Machine learning in physics

Part of a series of articles about
Quantum mechanics
${\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }$ Schrödinger equation
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Complementarity Decoherence Entanglement Energy level Measurement Nonlocality Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function Collapse
Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Leggett–Garg inequality Mach–Zehnder Popper Quantum eraser Delayed-choice Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Overview Bayesian Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Local Many-worlds Objective collapse Quantum logic Relational Transactional
Advanced topics Relativistic quantum mechanics Quantum field theory Quantum information science Quantum computing Quantum chaos Density matrix Scattering theory Quantum statistical mechanics Quantum machine learning
Scientists Aharonov Bell Bethe Blackett Bloch Bohm Bohr Born Bose de Broglie Compton Dirac Davisson Debye Ehrenfest Einstein Everett Fock Fermi Feynman Glauber Gutzwiller Heisenberg Hilbert Jordan Kramers Pauli Lamb Landau Laue Moseley Millikan Onnes Planck Rabi Raman Rydberg Schrödinger Simmons Sommerfeld von Neumann Weyl Wien Wigner Zeeman Zeilinger
v t

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][3] learning quantum phase transitions,^[4][5] and automatically generating new quantum experiments.^[6][7][8][9] 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^[10] or directly solving the Schrödinger equation with a variational method.^[11]

Applications of machine learning to physics[]

Noisy data[]

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[]

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[]

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[]

Machine learning techniques can be used to find a better manifold of integration for path integrals in order to avoid the sign problem.^[35]

See also[]

• Quantum computing
• Quantum machine learning
• Quantum algorithm for linear systems of equations
• Quantum annealing
• Quantum neural network

References[]