Related papers: Effect of barren plateaus on gradient-free optimiz…
In hybrid classical-quantum computing, variational quantum algorithms (VQAs) have emerged as a promising approach in the Noisy Intermediate-Scale Quantum (NISQ) era; however, their performance is often hindered by barren plateaus, where…
Quantum neural networks (QNNs) encounter significant challenges in realizing nonlinear behavior and effectively optimizing parameters. This study addresses these issues by modeling nonlinearity through a Taylor series expansion, where the…
The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing…
We analyze the optimization landscapes of deep learning with wide networks. We highlight the importance of constraints for such networks and show that constraint -- as well as unconstraint -- empirical-risk minimization over such networks…
The training of Quantum Neural Networks (QNNs) is hindered by the high computational cost of gradient estimation and the barren plateau problem, where optimization landscapes become intractably flat. To address these challenges, we…
Inspired by the Fleming-Viot stochastic process, we propose a parallel implementation of variational quantum algorithms with the aim of reducing the time spent by the algorithm in barren plateaus, where optimization direction is unclear. In…
The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum…
In the last decade, the approximate vanishing ideal and its basis construction algorithms have been extensively studied in computer algebra and machine learning as a general model to reconstruct the algebraic variety on which noisy data…
This work characterizes the effect of depth on the optimization landscape of linear regression, showing that, despite their nonconvexity, deeper models have more desirable optimization landscape. We consider a robust and over-parameterized…
Barren-plateau results have established exponential gradient suppression as a widely cited obstacle to the scalability of variational quantum algorithms. When and whether these results extend to a given objective has been addressed through…
Due to the increase in data availability in urban and regional studies, various spatial panel models have emerged to model spatial panel data, which exhibit spatial patterns and spatial dependencies between observations across time.…
We explore why many recently proposed robust estimation problems are efficiently solvable, even though the underlying optimization problems are non-convex. We study the loss landscape of these robust estimation problems, and identify the…
One advantage of decision tree based methods like random forests is their ability to natively handle categorical predictors without having to first transform them (e.g., by using feature engineering techniques). However, in this paper, we…
The ability of neural networks to provide `best in class' approximation across a wide range of applications is well-documented. Nevertheless, the powerful expressivity of neural networks comes to naught if one is unable to effectively train…
We propose a quantum algorithm, inspired by ADAPT-VQE, to variationally prepare the ground state of a quantum Hamiltonian, with the desirable property that if it fails to find the ground state, it still yields a physically meaningful…
The conflict between trainability and expressibility is a key challenge in variational quantum computing and quantum machine learning. Resolving this conflict necessitates designing specific quantum neural networks (QNN) tailored for…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients. Focusing on non-asymptotic bounds on convergence rates, we show that if pairs of…
For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into…
Recent analyses of certain gradient descent optimization methods have shown that performance can degrade in some settings - such as with stochasticity or implicit momentum. In deep reinforcement learning (Deep RL), such optimization methods…