Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 10,000 papers for “Distributed algorithm”

Distributed Phase Estimation Algorithm and Distributed Shor's Algorithm

Ligang Xiao, Daowen Qiu, Le Luo et al. · arXiv (Cornell University) · 2023

Shor's algorithm is one of the most significant quantum algorithms. Shor's algorithm can factor large integers with a certain success probability in polynomial time. However, Shor's algorithm requires an unbearable amount of qubits in the NISQ (Noisy Intermediate-scale Quantum) era. To reduce the resources required for Shor's algorithm, in this paper we first propose a new distributed phase estimation algorithm. Our distributed phase estimation algorithm does not require quantum communication and it reduces the number of qubits of a single node compared to the traditional phase estimation algorithm (non-iterative version). Then we apply our distributed phase estimation algorithm to form a distributed order-finding algorithm for Shor's algorithm. Compared with the traditional Shor's algorithm (non-iterative version), the maximum number of qubits required by a single node of our dristributed order-finding algorithm is reduced by $(2-\dfrac{2}{k})L-\log_2k-O(1)$ when factoring an $L$-bit integer ($k$ is the number of compute nodes). The communication complexity of our distributed order-finding algorithm is $O(kL)$.

Cited by 6Open access

Distributed Kuperberg’s algorithm

Peng-Yu Yang, Xin Zhang, Song Lin · Chinese Physics B · 2025

Abstract As an important quantum cryptanalysis algorithm, Kuperberg’s algorithm efficiently addresses the dihedral hidden subgroup problem with sub-exponential acceleration. However, when dealing with large numbers, the algorithm demands a deeper quantum circuit depth, rendering its implementation on current quantum devices prone to noise interference and thereby significantly reducing its efficiency. To mitigate this challenge, this paper proposes a distributed Kuperberg’s algorithm. It decomposes the original function into sub-functions which can be executed on different nodes in parallel. The implementation of these sub-functions necessitates a shallower quantum circuit depth and a reduced number of qubits when contrasted with the execution of the original function. Furthermore, the proposed algorithm can be directly generalized to an arbitrary number of nodes by adjusting the quantity of input qubits. The utilization of multi-node parallel processing makes the proposed algorithm a linear enhancement in query complexity relative to the original algorithm. To validate the feasibility and demonstrate the superiority of our algorithm, experiments are conducted on the Qiskit platform.

Cited by 0Open access

Distributed Shor's algorithm

Ligang Xiao, Daowen Qiu, Le Luo et al. · arXiv (Cornell University) · 2022

Shor's algorithm is one of the most important quantum algorithm proposed by Peter Shor [Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994, pp. 124--134]. Shor's algorithm can factor a large integer with certain probability and costs polynomial time in the length of the input integer. The key step of Shor's algorithm is the order-finding algorithm. Specifically, given an $L$-bit integer $N$, we first randomly pick an integer $a$ with $gcd(a,N)=1$, the order of $a$ modulo $N$ is the smallest positive integer $r$ such that $a^r\equiv 1 (\bmod N)$. The order-finding algorithm in Shor's algorithm first uses quantum operations to obtain an estimation of $\dfrac{s}{r}$ for some $s\in\{0, 1, \cdots, r-1\}$, then $r$ is obtained by means of classical algorithms. In this paper, we propose a distributed Shor's algorithm. The difference between our distributed algorithm and the traditional order-finding algorithm is that we use two quantum computers separately to estimate partial bits of $\dfrac{s}{r}$ for some $s\in\{0, 1, \cdots, r-1\}$. To ensure their measuring results correspond to the same $\dfrac{s}{r}$, we need employ quantum teleportation. We integrate the measuring results via classical post-processing. After that, we get an estimation of $\dfrac{s}{r}$ with high precision. Compared with the traditional Shor's algorithm that uses multiple controlling qubits, our algorithm reduces nearly $\dfrac{L}{2}$ qubits and reduces the circuit depth of each computer.

Cited by 0Open access

Distributed quantum computing: a distributed Shor algorithm

Anocha Yimsiriwattana, Samuel J. Lomonaco Jr. · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2004

We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large capacity quantum computer. In this paper, entanglement is used as a resource for implementing non-local operations between two or more quantum computers. These non-local operations are used to implement a distributed factoring circuit with polynomially many gates. This distributed version of Shor's algorithm requires an additional overhead of O((log N)^2) communication complexity, where N denotes the integer to be factored.

Cited by 83Open access

Distributed k-means algorithm

Gabriele Oliva, Roberto Setola, Hadjicostis, Christoforos N. · arXiv (Cornell University) · 2013

In this paper we provide a fully distributed implementation of the k-means clustering algorithm, intended for wireless sensor networks where each agent is endowed with a possibly high-dimensional observation (e.g., position, humidity, temperature, etc.) The proposed algorithm, by means of one-hop communication, partitions the agents into measure-dependent groups that have small in-group and large out-group "distances". Since the partitions may not have a relation with the topology of the network--members of the same clusters may not be spatially close--the algorithm is provided with a mechanism to compute the clusters'centroids even when the clusters are disconnected in several sub-clusters.The results of the proposed distributed algorithm coincide, in terms of minimization of the objective function, with the centralized k-means algorithm. Some numerical examples illustrate the capabilities of the proposed solution.

Cited by 28Open access

Distributed exact Grover’s algorithm

Xu Zhou, Daowen Qiu, Le Luo · Frontiers of Physics · 2023

Distributed quantum computation has gained extensive attention. In this paper, we consider a search problem that includes only one target item in the unordered database. After that, we propose a distributed exact Grover’s algorithm (DEGA), which decomposes the original search problem into ⌊n/2⌋ parts. Specifically, (i) our algorithm is as exact as the modified version of Grover’s algorithm by Long, which means the theoretical probability of finding the objective state is 100%; (ii) the actual depth of our circuit is 8(n mod 2) + 9, which is less than the circuit depths of the original and modified Grover’s algorithms, $$1 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} } \right\rfloor $$ and $$9 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} - {1 \over 2}} \right\rfloor $$ , respectively. It only depends on the parity of n, and it is not deepened as n increases; (iii) we provide particular situations of the DEGA on MindQuantum (a quantum software) to demonstrate the practicality and validity of our method. Since our circuit is shallower, it will be more resistant to the depolarization channel noise.

Cited by 20

A Distributed Clustering Algorithm

Hulth, Nils, Grenholm, P · Lund University Publications (Lund University) · 1998

A new algorithm for clustering is presented --- the Distributed Clustering Algorithm (DCA). It is designed to be incremental and to work in a real-time situation, thus making it suitable for robotics and in models of concept formation. The DCA starts with one cluster (or rather prototype at the center of the cluster), successively adding prototypes and distributing them according to data density until a certain criteria is fulfilled. This criteria is that new prototypes do not add enough extra precision in the representation of the data. A local measure called emph{roundness} is used to predict how much extra precision a new prototype will add.

Cited by 0

Stochastic distributed optimization algorithm

T. Fukao, Yue Zhao · Electronics and Communications in Japan (Part I Communications) · 1988

Abstract Expect for special cases, the solution of the combinational optimization problem depends greatly on the heuristic approach. Recently, Kirkpatrick et al. proposed with success the “simulated annealing” algorithm based on the analogy to the statistical thermodynamics. The method has already been applied with success to the large‐scale combinational optimization problem, such as partitioning, allocation, and wiring in VLSI design. The algorithm based on the analogy to the physical system may not be considered as an analog approach in the sense that the discrete representation is used. It can provide the parallel and distributed representation of the events in a natural way. Although the present simulated annealing algorithm does not contain such a parallel and distributed representation, those ideas should naturally be introduced. This paper adopts a viewpoint which is more general than the physical model such as the Ising model, and discusses the stochastic algorithm and its distributed representation for the optimization from the viewpoint of the Markov field. Various schemes under such a parallelism, i.e., synchronization and distributed‐lumped analogy to the field are discussed. As an application, the result of distributed formulation and computation for the decomposition problem are presented.

Cited by 7

Distributed quantum logic algorithm

Boris Arseniev · arXiv (Cornell University) · 2024

Parallel computation enables multiple processors to execute different parts of a task simultaneously, improving processing speed and efficiency. In quantum computing, parallel gate implementation involves executing gates independently in different registers, directly impacting the circuit depth, the number of sequential quantum gate operations, and thus the algorithm execution time. This work examines a method for reducing circuit depth by introducing auxiliary qubits to enable parallel gate execution, potentially enhancing the performance of quantum simulations on near-term quantum devices. We show that any circuit on $n$ qubits with depth $O\left(M n^2\right)$, where $M = M(n)$ is some function of $n$, can be transformed into a circuit with depth $O\left(\log_2(M) n^2\right)$ operating on $O\left(M n\right)$ qubits. This technique may be particularly useful in noisy environments, where recent findings indicate that only the final $O\left(\log n\right)$ layers influence the expectation value of observables. It may also optimize Trotterization by exponentially reducing the number of Trotter steps. Additionally, the method may offer advantages for distributed quantum computing, and the intuition of treating quantum states as gates and operators as vectors used in this work may have broader applications in quantum computation.

Cited by 0Open access

Distributed algorithm visualization engine

McGinnis, Sean W. (Sean William), 1975- · DSpace@MIT (Massachusetts Institute of Technology) · 1998

Thesis (S.B. and M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.

Cited by 0Open access

Distributed Hash table-based distributed subspace clustering algorithm

Yaowu Chen · 2010

A distributed subspace clustering (DISCLUS) algorithm based on distributed Hash table(DHT) was proposed.Each node executed subspace clustering on its local data.Then the clustering results of nodes were combined to form the final clustering results of the distributed system.The dataset reducing and pruning schemes were proposed to optimize the communication between nodes according to the speciality of subspace clustering.A DHT-based distributed voting (DDV) algorithm was proposed to combine the clustering results of nodes.The algorithm used the topology of the underlying overlay to hierarchically collect the voting information.All the nodes in the system can be covered without redundancy.The theoretical and experimental results show that the clustering error and the communication cost of DISCLUS algorithm are scalable to the dataset,nodes and dimensionality.

Cited by 0