Related papers: Shor's algorithm on a nearest-neighbor machine
Several applications of the QR-AAA algorithm, a greedy scheme for vector-valued rational approximation, are presented. The focus is on demonstrating the flexibility and practical effectiveness of QR-AAA in a variety of computational…
The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation…
In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R…
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic…
Neural architecture search (NAS) recently attracts much research attention because of its ability to identify better architectures than handcrafted ones. However, many NAS methods, which optimize the search process in a discrete search…
Many theoretical and experimental studies have used heuristic methods to investigate the dynamic behaviour of the passive coupling of adjacent structures. However, few papers have used optimization techniques with guaranteed convergence in…
Shor's algorithm is one of the most promising applications of quantum computers. However, since $\sim 10^6$ physical qubits are believed to be required for established approaches, the algorithm will need to be distributed across many…
In this paper, we consider Wiener filters to reconstruct deterministic and (wide-band) stationary graph signals from their observations corrupted by random noises, and we propose distributed algorithms to implement Wiener filters and…
Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve…
Despite their power, Transformers face challenges with long sequences due to the quadratic complexity of self-attention. To address this limitation, methods like $k$-Nearest-Neighbor ($k$NN) attention have been introduced [Roy, Saffar,…
The search task is one of the most difficult when it comes to execution speed, and reducing the latter is important both when working with large data and with small samples, if they need to be processed frequently and in a limited time.…
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
We introduce a distributed algorithm for clock synchronization in sensor networks. Our algorithm assumes that nodes in the network only know their immediate neighborhoods and an upper bound on the network's diameter. Clock-synchronization…
Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of $T/T^{\dagger}$-gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains 3 qubits. The…
A modified version of the Dijkstra algorithm using an inventive contraction hierarchy is proposed. The algorithm considers a directed acyclic graph with a conical or semi-circular structure for which a pair of edges is chosen iteratively…
The Chord algorithm is a popular, simple method for the succinct approximation of curves, which is widely used, under different names, in a variety of areas, such as, multiobjective and parametric optimization, computational geometry, and…
We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the…
Quantum computers require quantum processors. An important part of the processor of any computer is the arithmetic unit, which performs binary addition, subtraction, division and multiplication, however multiplication can be performed using…