Machine learning in physics

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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]

Contents

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:

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

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]

Fluid dynamics

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 relies on. [37] [38]

Physics discovery and prediction

Illustration of how an AI learns the basic fundamental physical concept of 'unchangeableness' An AI learns basic physical principles.webp
Illustration of how an AI learns the basic fundamental physical concept of 'unchangeableness'

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

Related Research Articles

Quantum metrology is the study of making high-resolution and highly sensitive measurements of physical parameters using quantum theory to describe the physical systems, particularly exploiting quantum entanglement and quantum squeezing. This field promises to develop measurement techniques that give better precision than the same measurement performed in a classical framework. Together with quantum hypothesis testing, it represents an important theoretical model at the basis of quantum sensing.

The Bose–Hubbard model gives a description of the physics of interacting spinless bosons on a lattice. It is closely related to the Hubbard model that originated in solid-state physics as an approximate description of superconducting systems and the motion of electrons between the atoms of a crystalline solid. The model was introduced by Gersch and Knollman in 1963 in the context of granular superconductors. The model rose to prominence in the 1980s after it was found to capture the essence of the superfluid-insulator transition in a way that was much more mathematically tractable than fermionic metal-insulator models.

Reservoir computing is a framework for computation derived from recurrent neural network theory that maps input signals into higher dimensional computational spaces through the dynamics of a fixed, non-linear system called a reservoir. After the input signal is fed into the reservoir, which is treated as a "black box," a simple readout mechanism is trained to read the state of the reservoir and map it to the desired output. The first key benefit of this framework is that training is performed only at the readout stage, as the reservoir dynamics are fixed. The second is that the computational power of naturally available systems, both classical and quantum mechanical, can be used to reduce the effective computational cost.

<span class="mw-page-title-main">Landau–Zener formula</span> Formula for the probability that a system will change between two energy states.

The Landau–Zener formula is an analytic solution to the equations of motion governing the transition dynamics of a two-state quantum system, with a time-dependent Hamiltonian varying such that the energy separation of the two states is a linear function of time. The formula, giving the probability of a diabatic transition between the two energy states, was published separately by Lev Landau, Clarence Zener, Ernst Stueckelberg, and Ettore Majorana, in 1932.

Within quantum technology, a quantum sensor utilizes properties of quantum mechanics, such as quantum entanglement, quantum interference, and quantum state squeezing, which have optimized precision and beat current limits in sensor technology. The field of quantum sensing deals with the design and engineering of quantum sources and quantum measurements that are able to beat the performance of any classical strategy in a number of technological applications. This can be done with photonic systems or solid state systems.

<span class="mw-page-title-main">Topological insulator</span> State of matter with insulating bulk but conductive boundary

A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material.

The toric code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice. It is the simplest and most well studied of the quantum double models. It is also the simplest example of topological order—Z2 topological order (first studied in the context of Z2 spin liquid in 1991). The toric code can also be considered to be a Z2 lattice gauge theory in a particular limit. It was introduced by Alexei Kitaev.

In quantum many-body physics, topological degeneracy is a phenomenon in which the ground state of a gapped many-body Hamiltonian becomes degenerate in the limit of large system size such that the degeneracy cannot be lifted by any local perturbations.

<span class="mw-page-title-main">Time crystal</span> Structure that repeats in time; a novel type or phase of non-equilibrium matter

In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is already in its quantum ground state. Time crystals were first proposed theoretically by Frank Wilczek in 2012 as a time-based analogue to common crystals – whereas the atoms in crystals are arranged periodically in space, the atoms in a time crystal are arranged periodically in both space and time. Several different groups have demonstrated matter with stable periodic evolution in systems that are periodically driven. In terms of practical use, time crystals may one day be used as quantum computer memory.

<span class="mw-page-title-main">Quantum scar</span> Phenomenon in quantum systems

In quantum mechanics, quantum scarring is a phenomenon where the eigenstates of a classically chaotic quantum system have enhanced probability density around the paths of unstable classical periodic orbits. The instability of the periodic orbit is a decisive point that differentiates quantum scars from the more trivial observation that the probability density is enhanced in the neighborhood of stable periodic orbits. The latter can be understood as a purely classical phenomenon, a manifestation of the Bohr correspondence principle, whereas in the former, quantum interference is essential. As such, scarring is both a visual example of quantum-classical correspondence, and simultaneously an example of a (local) quantum suppression of chaos.

<span class="mw-page-title-main">Quantum machine learning</span> Interdisciplinary research area at the intersection of quantum physics and machine learning

Quantum machine learning is the integration of quantum algorithms within machine learning programs.

<span class="mw-page-title-main">Interatomic potential</span> Functions for calculating potential energy

Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space. Interatomic potentials are widely used as the physical basis of molecular mechanics and molecular dynamics simulations in computational chemistry, computational physics and computational materials science to explain and predict materials properties. Examples of quantitative properties and qualitative phenomena that are explored with interatomic potentials include lattice parameters, surface energies, interfacial energies, adsorption, cohesion, thermal expansion, and elastic and plastic material behavior, as well as chemical reactions.

A quantum heat engine is a device that generates power from the heat flow between hot and cold reservoirs. The operation mechanism of the engine can be described by the laws of quantum mechanics. The first realization of a quantum heat engine was pointed out by Scovil and Schulz-DuBois in 1959, showing the connection of efficiency of the Carnot engine and the 3-level maser. Quantum refrigerators share the structure of quantum heat engines with the purpose of pumping heat from a cold to a hot bath consuming power first suggested by Geusic, Schulz-DuBois, De Grasse and Scovil. When the power is supplied by a laser the process is termed optical pumping or laser cooling, suggested by Wineland and Hänsch. Surprisingly heat engines and refrigerators can operate up to the scale of a single particle thus justifying the need for a quantum theory termed quantum thermodynamics.

In physics, non-Hermitian quantum mechanics describes quantum mechanical systems where Hamiltonians are not Hermitian.

Many-body localization (MBL) is a dynamical phenomenon occurring in isolated many-body quantum systems. It is characterized by the system failing to reach thermal equilibrium, and retaining a memory of its initial condition in local observables for infinite times.

Shortcuts to adiabaticity (STA) are fast control protocols to drive the dynamics of system without relying on the adiabatic theorem. The concept of STA was introduced in a 2010 paper by Xi Chen et al. Their design can be achieved using a variety of techniques. A universal approach is provided by counterdiabatic driving, also known as transitionless quantum driving. Motivated by one of authors systematic study of dissipative Landau-Zener transition, the key idea was demonstrated earlier by a group of scientists from China, Greece and USA in 2000, as steering an eigenstate to destination. Counterdiabatic driving has been demonstrated in the laboratory using a time-dependent quantum oscillator.

Adolfo del Campo is a Spanish physicist and a professor of physics at the University of Luxembourg. He is best known for his work in quantum control and theoretical physics. He is notable as one of the pioneers of shortcuts to adiabaticity. He was elected as a Fellow of the American Physical Society in 2023.

Randomized benchmarking is an experimental method for measuring the average error rates of quantum computing hardware platforms. The protocol estimates the average error rates by implementing long sequences of randomly sampled quantum gate operations. Randomized benchmarking is the industry-standard protocol used by quantum hardware developers such as IBM and Google to test the performance of the quantum operations.

<span class="mw-page-title-main">Giuseppe Carleo</span> Italian physicist

Giuseppe Carleo is an Italian physicist. He is a professor of computational physics at EPFL and the head of the Laboratory of Computational Quantum Science.

Robert W. Spekkens is a Canadian theoretical quantum physicist working in the fields of quantum foundations and quantum information.

References

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