ﻻ يوجد ملخص باللغة العربية
Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core of which amounts to evaluating the logarithm of the marginal likelihood (LML) of a given model. LML gives a concrete measure of the quality of prediction that a GP model is expected to achieve. The classical computation of LML typically carries a polynomial time overhead with respect to the input size. We propose a quantum algorithm that computes the logarithm of the determinant of a Hermitian matrix, which runs in logarithmic time for sparse matrices. This is applied in conjunction with a variant of the quantum linear system algorithm that allows for logarithmic time computation of the form $mathbf{y}^TA^{-1}mathbf{y}$, where $mathbf{y}$ is a dense vector and $A$ is the covariance matrix. We hence show that quantum computing can be used to estimate the LML of a GP with exponentially improved efficiency under certain conditions.
Variational quantum algorithms (VQAs) promise efficient use of near-term quantum computers. However, training VQAs often requires an extensive amount of time and suffers from the barren plateau problem where the magnitude of the gradients vanishes wi
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient Kalman filter
Applications such as simulating large quantum systems or solving large-scale linear algebra problems are immensely challenging for classical computers due their extremely high computational cost. Quantum computers promise to unlock these applications
Quantum annealing (QA) is a hardware-based heuristic optimization and sampling method applicable to discrete undirected graphical models. While similar to simulated annealing, QA relies on quantum, rather than thermal, effects to explore complex sear
This paper is concerned with exponential moments of integral-of-quadratic functions of quantum processes with canonical commutation relations of position-momentum type. Such quadratic-exponential functionals (QEFs) arise as robust performance criteri