Related papers: Quantum Approximation I. Embeddings of Finite Dime…

Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…

One-dimensional function approximation is a fundamental problem in scientific computing and engineering applications. While neural networks possess powerful universal approximation capabilities, their optimization process is often hindered…

A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…

We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum…

Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…

We study integration and $L^2$-approximation of functions of infinitely many variables in the following setting: The underlying function space is the countably infinite tensor product of univariate Hermite spaces and the probability measure…

Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…

Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…

Quantum computing devices require exceptional control of their experimental parameters to prepare quantum states and simulate other quantum systems. Classical optimization procedures used to find such optimal control parameters, have…

The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…

Yudin's lower bound for the spherical designs is generalized to the cubature formulas on the projective spaces over a field K, where K can be R, C, or H (the field of quaternions), and thus to isometric embeddings of l_2 into l_p with p an…

One-dimensional quantum optical models usually rest on the intuition of large scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially…

A software product line models the variability of highly configurable systems. Complete exploration of all valid configurations (the configuration space) is infeasible as it grows exponentially with the number of features in the worst case.…

This paper introduces a novel quantum embedding search algorithm (QES, pronounced as "quest"), enabling search for optimal quantum embedding design for a specific dataset of interest. First, we establish the connection between the…

Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…

Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…

Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…

Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…