Related papers: A note on multipivot Quicksort

We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…

This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…

Single-linkage clustering is a fundamental method for data analysis. Algorithmically, one can compute a single-linkage $k$-clustering (a partition into $k$ clusters) by computing a minimum spanning tree and dropping the $k-1$ most costly…

A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…

This work examines the expected computational cost to determine an approximate global minimum of a class of cost functions characterized by the variance of coefficients. The cost function takes $N$-dimensional binary states as arguments and…

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…

This article introduces a new optimization method to improve mergesort's runtime complexity, when sorting sequences that have equal keys to $O(n log_2 k)$, where $k$ is the number of distinct keys in the sequence. When $k$ is constant, it…

Quicksort is a classical divide-and-conquer sorting algorithm. It is a comparison sort that makes an average of $2(n+1)H_n - 4n$ comparisons on an array of size $n$ ordered uniformly at random, where $H_n = \sum_{i=1}^n\frac{1}{i}$ is the…

We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…

We describe a scalable experimental protocol for obtaining estimates of the error rate of individual quantum computational gates. This protocol, in which random Clifford gates are interleaved between a gate of interest, provides a bounded…

Real-world applications of computing can be extremely time-sensitive. It would be valuable if we could accelerate such tasks by performing some of the work ahead of time. Motivated by this, we propose a cost model for quantum algorithms…

In this paper, a sorting technique is presented that takes as input a data set whose primary key domain is known to the sorting algorithm, and works with an time efficiency of O(n+k), where k is the primary key domain. It is shown that the…

An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters, and pairwise…

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

We present a new analysis for QuickHeapsort splitting it into the analysis of the partition-phases and the analysis of the heap-phases. This enables us to consider samples of non-constant size for the pivot selection and leads to better…

We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…

Smoothed analysis is a framework for analyzing the complexity of an algorithm, acting as a bridge between average and worst-case behaviour. For example, Quicksort and the Simplex algorithm are widely used in practical applications, despite…

Because of unmatched improvements in CPU performance, memory transfers have become a bottleneck of program execution. As discovered in recent years, this also affects sorting in internal memory. Since partitioning around several pivots…

We describe a simple algorithm for sampling $n$-qubit Clifford operators uniformly at random. The algorithm outputs the Clifford operators in the form of quantum circuits with at most $5n + 2n^2$ elementary gates and a maximum depth of…