Related papers: Quantum Dynamics with the Parallel Transport Gauge
In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian…
We propose a new framework for generative modeling based on a discrete-time stochastic control formulation of measure transport. Adapting classic results from control theory, we formulate our problem as a linear program whose dual variables…
We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
The molecular junction geometry is modelled in terms of nuclear degrees of freedom that are embedded in a stochastic quantum environment of non-equilibrium electrons. Time-evolution of the molecular geometry is governed via a mean force, a…
Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic…
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence…
We propose a new method for simulating electron dynamics in open quantum systems out of equilibrium, using a finite atomistic model. The proposed method is motivated by the intuitive and practical nature of the driven Liouville von-Neumann…
The static optimal transport $(\mathrm{OT})$ problem between Gaussians seeks to recover an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been well studied and applied to a wide variety of tasks. Here we…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…
Quantum simulation of non-Abelian gauge theories requires careful handling of gauge redundancy. We address this challenge by presenting universal principles for treating gauge symmetry that apply to any quantum simulation approach,…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
The application of adiabatic protocols in quantum technologies is severely limited by environmental sources of noise and decoherence. Shortcuts to adiabaticity by counterdiabatic driving constitute a powerful alternative that speed up…
We study a dynamic optimal transport type problem on a domain that consists of two parts: a compact set $\Omega \subset \mathbb{R}^d$ (bulk) and a non-intersecting and sufficiently regular curve $\Gamma \subset \Omega$. On each of them, a…
The proposal of the optical scheme for holonomic quantum computation is evaluated based on dynamical resolution to the system beyond adiabatic limitation. The time-dependent Schr\"{o}dinger equation is exactly solved by virtue of the…
We show how to evaluate mobility profiles, characterizing the transport of confined fluids under a perturbation, from equilibrium molecular simulations. The correlation functions derived with the Green-Kubo formalism are difficult to sample…
This work presents a quantum mechanical framework for analyzing quantization-based optimization algorithms. The sampling process of the quantization-based search is modeled as a gradient-flow dissipative system, leading to a…
It is common practice to approximate a weakly nonlinear wave equation through a kinetic transport equation, thus raising the issue of controlling the validity of the kinetic limit for a suitable choice of the random initial data. While for…
Non-equilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady state non-equilibrium transport…