Related papers: Accelerating two-dimensional tensor network optimi…
The aim of this paper is to solve large-and-sparse linear Semidefinite Programs (SDPs) with low-rank solutions. We propose to use a preconditioned conjugate gradient method within second-order SDP algorithms and introduce a new efficient…
We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as…
Folding grid value vectors of size $2^L$ into $L$th order tensors of mode sizes $2\times \cdots\times 2$, combined with low-rank representation in the tensor train format, has been shown to lead to highly efficient approximations for…
Many state-of-the-art Segment Routing (SR) Traffic Engineering (TE) algorithms rely on Linear Program (LP)-based optimization. However, the poor scalability of the latter and the resulting high computation times impose severe restrictions…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
Variational quantum algorithms are practical approaches to prepare ground states, but their potential for quantum advantage remains unclear. Here, we use differentiable 2D tensor networks (TN) to optimize parameterized quantum circuits that…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
The projected entangled pair state (PEPS) ansatz can represent a thermal state in a strongly correlated system. We introduce a novel variational algorithm to optimize this tensor network. Since full tensor environment is taken into account,…
We propose conditioning field initialization for neural network based topology optimization. In this work, we focus on (1) improving upon existing neural network based topology optimization, (2) demonstrating that by using a prior initial…
Many techniques for real-time trajectory optimization and control require the solution of optimization problems at high frequencies. However, ill-conditioning in the optimization problem can significantly reduce the speed of first-order…
Owing to their great expressivity and versatility, neural networks have gained attention for simulating large two-dimensional quantum many-body systems. However, their expressivity comes with the cost of a challenging optimization due to…
Memory efficiency is crucial in training deep learning networks on resource-restricted devices. During backpropagation, forward tensors are used to calculate gradients. Despite the option of keeping those dependencies in memory until they…
This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while…
We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtain an inf-sup problem whose loss functional involves…
The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…