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Analyzing large sparse electrical networks is a fundamental task in physics, electrical engineering and computer science. We propose two classes of quantum algorithms for this task. The first class is based on solving linear systems, and…
We propose and implement a priority queue suitable for use in event driven molecular dynamics simulations. All operations on the queue take on average O(1) time per collision. In comparison, previously studied queues for event driven…
Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing…
We develop and analyse a first-order algorithm for the A-optimal experimental design problem. The problem is first presented as a special case of a parametric family of optimal design problems for which duality results and optimality…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
Using Monte Carlo simulations, we study thermal and critical properties of two systems, in which domain walls and so-called $Z_2$-vortices as topological defects are presented. The main model is a lattice version of the $O(3)$ principal…
The discovery of the backpropagation algorithm ranks among one of the most important moments in the history of machine learning, and has made possible the training of large-scale neural networks through its ability to compute gradients at…
We present an $\tilde{O}(m^{10/7})=\tilde{O}(m^{1.43})$-time algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities. This is the first improvement over the sparse-graph case of the…
Topology Optimization (TO), which maximizes structural robustness under material weight constraints, is becoming an essential step for the automatic design of mechanical parts. However, existing TO algorithms use the Finite Element Analysis…
We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
The computational complexity of the self-attention mechanism in popular transformer architectures poses significant challenges for training and inference, and becomes the bottleneck for long inputs. Is it possible to significantly reduce…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
In this work, we present a quantum algorithm for direct first-principles simulation of electron-nuclear dynamics on a first-quantized real-space grid. Our algorithm achieves best-in-class efficiency for block-encoding the…
We give new and efficient black-box reconstruction algorithms for some classes of depth-$3$ arithmetic circuits. As a consequence, we obtain the first efficient algorithm for computing the tensor rank and for finding the optimal tensor…
Cryocooler conduction cooled devices can experience significant cooldown time due to lower available cooling capacity compares to convection cooled devices. Therefore, the cooldown time is an important design parameter for conduction cooled…
Computing the Euler genus of a graph is a fundamental problem in graph theory and topology. It has been shown to be NP-hard by [Thomassen '89] and a linear-time fixed-parameter algorithm has been obtained by [Mohar '99]. Despite extensive…
The latest generation of transistors are nanoscale devices whose performance and reliability are limited by thermal noise in low-power applications. Therefore developing efficient methods to compute the voltage and current fluctuations in…