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Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
A \emph{linear extension} of a partial order \(\preceq\) over items \(A = \{ 1, 2, \ldots, n \}\) is a permutation \(\sigma\) such that for all \(i < j\) in \(A\), it holds that \(\neg(\sigma(j) \preceq \sigma(i))\). Consider the problem of…
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…
The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. Previous known results show that for any $N$-dimensional subspace of the space of continuous functions it is…
Fast secure random number generation is essential for high-speed encrypted communication, and is the backbone of information security. Generation of truly random numbers depends on the intrinsic randomness of the process used and is usually…
We present an implementation of a Monte Carlo algorithm that generates points randomly and uniformly on a set of arbitrary surfaces. The algorithm is completely general and only requires the geometry modeling software to provide the…
In this paper, we introduce a novel approach for generating random elements of a finite group given a set of generators of that. Our method draws upon combinatorial group theory and automata theory to achieve this objective. Furthermore, we…
We describe a technique for drawing values from discrete distributions, such as sampling from the random variables of a mixture model, that avoids computing a complete table of partial sums of the relative probabilities. A table of…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
In this work we present a model for computation of random processes in digital computers which solves the problem of periodic sequences and hidden errors produced by correlations. We show that systems with non-invertible non-linearities can…
In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…
Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
Microaggregation is a method to coarsen a dataset, by optimally clustering data points in groups of at least $k$ points, thereby providing a $k$-anonymity type disclosure guarantee for each point in the dataset. Previous algorithms for…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)---an analogue of optimal mass transport…
In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been…
Unitary $T$-designs play an important role in quantum information, with diverse applications in quantum algorithms, benchmarking, tomography, and communication. Until now, the most efficient construction of unitary $T$-designs for $n$-qudit…