Related papers: Estimating the Euclidean quantum propagator with d…
Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
Frequency-encoded quantum information offers intriguing opportunities for quantum communications and networking, with the quantum frequency processor paradigm -- based on electro-optic phase modulators and Fourier-transform pulse shapers --…
We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in…
The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct…
Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a…
Quantum states defined over a parameter space form a Grassmann manifold. To capture the geometry of the associated gauge structure, gauge-invariant quantities are essential. We employ the projector of a multilevel system to quantify the…
We propose a new rigorous time-slicing construction of the phase space Path Integrals for propagators both in Quantum Mechanics and Quantum Field Theory for a fairly general class of quantum observables (e.g. the Schroedinger hamiltonians…
In the Euclidean-space formulation of integral equations for the structure of quantum chromodynamics (QCD) bound states, the quark propagators with complex-valued momentum are densely sampled. We therefore propose an accurate and efficient…
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…
In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the…
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based…
Continuous time Feynman-Kac measures on path spaces are central in applied probability, partial differential equation theory, as well as in quantum physics. This article presents a new duality formula between normalized Feynman-Kac…
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…
Quantum machine learning models based on parametrized quantum circuits, also called quantum neural networks (QNNs), are considered to be among the most promising candidates for applications on near-term quantum devices. Here we explore the…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
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.…
Quantum machine learning methods often rely on fixed, hand-crafted quantum encodings that may not capture optimal features for downstream tasks. In this work, we study the power of quantum autoencoders in learning data-driven quantum…
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…