Machine learning in physics

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,{{cite journal|last1=Sentís|first1=Gael|last2=Calsamiglia|first2=John|last3=Muñoz-Tapia|first3=Raúl|last4=Bagan|first4=Emilio|year=2012|title=Quantum learning without quantum memory|journal=Scientific Reports|volume=2|page=708|arxiv=1106.2742|bibcode=2012NatSR...2..708S|doi=10.1038/srep00708|pmc=3464493|pmid=23050092}} Hamiltonian learning,{{cite journal|last1=Wiebe|first1=Nathan|last2=Granade|first2=Christopher|last3=Ferrie|first3=Christopher|last4=Cory|first4=David|year=2014|title=Quantum Hamiltonian learning using imperfect quantum resources|journal=Physical Review A|volume=89|issue=4|page=042314|arxiv=1311.5269|bibcode=2014PhRvA..89d2314W|doi=10.1103/physreva.89.042314|hdl=10453/118943|s2cid=55126023}} and the characterization of an unknown unitary transformation.{{Cite journal|last1=Bisio|first1=Alessandro|last2=Chiribella|first2=Giulio|last3=D'Ariano|first3=Giacomo Mauro|last4=Facchini|first4=Stefano|last5=Perinotti|first5=Paolo|year=2010|title=Optimal quantum learning of a unitary transformation|journal=Physical Review A|volume=81|issue=3|pages=032324|arxiv=0903.0543|bibcode=2010PhRvA..81c2324B|doi=10.1103/PhysRevA.81.032324|s2cid=119289138}}{{cite journal|last1=Jeongho|last2=Junghee Ryu|first2=Bang|last3=Yoo|first3=Seokwon|last4=Pawłowski|first4=Marcin|last5=Lee|first5=Jinhyoung|year=2014|title=A strategy for quantum algorithm design assisted by machine learning|journal=New Journal of Physics|volume=16|issue=1|page=073017|arxiv=1304.2169|bibcode=2014NJPh...16a3017K|doi=10.1088/1367-2630/16/1/013017|s2cid=54494244}} 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;{{Cite journal|last1=Granade|first1=Christopher E.|last2=Ferrie|first2=Christopher|last3=Wiebe|first3=Nathan|last4=Cory|first4=D. G.|date=2012-10-03|title=Robust Online Hamiltonian Learning|journal=New Journal of Physics|volume=14|issue=10|pages=103013|arxiv=1207.1655|bibcode=2012NJPh...14j3013G|doi=10.1088/1367-2630/14/10/103013|s2cid=9928389|issn=1367-2630}}{{Cite journal|last1=Wiebe|first1=Nathan|last2=Granade|first2=Christopher|last3=Ferrie|first3=Christopher|last4=Cory|first4=D. G.|year=2014|title=Hamiltonian Learning and Certification Using Quantum Resources|journal=Physical Review Letters|volume=112|issue=19|pages=190501|arxiv=1309.0876|bibcode=2014PhRvL.112s0501W|doi=10.1103/PhysRevLett.112.190501|issn=0031-9007|pmid=24877920|s2cid=39126228}}{{Cite journal|last1=Wiebe|first1=Nathan|last2=Granade|first2=Christopher|last3=Ferrie|first3=Christopher|last4=Cory|first4=David G.|date=2014-04-17|title=Quantum Hamiltonian Learning Using Imperfect Quantum Resources|journal=Physical Review A|volume=89|issue=4|pages=042314|arxiv=1311.5269|bibcode=2014PhRvA..89d2314W|doi=10.1103/PhysRevA.89.042314|issn=1050-2947|hdl=10453/118943|s2cid=55126023}}
• Extracting information on unknown states;{{Cite journal|last1=Sasaki|first1=Madahide|last2=Carlini|first2=Alberto|last3=Jozsa|first3=Richard|date=2001|title=Quantum Template Matching|journal=Physical Review A|volume=64|issue=2|pages=022317|arxiv=quant-ph/0102020|bibcode=2001PhRvA..64b2317S|doi=10.1103/PhysRevA.64.022317|s2cid=43413485}}{{Cite journal|last=Sasaki|first=Masahide|date=2002|title=Quantum learning and universal quantum matching machine|journal=Physical Review A|volume=66|issue=2|pages=022303|arxiv=quant-ph/0202173|bibcode=2002PhRvA..66b2303S|doi=10.1103/PhysRevA.66.022303|s2cid=119383508}}{{Cite journal|last1=Sentís|first1=Gael|last2=Guţă|first2=Mădălin|last3=Adesso|first3=Gerardo|date=2015-07-09|title=Quantum learning of coherent states|journal=EPJ Quantum Technology|language=en|volume=2|issue=1|pages=17|doi=10.1140/epjqt/s40507-015-0030-4|issn=2196-0763|arxiv=1410.8700|bibcode=2015EPJQT...2...17S |s2cid=6980007}}{{Cite journal|last1=Lee|first1=Sang Min|last2=Lee|first2=Jinhyoung|last3=Bang|first3=Jeongho|date=2018-11-02|title=Learning unknown pure quantum states|journal=Physical Review A|language=en|volume=98|issue=5|pages=052302|arxiv=1805.06580|doi=10.1103/PhysRevA.98.052302|bibcode=2018PhRvA..98e2302L|s2cid=119095806}}
• Learning unknown unitary transformations and measurements;
• Engineering of quantum gates from qubit networks with pairwise interactions, using time dependent{{Cite journal|last1=Zahedinejad|first1=Ehsan|last2=Ghosh|first2=Joydip|last3=Sanders|first3=Barry C.|date=2016-11-16|title=Designing High-Fidelity Single-Shot Three-Qubit Gates: A Machine Learning Approach|journal=Physical Review Applied|volume=6|issue=5|pages=054005|arxiv=1511.08862|bibcode=2016PhRvP...6e4005Z|doi=10.1103/PhysRevApplied.6.054005|s2cid=7299645|issn=2331-7019}} or independent{{Cite journal|last1=Banchi|first1=Leonardo|last2=Pancotti|first2=Nicola|last3=Bose|first3=Sougato|date=2016-07-19|title=Quantum gate learning in qubit networks: Toffoli gate without time-dependent control|journal=npj Quantum Information|volume=2|issue=1 |pages=16019|bibcode=2016npjQI...216019B|doi=10.1038/npjqi.2016.19|doi-access=free|hdl=11858/00-001M-0000-002C-AA64-F|hdl-access=free}} 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.{{Cite journal|last1=Ness|first1=Gal|last2=Vainbaum|first2=Anastasiya|last3=Shkedrov|first3=Constantine|last4=Florshaim|first4=Yanay|last5=Sagi|first5=Yoav|date=2020-07-06|title=Single-exposure absorption imaging of ultracold atoms using deep learning|journal=Physical Review Applied|volume=14|issue=1 |pages=014011|arxiv=2003.01643|doi=10.1103/PhysRevApplied.14.014011|bibcode=2020PhRvP..14a4011N |s2cid=211817864}}

Quantum machine learning can also be applied to dramatically accelerate the prediction of quantum properties of molecules and materials.{{Cite journal|last=von Lilienfeld|first=O. Anatole|date=2018-04-09|title=Quantum Machine Learning in Chemical Compound Space|journal=Angewandte Chemie International Edition|volume=57|issue=16|pages=4164–4169|doi=10.1002/anie.201709686|pmid=29216413}} This can be helpful for the computational design of new molecules or materials. Some examples include

• Interpolating interatomic potentials;{{Cite journal|last1=Bartok|first1=Albert P.|last2=Payne|first2=Mike C.|last3=Risi|first3=Kondor|last4=Csanyi|first4=Gabor|date=2010|title=Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons|url=https://authors.library.caltech.edu/18339/1/Bartok2010p9871Phys_Rev_Lett.pdf|journal=Physical Review Letters|volume=104|issue=13|pages=136403|doi=10.1103/PhysRevLett.104.136403|pmid=20481899|arxiv=0910.1019|bibcode=2010PhRvL.104m6403B|s2cid=15918457}}
• Inferring molecular atomization energies throughout chemical compound space;{{Cite journal|last1=Rupp|first1=Matthias|last2=Tkatchenko|first2=Alexandre|last3=Müller|first3=Klaus-Robert|author-link3=Klaus-Robert Müller|last4=von Lilienfeld|first4=O. Anatole|date=2012-01-31|title=Fast and Accurate Modeling of Molecular Atomization Energies With Machine Learning|journal=Physical Review Letters|volume=355|issue=6325|pages=602|arxiv=1109.2618|bibcode=2012PhRvL.108e8301R|doi=10.1103/PhysRevLett.108.058301|pmid=22400967|s2cid=321566}}
• Accurate potential energy surfaces with restricted Boltzmann machines;{{Cite journal|last1=Xia|first1=Rongxin|last2=Kais|first2=Sabre|date=2018-10-10|title=Quantum machine learning for electronic structure calculations|journal=Nature Communications|volume=9|issue=1|pages=4195|doi=10.1038/s41467-018-06598-z|pmc=6180079|pmid=30305624|arxiv=1803.10296|bibcode=2018NatCo...9.4195X}}
• Automatic generation of new quantum experiments;
• Solving the many-body, static and time-dependent Schrödinger equation;{{Cite journal|last1=Carleo|first1=Giuseppe|last2=Troyer|first2=Matthias|date=2017-02-09|title=Solving the quantum many-body problem with artificial neural networks|journal=Science|volume=355|issue=6325|pages=602–606|arxiv=1606.02318|bibcode=2017Sci...355..602C|doi=10.1126/science.aag2302|pmid=28183973|s2cid=206651104}}
• Identifying phase transitions from entanglement spectra;{{Cite journal|last1=van Nieuwenburg|first1=Evert|last2=Liu|first2=Ye-Hua|last3=Huber|first3=Sebastian|year=2017|title=Learning phase transitions by confusion|journal=Nature Physics|volume=13|issue=5|pages=435|arxiv=1610.02048|bibcode=2017NatPh..13..435V|doi=10.1038/nphys4037|s2cid=119285403}}
• Generating adaptive feedback schemes for quantum metrology and quantum tomography.{{Cite journal|last=Hentschel|first=Alexander|date=2010-01-01|title=Machine Learning for Precise Quantum Measurement|journal=Physical Review Letters|volume=104|issue=6|pages=063603|arxiv=0910.0762|bibcode=2010PhRvL.104f3603H|doi=10.1103/PhysRevLett.104.063603|pmid=20366821|s2cid=14689659}}{{cite arXiv|last1=Quek|first1=Yihui|last2=Fort|first2=Stanislav|last3=Ng|first3=Hui Khoon|date=2018-12-17|title=Adaptive Quantum State Tomography with Neural Networks|eprint=1812.06693|class=quant-ph}}

Variational circuits are a family of algorithms which utilize training based on circuit parameters and an objective function.{{Cite web|url=https://qmlt.readthedocs.io/en/latest/variational.html|title=Variational Circuits — Quantum Machine Learning Toolbox 0.7.1 documentation|website=qmlt.readthedocs.io|access-date=2018-12-06}} 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.{{Cite web|url=https://medium.com/xanaduai/quantum-machine-learning-1-0-76a525c8cf69|title=Quantum Machine Learning 1.0|last=Schuld|first=Maria|date=2018-06-12|website=XanaduAI|access-date=2018-12-07}} 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.

Machine learning techniques can be used to find a better manifold of integration for path integrals in order to avoid the sign problem.{{cite journal|arxiv=1709.01971|title=Deep Learning Beyond Lefschetz Thimbles|doi=10.1103/PhysRevD.96.094505|bibcode=2017PhRvD..96i4505A|year=2017|last1=Alexandru|first1=Andrei|last2=Bedaque|first2=Paulo F.|last3=Lamm|first3=Henry|last4=Lawrence|first4=Scott|journal=Physical Review D|volume=96|issue=9|pages=094505|s2cid=119074823}}

{{Excerpt|Deep learning|Partial differential equations}}

=== Physics discovery and prediction ===

{{See also|Laboratory robotics}}

File:An AI learns basic physical principles.webp

A deep learning system was reported to learn intuitive physics from visual data (of virtual 3D environments) based on an unpublished approach inspired by studies of visual cognition in infants.{{cite news |title=DeepMind AI learns physics by watching videos that don't make sense |url=https://www.newscientist.com/article/2327766-deepmind-ai-learns-physics-by-watching-videos-that-dont-make-sense |access-date=21 August 2022 |work=New Scientist}}{{cite journal |last1=Piloto |first1=Luis S. |last2=Weinstein |first2=Ari |last3=Battaglia |first3=Peter |last4=Botvinick |first4=Matthew |title=Intuitive physics learning in a deep-learning model inspired by developmental psychology |journal=Nature Human Behaviour |date=11 July 2022 |volume=6 |issue=9 |pages=1257–1267 |doi=10.1038/s41562-022-01394-8 |pmid=35817932 |pmc=9489531 |language=en |issn=2397-3374|doi-access=free}} Other researchers have developed a machine learning algorithm that could discover sets of basic variables of various physical systems and predict the systems' future dynamics from video recordings of their behavior.{{cite news |last1=Feldman |first1=Andrey |title=Artificial physicist to unravel the laws of nature |url=https://www.advancedsciencenews.com/an-artificial-physicist-to-unravel-the-laws-of-nature/ |access-date=21 August 2022 |work=Advanced Science News |date=11 August 2022}}{{cite journal |last1=Chen |first1=Boyuan |last2=Huang |first2=Kuang |last3=Raghupathi |first3=Sunand |last4=Chandratreya |first4=Ishaan |last5=Du |first5=Qiang |last6=Lipson |first6=Hod |title=Automated discovery of fundamental variables hidden in experimental data |journal=Nature Computational Science |date=July 2022 |volume=2 |issue=7 |pages=433–442 |doi=10.1038/s43588-022-00281-6 |pmid=38177869 |s2cid=251087119 |language=en |issn=2662-8457}} In the future, it may be possible that such can be used to automate the discovery of physical laws of complex systems. Beyond discovery and prediction, "blank slate"-type of learning of fundamental aspects of the physical world may have further applications such as improving adaptive and broad artificial general intelligence.{{additional citation needed|date=August 2022}} In specific, prior machine learning models were "highly specialised and lack a general understanding of the world".

• Quantum computing
• Quantum machine learning
• Quantum annealing
• Quantum neural network
• HHL Algorithm

{{Reflist |30em}}

{{Differentiable computing}}

{{Quantum computing}}

Category:Machine learning

Category:Quantum information science

Category:Theoretical computer science

Category:Quantum programming