Related papers: Optimal algorithmic complexity of inference in qua…
Quantum neural networks (QNNs) suffer from a fundamental sampling bottleneck since quantum measurements are probabilistic, requiring many circuit executions to estimate outputs with sufficient accuracy. Conventional Monte-Carlo (MC)…
One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version…
Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations and…
This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…
We show how to find all $k$ marked elements in a list of size $N$ using the optimal number $O(\sqrt{N k})$ of quantum queries and only a polylogarithmic overhead in the gate complexity, in the setting where one has a small quantum memory.…
We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are…
Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…
Survival analysis is a fundamental tool in medical research to identify predictors of adverse events and develop systems for clinical decision support. In order to leverage large amounts of patient data, efficient optimisation routines are…
We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence…
Quantum computing is a promising paradigm that may overcome the current computational power bottlenecks. The increasing maturity of quantum processors provides more possibilities for the development and implementation of quantum algorithms.…
Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…
The \emph{top-$k$-sum} operator computes the sum of the largest $k$ components of a given vector. The Euclidean projection onto the top-$k$-sum sublevel set serves as a crucial subroutine in iterative methods to solve composite…
We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well…
Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…
Quantum metrology plays a fundamental role in many scientific areas. However, the complexity of engineering entangled probes and the external noise raise technological barriers for realizing the expected precision of the to-be-estimated…
Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…
This study systematically benchmarks classical optimization strategies for the Quantum Approximate Optimization Algorithm when applied to Generalized Mean-Variance Problems under near-term Noisy Intermediate-Scale Quantum conditions. We…
While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a…