Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA divide-and-conquer algorithm for quantum state preparation
137
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.
rate research
Read More
We introduce a quantum divide and conquer algorithm that enables the use of distributed computing for constrained combinatorial optimization problems. The algorithm consists of three major components: classical partitioning of a target graph into multiple subgraphs, variational optimization over these subgraphs, and a quantum circuit cutting procedure that allows the optimization to take place independently on separate quantum processors. We simulate the execution of the quantum divide and conquer algorithm to find approximate solutions to instances of the Maximum Independent Set problem which have nearly twice as many nodes than the number of qubits available on a single quantum processor.
In this paper, a parallel structured divide-and-conquer (PSDC) eigensolver is proposed for symmetric tridiagonal matrices based on ScaLAPACK and a parallel structured matrix multiplication algorithm, called PSMMA. Computing the eigenvectors via matrix-matrix multiplications is the most computationally expensive part of the divide-and-conquer algorithm, and one of the matrices involved in such multiplications is a rank-structured Cauchy-like matrix. By exploiting this particular property, PSMMA constructs the local matrices by using generators of Cauchy-like matrices without any communication, and further reduces the computation costs by using a structured low-rank approximation algorithm. Thus, both the communication and computation costs are reduced. Experimental results show that both PSMMA and PSDC are highly scalable and scale to 4096 processes at least. PSDC has better scalability than PHDC that was proposed in [J. Comput. Appl. Math. 344 (2018) 512--520] and only scaled to 300 processes for the same matrices. Comparing with texttt{PDSTEDC} in ScaLAPACK, PSDC is always faster and achieves $1.4$x--$1.6$x speedup for some matrices with few deflations. PSDC is also comparable with ELPA, with PSDC being faster than ELPA when using few processes and a little slower when using many processes.
The information-based optimal subdata selection (IBOSS) is a computationally efficient method to select informative data points from large data sets through processing full data by columns. However, when the volume of a data set is too large to be processed in the available memory of a machine, it is infeasible to implement the IBOSS procedure. This paper develops a divide-and-conquer IBOSS approach to solving this problem, in which the full data set is divided into smaller partitions to be loaded into the memory and then subsets of data are selected from each partitions using the IBOSS algorithm. We derive both finite sample properties and asymptotic properties of the resulting estimator. Asymptotic results show that if the full data set is partitioned randomly and the number of partitions is not very large, then the resultant estimator has the same estimation efficiency as the original IBOSS estimator. We also carry out numerical experiments to evaluate the empirical performance of the proposed method.
Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the embedding space for all available data points, which may have a very complex non-uniform distribution with different notions of similarity between objects, e.g. appearance, shape, color or semantic meaning. Approaches for learning a single distance metric often struggle to encode all different types of relationships and do not generalize well. In this work, we propose a novel easy-to-implement divide and conquer approach for deep metric learning, which significantly improves the state-of-the-art performance of metric learning. Our approach utilizes the embedding space more efficiently by jointly splitting the embedding space and data into $K$ smaller sub-problems. It divides both, the data and the embedding space into $K$ subsets and learns $K$ separate distance metrics in the non-overlapping subspaces of the embedding space, defined by groups of neurons in the embedding layer of the neural network. The proposed approach increases the convergence speed and improves generalization since the complexity of each sub-problem is reduced compared to the original one. We show that our approach outperforms the state-of-the-art by a large margin in retrieval, clustering and re-identification tasks on CUB200-2011, CARS196, Stanford Online Products, In-shop Clothes and PKU VehicleID datasets.
We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks that are amenable to the principle of divide and conquer, and study what are its implications in terms of learning. This principle creates a powerful inductive bias that we leverage with neural architectures that are defined recursively and dynamically, by learning two scale-invariant atomic operations: how to split a given input into smaller sets, and how to merge two partially solved tasks into a larger partial solution. Our model can be trained in weakly supervised environments, namely by just observing input-output pairs, and in even weaker environments, using a non-differentiable reward signal. Moreover, thanks to the dynamic aspect of our architecture, we can incorporate the computational complexity as a regularization term that can be optimized by backpropagation. We demonstrate the flexibility and efficiency of the Divide-and-Conquer Network on several combinatorial and geometric tasks: convex hull, clustering, knapsack and euclidean TSP. Thanks to the dynamic programming nature of our model, we show significant improvements in terms of generalization error and computational complexity.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
