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Classical simulation of quantum computers is an irreplaceable step in the design of quantum algorithms. Exponential simulation costs demand the use of high-performance computing techniques, and in particular distribution, whereby the…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and…
This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we…
Order statistics play a fundamental role in statistical procedures such as risk estimation, outlier detection, and multiple hypothesis testing as well as in the analyses of mechanism design, queues, load balancing, and various other…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to…
We present a message-passing based parallel version of the Space Saving algorithm designed to solve the $k$--majority problem. The algorithm determines in parallel frequent items, i.e., those whose frequency is greater than a given…
This paper discusses about a sorting algorithm which uses the concept of buckets where each bucket represents a certain number of digits. A two dimensional data structure is used where one dimension represents buckets i. e; number of digits…
In this paper, we analyze the classical $K$-means alternating-minimization algorithm, also known as Lloyd's algorithm (Lloyd, 1956), for a mixture of Gaussians in a data-distributed setting that incorporates local iteration steps. Assuming…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP). In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
We describe a dynamic programming algorithm for computing the marginal distribution of discrete probabilistic programs. This algorithm takes a functional interpreter for an arbitrary probabilistic programming language and turns it into an…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
We show explicitly that high harmonics of the classical Liouville density distribution in the chaotic regime can be obtained efficiently on a quantum computer [1,2]. As was stated in [1], this provides information unaccessible for classical…