Related papers: Quantum Speedup for Network Coordination via Fouri…
There has been increasing interest in developing efficient quantum algorithms for hard classical problems. The Network Signal Coordination (NSC) problem is one such problem known to be NP complete. We implement Grover's search algorithm to…
Quantum computing promises exponential speedups for certain problems, yet fully universal quantum computers remain out of reach and near-term devices are inherently noisy. Motivated by this, we study noisy quantum algorithms and the…
Many real-world problems, like modelling environment dynamics, physical processes, time series etc., involve solving Partial Differential Equations (PDEs) parameterised by problem-specific conditions. Recently, a deep learning architecture…
(Abridged abstract.) In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms. Our first contribution is a formalism of restricted quantum operations, named…
We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the…
Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…
An algorithm is presented allowing the construction of fast Fourier transforms for any solvable group on a classical computer. The special structure of the recursion formula being the core of this algorithm makes it a good starting point to…
In this paper, we demonstrate that optimal control algorithms can be used to speed up the implementation of modules of quantum algorithms or quantum simulations in networks of coupled qubits. The gain is most prominent in realistic cases,…
Network coordination is considered in three basic settings, characterizing the generation of separable and classical-quantum correlations among multiple parties. First, we consider the simulation of a classical-quantum state between two…
Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…
Partitioning Around Medoids (PAM, k-Medoids) is a popular clustering technique to use with arbitrary distance functions or similarities, where each cluster is represented by its most central object, called the medoid or the discrete median.…
Fourier acceleration is a technique used in Hybrid Monte Carlo simulations to decrease the autocorrelation between subsequent field configurations in the generated ensemble. It has been shown, in the perturbative limit, to eliminate the…
This paper presents a Sparse Hierarchical Fourier Interaction Networks, an architectural building block that unifies three complementary principles of frequency domain modeling: A hierarchical patch wise Fourier transform that affords…
We describe a quantum algorithm for the Planted Noisy $k$XOR problem (also known as sparse Learning Parity with Noise) that achieves a nearly quartic ($4$th power) speedup over the best known classical algorithm while also only using…
Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
Efficient entanglement distribution is the foundational challenge in realizing large-scale Quantum Networks. However, state-of-the-art solutions are frequently limited by restrictive operational assumptions, prohibitive computational…
In large groups, every collaborative act requires balancing two pressures: the need to achieve behavioural synchrony and the need to keep free riding to a minimum. This paper introduces a model of collaboration that requires both…
The inevitable random frequency differences among semiconductor lasers present an obstacle to achieving their collective coherence, but previous worked showed that fully (all-to-all) coupled networks can still be synchronized even in the…
The Forrelation problem, introduced by Aaronson [A10] and Aaronson and Ambainis [AA15], is a well studied problem in the context of separating quantum and classical models. Variants of this problem were used to give exponential separations…