Related papers: Hamiltonian Learning in Quantum Field Theories
The relativistic free particle system in 1+1 dimensions is formulated as a ``bi-Hamiltonian system''. One Hamiltonian generates ordinary time translations, and another generates (essentially) boosts. Any observer, accelerated or not, sees…
Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e^{-iHt}. A variety of techniques exist that accomplish this task, with the most common…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…
In this paper, we develop a wave function renormalization scheme for models of non-relativistic quantum particles interacting with a quantized relativistic field, in the Hamiltonian formalism of quantum field theory. We construct the…
Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the…
This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072,…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to…
We consider the problem of learning an interpretable potential energy function from a Hamiltonian system's trajectories. We address this problem for classical, separable Hamiltonian systems. Our approach first constructs a neural network…
Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…
A simple example is used to show that renormalization group limit cycles of effective quantum theories can be studied in a new way. The method is based on the similarity renormalization group procedure for Hamiltonians. The example contains…
Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…
We propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory. We consider the following essential and related problems : i) how to find the correct…
Learning about physical systems from quantum-enhanced experiments, relying on a quantum memory and quantum processing, can outperform learning from experiments in which only classical memory and processing are available. Whereas quantum…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators. Yet rigorous methods for time-dependent Hamiltonians and Lindbladians remain scarce despite their wide use. We close this gap by learning the…
The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and…