Machine learning in physics

Applications of machine learning to quantum physics

This article is about classical machine learning of quantum systems. For machine learning enhanced by quantum computation, see quantum machine learning.

Part of a series of articles about

Quantum mechanics
i ℏ d d t | Ψ ⟩ = H ^ | Ψ ⟩ {\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }

Schrödinger equation

* Introduction
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Background

* Classical mechanics
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Fundamentals

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Formulations

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Interpretations

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Advanced topics

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Applying machine learning (ML) (including deep learning) methods to the study of quantum systems is 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][3] learning quantum phase transitions,[4][5] and automatically generating new quantum experiments.[6][7][8][9] ML 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 technology development, and computational materials design. In this context, for example, it can be used as a tool to interpolate pre-calculated interatomic potentials,[10] or directly solving the Schrödinger equation with a variational method.[11]

## 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,[12] Hamiltonian learning,[13] and the characterization of an unknown unitary transformation.[14][15] 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;[16][17][18]
* Extracting information on unknown states;[19][20][21][12][22][1]
* Learning unknown unitary transformations and measurements;[14][15]
* Engineering of quantum gates from qubit networks with pairwise interactions, using time dependent[23] or independent[24] 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.[25]

### 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.[26] This can be helpful for the computational design of new molecules or materials. Some examples include

* Interpolating interatomic potentials;[27]
* Inferring molecular atomization energies throughout chemical compound space;[28]
* Accurate potential energy surfaces with restricted Boltzmann machines;[29]
* Automatic generation of new quantum experiments;[6][7]
* Solving the many-body, static and time-dependent Schrödinger equation;[11]
* Identifying phase transitions from entanglement spectra;[30]
* Generating adaptive feedback schemes for quantum metrology and quantum tomography.[31][32]

### Variational circuits

[edit]

Variational circuits are a family of algorithms which utilize training based on circuit parameters and an objective function.[33] 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.[34] 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.[35]

### Fluid dynamics

[edit]

This section is an excerpt from Deep learning § Partial differential equations.[edit]

Physics informed neural networks have been used to solve partial differential equations in both forward and inverse problems in a data driven manner.[36] One example is the reconstructing fluid flow governed by the Navier-Stokes equations. Using physics informed neural networks does not require the often expensive mesh generation that conventional CFD methods rely on.[37][38]

### Physics discovery and prediction

[edit]

See also: Laboratory robotics

Illustration of how an AI learns the basic fundamental physical concept of 'unchangeableness'[39]

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.[40][39] 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.[41][42] In the future, it may be possible that such can be used to automate the discovery of physical laws of complex systems.[41] 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(s) needed] In specific, prior machine learning models were "highly specialised and lack a general understanding of the world".[40]

## See also

[edit]

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

## References

[edit]

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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. S2CID 9928389.
3. ^ Cao, Chenfeng; Hou, Shi-Yao; Cao, Ningping; Zeng, Bei (2020-02-10). "Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates". Journal of Physics: Condensed Matter. 33 (6): 064002. arXiv:2007.05962. doi:10.1088/1361-648x/abc4cf. ISSN 0953-8984. PMID 33105109. S2CID 220496757.
4. ^ Broecker, Peter; Assaad, Fakher F.; Trebst, Simon (2017-07-03). "Quantum phase recognition via unsupervised machine learning". arXiv:1707.00663 [cond-mat.str-el].
5. ^ 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. S2CID 125593239.
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18. ^ 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. S2CID 55126023.
19. ^ 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. S2CID 43413485.
20. ^ 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. S2CID 119383508.
21. ^ Sentís, Gael; Guţă, Mădălin; Adesso, Gerardo (2015-07-09). "Quantum learning of coherent states". EPJ Quantum Technology. 2 (1): 17. arXiv:1410.8700. Bibcode:2015EPJQT...2...17S. doi:10.1140/epjqt/s40507-015-0030-4. ISSN 2196-0763. S2CID 6980007.
22. ^ 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. S2CID 119095806.
23. ^ 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. S2CID 7299645.
24. ^ 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 (1): 16019. arXiv:1509.04298. Bibcode:2016npjQI...216019B. doi:10.1038/npjqi.2016.19. hdl:11858/00-001M-0000-002C-AA64-F.
25. ^ 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 (1): 014011. arXiv:2003.01643. Bibcode:2020PhRvP..14a4011N. doi:10.1103/PhysRevApplied.14.014011. S2CID 211817864.
26. ^ 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.
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* v
* t
* e

Differentiable computing

General|

* Differentiable programming
* Information geometry
* Statistical manifold
* Automatic differentiation
* Neuromorphic computing
* Pattern recognition
* Ricci calculus
* Computational learning theory
* Inductive bias

Hardware|

* IPU
* TPU
* VPU
* Memristor
* SpiNNaker

Software libraries|

* TensorFlow
* PyTorch
* Keras
* scikit-learn
* Theano
* JAX
* Flux.jl
* MindSpore

* Portals
* Computer programming
* Technology

* v
* t
* e

Quantum information science

General|

* DiVincenzo's criteria
* NISQ era
* Quantum computing
* timeline
* Quantum information
* Quantum programming
* Quantum simulation
* Qubit
* physical vs. logical
* Quantum processors
* cloud-based

Theorems|

* Bell's
* Eastin–Knill
* Gleason's
* Gottesman–Knill
* Holevo's
* No-broadcasting
* No-cloning
* No-communication
* No-deleting
* No-hiding
* No-teleportation
* PBR
* Quantum speed limit
* Threshold
* Solovay–Kitaev
* Schrödinger-HJW

Quantum
communication|

* Classical capacity
* entanglement-assisted
* quantum capacity
* Entanglement distillation
* Entanglement swapping
* Monogamy of entanglement
* LOCC
* Quantum channel
* quantum network
* State purification
* Quantum teleportation
* quantum energy teleportation
* quantum gate teleportation
* Superdense coding

| Quantum cryptography|

* Post-quantum cryptography
* Quantum coin flipping
* Quantum money
* Quantum key distribution
* BB84
* SARG04
* other protocols
* Quantum secret sharing

|

Quantum algorithms|

* Algorithmic cooling
* Amplitude amplification
* Bernstein–Vazirani
* BHT
* Boson sampling
* Deutsch–Jozsa
* Grover's
* HHL
* Hidden subgroup
* Magic state distillation
* Quantum annealing
* Quantum counting
* Quantum Fourier transform
* Quantum optimization
* Quantum phase estimation
* Shor's
* Simon's
* VQE

Quantum
complexity theory|

* BQP
* DQC1
* EQP
* QIP
* QMA
* PostBQP

Quantum
processor benchmarks|

* Quantum supremacy
* Quantum volume
* Randomized benchmarking
* XEB
* Relaxation times
* T1
* T2

Quantum
computing models|

* Adiabatic quantum computation
* Continuous-variable quantum information
* One-way quantum computer
* cluster state
* Quantum circuit
* quantum logic gate
* Quantum machine learning
* quantum neural network
* Quantum Turing machine
* Topological quantum computer
* Hamiltonian quantum computation

Quantum
error correction|

* Codes
* 5 qubit
* CSS
* GKP
* quantum convolutional
* stabilizer
* Shor
* Bacon–Shor
* Steane
* Toric
* gnu
* Entanglement-assisted

Physical
implementations|

| Quantum optics|

* Cavity QED
* Circuit QED
* Linear optical QC
* KLM protocol

|

Ultracold atoms|

* Neutral atom QC
* Trapped-ion QC

Spin-based|

* Kane QC
* Spin qubit QC
* NV center
* NMR QC

Superconducting|

* Charge qubit
* Flux qubit
* Phase qubit
* Transmon

Quantum
programming|

* OpenQASM–Qiskit–IBM QX
* Quil–Forest/Rigetti QCS
* Cirq
* Q#
* libquantum
* many others...

* Quantum information science
* Quantum mechanics topics

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