Related papers: Analyzing and improving a classical Betti number e…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
We present a quantum-inspired classical algorithm that can be used for graph-theoretical problems, such as finding the densest $k$-subgraph and finding the maximum weight clique, which are proposed as applications of a Gaussian boson…
Given a chain complex with the only modification that each cell of the complex has a probability distribution assigned. We will call this complex - a random complex and what should be understood in practice, is that we have a classical…
We introduce a quantum algorithm for efficient biased sampling of the rare events generated by classical memoryful stochastic processes. We show that this quantum algorithm gives an extreme advantage over known classical biased sampling…
Predicting the winner of an election is a favorite problem both for news media pundits and computational social choice theorists. Since it is often infeasible to elicit the preferences of all the voters in a typical prediction scenario, a…
We study the sample complexity of estimating the covariance matrix $T$ of a distribution $\mathcal{D}$ over $d$-dimensional vectors, under the assumption that $T$ is Toeplitz. This assumption arises in many signal processing problems, where…
The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
We present two new problems on lower bounds for resolution Betti numbers of monomial ideals generated in a fixed degree. The first concerns any such ideal and bounds the total Betti numbers, while the second concerns ideals that are…
Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…
Drawing a sample from a discrete distribution is one of the building components for Monte Carlo methods. Like other sampling algorithms, discrete sampling suffers from the high computational burden in large-scale inference problems. We…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
In dense Erd\H{o}s-R\'enyi random graphs, we are interested in the events where large numbers of a given subgraph occur. The mean behavior of subgraph counts is known, and only recently were the related large deviations results discovered.…
Arnoldi method and conjugate gradient method are important classical iteration methods in solving linear systems and estimating eigenvalues. Their efficiency often affected by the high dimension of the space, where quantum computer can play…
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…