Related papers: Optimal block-tridiagonalization of matrices for c…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective…
Engineering effective Hamiltonians is essential for advancing quantum technologies including quantum simulation, sensing, and computing. This paper presents a general framework for effective Hamiltonian engineering, enabling robust,…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…
We present superconducting quantum circuits which exhibit atomic energy spectrum and selection rules as ladder and lambda three-level configurations designed by means of genetic algorithms. These heuristic optimization techniques are…
For quantum spin models defined on a two-dimensional lattice, we look for the best numbering of the lattice sites (a layout) that, at fixed bond dimension and other parameters of the density matrix renormalization group (DMRG) algorithm,…
We present a systematic derivation of three mathematical models of increasing complexity for optical design, based on Hamilton's characteristic functions and conservation of luminous flux, and briefly explain the connection with the…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
Variational quantum algorithms are a promising class of algorithms that can be performed on currently available quantum computers. In most settings, the free parameters of a variational circuit are optimized using a classical optimizer that…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
We consider the problem of electronic quantum transport through ballistic mesoscopic systems with chaotic dynamics, connected to a three-terminal architecture in which one of the terminals has a tunnel barrier. Using a semiclassical…
Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those…
Trapped-ion quantum simulators, in analog and digital modes, are considered a primary candidate to achieve quantum advantage in quantum simulation and quantum computation. The underlying controlled ion-laser interactions induce all-to-all…
Charged particle transport is an important energy transport mode in the combustion process of inertial confinement fusion plasma. On the one hand, charged particles inside the hot spot have a strong non-equilibrium effect, so it is…
We formulate a global-position colored-permutation encoding for the capacitated vehicle routing problem. Each of the $K$ vehicles selects a disjoint partial permutation, and the sum of these $K$ color layers forms a full $n\times n$…