger equation with a variational method.[10]

Applications of machine learning to physics[edit]

Noisy data[edit]

The ability to experimentally control and prepare increasingly complex quantum systems brings with it a growing need to turn large and noisy data sets into meaningful information. This is a problem that has already been studied extensively in the classical setting, and consequently, many existing machine learning techniques can be naturally adapted to more efficiently address experimentally relevant problems. For example, Bayesian methods and concepts of algorithmic learning can be fruitfully applied to tackle quantum state classification,[11] Hamiltonian learning,[12] and the characterization of an unknown unitary transformation.[13][14] Other problems that have been addressed with this approach are given in the following list:

  • Identifying an accurate model for the dynamics of a quantum system, through the reconstruction of the Hamiltonian;[15][16][17]
  • Extracting information on unknown states;[18][19][20][11][21][1]
  • Learning unknown unitary transformations and measurements;[13][14]
  • Engineering of quantum gates from qubit networks with pairwise interactions, using time dependent[22] or independent[23] Hamiltonians.
  • Improving the extraction accuracy of physical observables from absorption images of ultracold atoms (degenerate Fermi gas), by the generation of an ideal reference frame.[24]

Calculated and noise-free data[edit]

Quantum machine learning can also be applied to dramatically accelerate the prediction of quantum properties of molecules and materials.[25] This can be helpful for the computational design of new molecules or materials. Some examples include

  • Interpolating interatomic potentials;[26]
  • Inferring molecular atomization energies throughout chemical compound space;[27]
  • Accurate potential energy surfaces with restricted Boltzmann machines;[28]
  • Automatic generation of new quantum experiments;[5][6]
  • Solving the many-body, static and time-dependent Schrödinger equation;[10]
  • Identifying phase transitions from entanglement spectra;[29]
  • Generating adaptive feedback schemes for quantum metrology and quantum tomography.[30][31]

Variational Circuits[edit]

Variational circuits are a family of algorithms which utilize training based on circuit parameters and an objective function.[32] Variational circuits are generally composed of a classical device communicating input parameters (random or pre-trained parameters) into a quantum device, along with a classical Mathematical optimization function. These circuits are very heavily dependent on the architecture of the proposed quantum device because parameter adjustments are adjusted based solely on the classical components within the device.[33] Though the application is considerably infantile in the field of quantum machine learning, it has incredibly high promise for more efficiently generating efficient optimization functions.

Sign problem[edit]

Machine learning techniques can be used to find a better manifold of integration for path integrals in order to avoid the sign problem.[34]

See also[edit]


  1. ^ a b Torlai, Giacomo; Mazzola, Guglielmo; Carrasquilla, Juan; Troyer, Matthias; Melko, Roger; Carleo, Giuseppe (May 2018). "Neural-network quantum state tomography". Nature Physics. 14 (5): 447–450. arXiv:1703.05334. Bibcode:2018NatPh..14..447T. doi:10.1038/s41567-018-0048-5. ISSN 1745-2481.
  2. ^ Cory, D. G.; Wiebe, Nathan; Ferrie, Christopher; Granade, Christopher E. (2012-07-06). "Robust Online Hamiltonian Learning". New Journal of Physics. 14 (10): 103013. arXiv:1207.1655. Bibcode:2012NJPh...14j3013G. doi:10.1088/1367-2630/14/10/103013.
  3. ^ Broecker, Peter; Assaad, Fakher F.; Trebst, Simon (2017-07-03). "Quantum phase recognition via unsupervised machine learning". arXiv:1707.00663 [cond-mat.str-el].
  4. ^ Huembeli, Patrick; Dauphin, Alexandre; Wittek, Peter (2018). "Identifying Quantum Phase Transitions with Adversarial Neural Networks". Physical Review B. 97 (13): 134109. arXiv:1710.08382. Bibcode:2018PhRvB..97m4109H. doi:10.1103/PhysRevB.97.134109. ISSN 2469-9950.
  5. ^ a b Krenn, Mario (2016-01-01). "Automated Search for new Quantum Experiments". Physical Review Letters. 116 (9): 090405. arXiv:1509.02749. Bibcode:2016PhRvL.116i0405K. doi:10.1103/PhysRevLett.116.090405. PMID 26991161.
  6. ^ a b Knott, Paul (2016-03-22). "A search algorithm for quantum state engineering and metrology". New Journal of Physics. 18 (7): 073033. arXiv:1511.05327. Bibcode:2016NJPh...18g3033K. doi:10.1088/1367-2630/18/7/073033.
  7. ^ Dunjko, Vedran; Briegel, Hans J (2018-06-19). "Machine learning & artificial intelligence in the quantum domain: a review of recent progress". Reports on Progress in Physics. 81 (7): 074001. Bibcode:2018RPPh...81g4001D. doi:10.1088/1361-6633/aab406. hdl:1887/71084. ISSN 0034-4885. PMID 29504942.
  8. ^ Melnikov, Alexey A.; Nautrup, Hendrik Poulsen; Krenn, Mario; Dunjko, Vedran; Tiersch, Markus; Zeilinger, Anton; Briegel, Hans J. (1221). "Active learning machine learns to create new quantum experiments". Proceedings of the National Academy of Sciences. 115 (6): 1221–1226. arXiv:1706.00868. doi:10.1073/pnas.1714936115. ISSN 0027-8424. PMC 5819408. PMID 29348200.
  9. ^ Behler, Jörg; Parrinello, Michele (2007-04-02). "Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces". Physical Review Letters. 98 (14): 146401. Bibcode:2007PhRvL..98n6401B. doi:10.1103/PhysRevLett.98.146401. PMID 17501293.
  10. ^ a b Carleo, Giuseppe; Troyer, Matthias (2017-02-09). "Solving the quantum many-body problem with artificial neural networks". Science. 355 (6325): 602–606. arXiv:1606.02318. Bibcode:2017Sci...355..602C. doi:10.1126/science.aag2302. PMID 28183973.
  11. ^ a b Sentís, Gael; Calsamiglia, John; Muñoz-Tapia, Raúl; Bagan, Emilio (2012). "Quantum learning without quantum memory". Scientific Reports. 2: 708. arXiv:1106.2742. Bibcode:2012NatSR...2E.708S. doi:10.1038/srep00708. PMC 3464493. PMID 23050092.
  12. ^ Wiebe, Nathan; Granade, Christopher; Ferrie, Christopher; Cory, David (2014). "Quantum Hamiltonian learning using imperfect quantum resources". Physical Review A. 89 (4): 042314. arXiv:1311.5269. Bibcode:2014PhRvA..89d2314W. doi:10.1103/physreva.89.042314. hdl:10453/118943.
  13. ^ a b Bisio, Alessandro; Chiribella, Giulio; D'Ariano, Giacomo Mauro; Facchini, Stefano; Perinotti, Paolo (2010). "Optimal quantum learning of a unitary transformation". Physical Review A. 81 (3): 032324. arXiv:0903.0543. Bibcode:2010PhRvA..81c2324B. doi:10.1103/PhysRevA.81.032324.
  14. ^ a b Jeongho; Junghee Ryu, Bang; Yoo, Seokwon; Pawłowski, Marcin; Lee, Jinhyoung (2014). "A strategy for quantum algorithm design assisted by machine learning". New Journal of Physics. 16 (1): 073017. arXiv:1304.2169. Bibcode:2014NJPh...16a3017K. doi:10.1088/1367-2630/16/1/013017.
  15. ^ Granade, Christopher E.; Ferrie, Christopher; Wiebe, Nathan; Cory, D. G. (2012-10-03). "Robust Online Hamiltonian Learning". New Journal of Physics. 14 (10): 103013. arXiv:1207.1655. Bibcode:2012NJPh...14j3013G. doi:10.1088/1367-2630/14/10/103013. ISSN 1367-2630.
  16. ^ Wiebe, Nathan; Granade, Christopher; Ferrie, Christopher; Cory, D. G. (2014). "Hamiltonian Learning and Certification Using Quantum Resources". Physical Review Letters. 112 (19): 190501. arXiv:1309.0876. Bibcode:2014PhRvL.112s0501W. doi:10.1103/PhysRevLett.112.190501. ISSN 0031-9007. PMID 24877920.
  17. ^ Wiebe, Nathan; Granade, Christopher; Ferrie, Christopher; Cory, David G. (2014-04-17). "Quantum Hamiltonian Learning Using Imperfect Quantum Resources". Physical Review A. 89 (4): 042314. arXiv:1311.5269. Bibcode:2014PhRvA..89d2314W. doi:10.1103/PhysRevA.89.042314. hdl:10453/118943. ISSN 1050-2947.
  18. ^ Sasaki, Madahide; Carlini, Alberto; Jozsa, Richard (2001). "Quantum Template Matching". Physical Review A. 64 (2): 022317. arXiv:quant-ph/0102020. Bibcode:2001PhRvA..64b2317S. doi:10.1103/PhysRevA.64.022317.
  19. ^ Sasaki, Masahide (2002). "Quantum learning and universal quantum matching machine". Physical Review A. 66 (2): 022303. arXiv:quant-ph/0202173. Bibcode:2002PhRvA..66b2303S. doi:10.1103/PhysRevA.66.022303.
  20. ^ Sentís, Gael; Guţă, Mădălin; Adesso, Gerardo (2015-07-09). "Quantum learning of coherent states". EPJ Quantum Technology. 2 (1): 17. arXiv:1410.8700. doi:10.1140/epjqt/s40507-015-0030-4. ISSN 2196-0763.
  21. ^ Lee, Sang Min; Lee, Jinhyoung; Bang, Jeongho (2018-11-02). "Learning unknown pure quantum states". Physical Review A. 98 (5): 052302. arXiv:1805.06580. Bibcode:2018PhRvA..98e2302L. doi:10.1103/PhysRevA.98.052302.
  22. ^ Zahedinejad, Ehsan; Ghosh, Joydip; Sanders, Barry C. (2016-11-16). "Designing High-Fidelity Single-Shot Three-Qubit Gates: A Machine Learning Approach". Physical Review Applied. 6 (5): 054005. arXiv:1511.08862. Bibcode:2016PhRvP...6e4005Z. doi:10.1103/PhysRevApplied.6.054005. ISSN 2331-7019.
  23. ^ Banchi, Leonardo; Pancotti, Nicola; Bose, Sougato (2016-07-19). "Quantum gate learning in qubit networks: Toffoli gate without time-dependent control". npj Quantum Information. 2: 16019. Bibcode:2016npjQI...216019B. doi:10.1038/npjqi.2016.19.
  24. ^ Ness, Gal; Vainbaum, Anastasiya; Shkedrov, Constantine; Florshaim, Yanay; Sagi, Yoav (2020-07-06). "Single-exposure absorption imaging of ultracold atoms using deep learning". Physical Review Applied. 14: 014011. arXiv:2003.01643. doi:10.1103/PhysRevApplied.14.014011.
  25. ^ von Lilienfeld, O. Anatole (2018-04-09). "Quantum Machine Learning in Chemical Compound Space". Angewandte Chemie International Edition. 57 (16): 4164–4169. doi:10.1002/anie.201709686. PMID 29216413.
  26. ^ Bartok, Albert P.; Payne, Mike C.; Risi, Kondor; Csanyi, Gabor (2010). "Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons" (PDF). Physical Review Letters. 104 (13): 136403. arXiv:0910.1019. Bibcode:2010PhRvL.104m6403B. doi:10.1103/PhysRevLett.104.136403. PMID 20481899.
  27. ^ Rupp, Matthias; Tkatchenko, Alexandre; Muller, Klaus-Robert; von Lilienfeld, O. Anatole (2012-01-31). "Fast and Accurate Modeling of Molecular Atomization Energies With Machine Learning". Physical Review Letters. 355 (6325): 602. arXiv:1109.2618. Bibcode:2012PhRvL.108e8301R. doi:10.1103/PhysRevLett.108.058301. PMID 22400967.
  28. ^ Xia, Rongxin; Kais, Sabre (2018-10-10). "Quantum machine learning for electronic structure calculations". Nature Communications. 9 (1): 4195. arXiv:1803.10296. Bibcode:2018NatCo...9.4195X. doi:10.1038/s41467-018-06598-z. PMC 6180079. PMID 30305624.
  29. ^ van Nieuwenburg, Evert; Liu, Ye-Hua; Huber, Sebastian (2017). "Learning phase transitions by confusion". Nature Physics. 13 (5): 435. arXiv:1610.02048. Bibcode:2017NatPh..13..435V. doi:10.1038/nphys4037.
  30. ^ Hentschel, Alexander (2010-01-01). "Machine Learning for Precise Quantum Measurement". Physical Review Letters. 104 (6): 063603. arXiv:0910.0762. Bibcode:2010PhRvL.104f3603H. doi:10.1103/PhysRevLett.104.063603. PMID 20366821.
  31. ^ Quek, Yihui; Fort, Stanislav; Ng, Hui Khoon (2018-12-17). "Adaptive Quantum State Tomography with Neural Networks". arXiv:1812.06693 [quant-ph].
  32. ^ "Variational Circuits — Quantum Machine Learning Toolbox 0.7.1 documentation". Retrieved 2018-12-06.
  33. ^ Schuld, Maria (2018-06-12). "Quantum Machine Learning 1.0". XanaduAI. Retrieved 2018-12-07.
  34. ^ Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry; Lawrence, Scott (2017). "Deep Learning Beyond Lefschetz Thimbles". Physical Review D. 96 (9): 094505. arXiv:1709.01971. Bibcode:2017PhRvD..96i4505A. doi:10.1103/PhysRevD.96.094505.