相关论文: Shor's algorithm on a nearest-neighbor machine

We present reversible classical circuits for performing various arithmetic operations aided by dirty ancillae (i.e. extra qubits in an unknown state that must be restored before the circuit ends). We improve the number of clean qubits…

We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the…

We consider the fundamental problem of constructing fast and small circuits for binary addition. We propose a new algorithm with running time $\mathcal O(n \log_2 n)$ for constructing linear-size $n$-bit adder circuits with a significantly…

Shor's quantum algorithm is very important for cryptography, since it can factor large numbers much faster than classical algorithms. In this study, we implement a simulator for Shor's quantum algorithm on graphic processor units (GPU) and…

This paper presents a computer program, written in Maple, that allows a user to simulate certain aspects of Shor's quantum factoring algorithm on a desktop or laptop computer. The program does not simulate the unitary operations carried out…

We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…

The practical use of many types of near-term quantum computers requires accounting for their limited connectivity. One way of overcoming limited connectivity is to insert swaps in the circuit so that logical operations can be performed on…

Neighbor search is a computationally demanding problem, usually both time- and memory-consuming. The main problem of this kind of algorithms is the long execution time due to cache misses. In this work, we propose a quantum algorithm for…

These are pedagogical notes on Shor's factoring algorithm, which is a quantum algorithm for factoring very large numbers (of order of hundreds to thousands of bits) in polynomial time. In contrast, all known classical algorithms for the…

Graph search is one of the most successful algorithmic trends in near neighbor search. Several of the most popular and empirically successful algorithms are, at their core, a simple walk along a pruned near neighbor graph. Such algorithms…

We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed…

We present a novel approach for designing complex approximate arithmetic circuits that trade correctness for power consumption and play important role in many energy-aware applications. Our approach integrates in a unique way formal methods…

Relative Nearest Neighbor Descent (RNN-Descent) is a state-of-the-art algorithm for constructing sparse approximate nearest neighbor (ANN) graphs by combining the iterative refinement of NN-Descent with the edge-pruning rules of the…

We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected…

Some of the secret sharing schemes having unique quantum features like parallelism and entanglement are supposed to be relatively secure. Different schemes proposed by various researchers over the years have features which could be specific…

Reversible circuits for modular multiplication $Cx$%$M$ with $x<M$ arise as components of modular exponentiation in Shor's quantum number-factoring algorithm. However, existing generic constructions focus on asymptotic gate count and…

We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…

Multiplier circuits play an important role in reversible computation, which is helpful in diverse areas such as low power CMOS design, optical computing, DNA computing and bioinformatics. Here we propose a new reversible multiplier circuit…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…