Related papers: Fourier-Flow model generating Feynman paths

This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…

In the present paper the author evaluates the path integral of a charged anisotropic Harmonic Oscillator (HO) in crossed electric and magnetic fields by two alternative methods. Both methods enable a rather formal calculation and circumvent…

The first application of a quantum algorithm to Feynman loop integrals is reviewed. The connection between quantum computing and perturbative quantum field theory is feasible due to fact that the two on-shell states of a Feynman propagator…

We extend the auxiliary-mass-flow (AMF) method originally developed for Feynman loop integration to calculate integrals involving also phase-space integration. Flow of the auxiliary mass from the boundary ($\infty$) to the physical point…

We {\em derive} the exact configuration space path integral, together with the way how to evaluate it, from the Hamiltonian approach for any quantum mechanical system in flat spacetime whose Hamiltonian has at most two momentum operators.…

We propose a classical simulation method for quantum circuits based on decomposing unitary gates into a sum of stabilizer projectors. By only decomposing the non-Clifford gates, we take advantage of the Gottesman-Knill theorem and build a…

This paper proposes the TrafficFlowGAN, a physics-informed flow based generative adversarial network (GAN), for uncertainty quantification (UQ) of dynamical systems. TrafficFlowGAN adopts a normalizing flow model as the generator to…

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…

We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of…

Spin foams arose as the covariant (path integral) formulation of quantum gravity depicting transition amplitudes between different quantum geometry states. As such, they provide a scheme to study the no boundary proposal, specifically the…

What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…

Graph generation has emerged as a critical task in fields ranging from drug discovery to circuit design. Contemporary approaches, notably diffusion and flow-based models, have achieved solid graph generative performance through constructing…

We propose a simple quantum algorithm for implementing the diffusion step of grid-based Bayesian filters. The method encodes the advected state density and the process noise density into quantum registers and realizes diffusion using a…

Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…

Flow-based generative models have been employed for sampling the Boltzmann distribution, but their application to high-dimensional systems is hindered by the significant computational cost of obtaining the Jacobian of the flow. To overcome…

Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…

In this work, within the framework of path integral Monte Carlo, we construct a pseudo-fermion propagator by replacing the original fermionic determinant with its absolute value. This modified propagator defines an auxiliary system free…

We study approximations of Feynman path integrals in finite dimensional spaces and how the approximations determine the propagator.

Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…

Generative machine learning has emerged as a powerful tool for design representation and exploration. However, its application is often constrained by the need for large datasets of existing designs and the lack of interpretability about…