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Lecture

Computational Quantum Physics

In course

PHYS-463: Computational quantum physics

The numerical simulation of quantum systems plays a central role in modern physics. This course gives an introduction to key simulation approaches, through lectures and practical programming exercises. Simulation methods based both on classical and quantum ...

Description

This lecture covers Variational Monte Carlo methods for discrete and continuous systems, including Jastrow states and Markov-chain Monte Carlo algorithms. It also discusses the detailed balance principle and the Jastrow-Feynman expansion.

Instructor

Giuseppe Carleo

Giuseppe Carleo is a computational quantum physicist, whose main focus is the development of advanced numerical algorithms tostudy challenging problems involving strongly interacting quantum systems.He is best known for the introduction of machine learning techniques to study both equilibrium and dynamical properties,based on a neural-network representations of quantum states, as well for the time-dependent variational Monte Carlo method.He earned a Ph.D. in Condensed Matter Theory from the International School for Advanced Studies (SISSA) in Italy in 2011.He held postdoctoral positions at the Institut d’Optique in France and ETH Zurich in Switzerland, where he alsoserved as a lecturer in computational quantum physics.In 2018, he joined the Flatiron Institute in New York City in 2018 at the Center for Computational Quantum Physics (CCQ), working as a Research Scientist and project leader, and also leading the development of the open-source project NetKet.Since September 2020 he is an assistant professor at EPFL, in Switzerland, leading the Computational Quantum Science Laboratory (CQSL).

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Related concepts (32)

Continuous or discrete variable

In mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively. If it can take on two particular real values such that it can also take on all real values between them (even values that are arbitrarily close together), the variable is continuous in that interval. If it can take on a value such that there is a non-infinitesimal gap on each side of it containing no values that the variable can take on, then it is discrete around that value.

Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm.

Measurement in quantum mechanics

In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule.

Quantum mechanics

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.

Philosophy of physics

In philosophy, philosophy of physics deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists. Philosophy of physics can be broadly divided into three areas: interpretations of quantum mechanics: mainly concerning issues with how to formulate an adequate response to the measurement problem and understand what the theory says about reality.

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