Related papers: Constructing Optimal Contraction Trees for Tensor …
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
We consider global problems, i.e. problems that take at least diameter time, even when the bandwidth is not restricted. We show that all problems considered admit efficient solutions in low-treewidth graphs. By ``efficient'' we mean that…
We study approaches for the exact solution of the \NP--hard minimum spanning tree problem under conflict constraints. Given a graph $G(V,E)$ and a set $C \subset E \times E$ of conflicting edge pairs, the problem consists of finding a…
Quantum optimization as a field has largely been restricted by the constraints of current quantum computing hardware, as limitations on size, performance, and fidelity mean most non-trivial problem instances won't fit on quantum devices.…
Hamiltonian simulation is one of the most promising paths toward quantum advantage. Most prior approaches to Hamiltonian simulation circuit synthesis focus on local rewrite rules and low-level optimizations, and give limited attention to…
Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
Gradient descent methods have long been the de facto standard for training deep neural networks. Millions of training samples are fed into models with billions of parameters, which are slowly updated over hundreds of epochs. Recently, it's…
Simulating molecular systems on quantum processors has the potential to surpass classical methods in computational resource efficiency. The limited qubit connectivity, small processor size, and short coherence times of near-term quantum…
We study the problem of efficient exact partitioning of the hypergraphs generated by high-order planted models. A high-order planted model assumes some underlying cluster structures, and simulates high-order interactions by placing…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
Many computational problems can be formulated in terms of high-dimensional functions. Simple representations of such functions and resulting computations with them typically suffer from the "curse of dimensionality", an exponential cost…
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
Dynamic quantum simulation is a leading application for achieving quantum advantage. However, high circuit depths remain a limiting factor on near-term quantum hardware. We present a compilation algorithm based on Matrix Product Operators…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…
Recent advances in learning-based image compression typically come at the cost of high complexity. Designing computationally efficient architectures remains an open challenge. In this paper, we empirically investigate the impact of…
Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…
In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units (QPUs) suffer from, among others, highly limited connectivity between physical qubits. To make a quantum circuit effectively executable, a circuit transformation…