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We analyze geometry of the second order differential operators, having in mind applications to Batalin--Vilkovisky formalism in quantum field theory. As we show, an exhaustive picture can be obtained by considering pencils of differential…
In this paper, the stability analysis of quaternion-valued neural networks (QVNNs) with both leakage delay and additive time-varying delays is proposed. By employing the Lyapunov-Krasovskii functional method and fully considering the…
In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we…
In this paper we consider the localization problem for a visual sensor network. Inspired by the alternate attitude and position distributed optimization framework discussed in [1], we propose an estimation scheme that exploits the unit dual…
We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set.…
Outlier detection is a major topic in robust statistics due to the high practical significance of anomalous observations. Many existing methods are, however, either parametric or cease to perform well when the data is far from linearly…
We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…
Quadratic approximations form a fundamental building block of machine learning methods. E.g., second-order optimizers try to find the Newton step into the minimum of a local quadratic proxy to the objective function; and the second-order…
To make deep neural networks feasible in resource-constrained environments (such as mobile devices), it is beneficial to quantize models by using low-precision weights. One common technique for quantizing neural networks is the…
Quantization for deep neural networks (DNNs) is the process of mapping the parameter values of DNNs from original data types to other data types of lower precision to reduce model sizes and make inference faster. Quantization often maps…
It is common in pose graph optimization (PGO) algorithms to assume that noise in the translations and rotations of relative pose measurements is uncorrelated. However, existing work shows that in practice these measurements can be highly…
Deep neural networks (DNNs) offer the highest performance in a wide range of applications in computer vision. These results rely on over-parameterized backbones, which are expensive to run. This computational burden can be dramatically…
Let S be a planar point set. Krznaric and Levcopoulos proved that given the Delaunay triangulation DT(S) for S, one can find the greedy triangulation GT(S) in linear time. We provide a (partial) converse of this result: given GT(S), it is…
In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of…
Normalization layers in neural operators usually compute statistics by uniformly averaging discrete grid values, making the normalization itself discretization-dependent and thereby a source of transfer error across different resolutions or…
We search for efficient disentanglers on random Clifford circuits of two-qubit gates arranged in a brick-wall pattern, using the proximal policy optimization (PPO) algorithm \cite{schulman2017proximalpolicyoptimizationalgorithms}.…
We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a…
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use…
Quadratically regularized optimal transport (QOT) is an alternative to entropic regularization that yields sparse couplings and avoids numerical instabilities due to exponential scaling. From an optimization viewpoint, the dual QOT…