相关论文: Quantum Speedup for Network Coordination via Fouri…
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…
We study the problem of optimal traffic prediction and monitoring in large-scale networks. Our goal is to determine which subset of K links to monitor in order to "best" predict the traffic on the remaining links in the network. We consider…
A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Pr\=usis and Vihrovs (SODA'19) showed how to construct faster quantum algorithms for the Traveling Salesman Problem and a few other NP-hard problems by combining in a novel way…
Motivated by limitations on the depth of near-term quantum devices, we study the depth-computation trade-off in the query model, where the depth corresponds to the number of adaptive query rounds and the computation per layer corresponds to…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…
We study the forrelation problem: given a pair of $n$-bit Boolean functions $f$ and $g$, estimate the correlation between $f$ and the Fourier transform of $g$. This problem is known to provide the largest possible quantum speedup in terms…
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
Training quantum neural networks (QNNs) using gradient-based or gradient-free classical optimisation approaches is severely impacted by the presence of barren plateaus in the cost landscapes. In this paper, we devise a framework for…
In this paper we address distributed learning problems over peer-to-peer networks. In particular, we focus on the challenges of quantized communications, asynchrony, and stochastic gradients that arise in this set-up. We first discuss how…
The focus of this paper is on {\em quantum distributed} computation, where we investigate whether quantum communication can help in {\em speeding up} distributed network algorithms. Our main result is that for certain fundamental network…
Quantum compilation requires the development of new algorithms that optimise the cost of implementing quantum computations on physical hardware. Often this gives rise to problems which are asymptotically hard to solve classically, and for…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when…
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…
The quantum Fourier transform (QFT) has emerged as the primary tool in quantum algorithms which achieve exponential advantage over classical computation and lies at the heart of the solution to the abelian hidden subgroup problem, of which…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
The distribution of entanglement in quantum networks is typically approached under idealized assumptions such as perfect synchronization and centralized control, while classical communication is often neglected. However, these assumptions…