Related papers: Almost all decision trees do not allow significant…
Decision trees provide a rich family of highly non-linear but efficient models, due to which they continue to be the go-to family of predictive models by practitioners across domains. But learning trees is challenging due to their discrete…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to…
We consider two core algorithmic problems for probabilistic verification: the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs). For MDPs with treewidth $k$, we present…
We prove the following conjecture, raised by Aaronson and Ambainis in 2008: Let $f:\{-1,1\}^n \rightarrow [-1,1]$ be a multilinear polynomial of degree $d$. Then there exists a variable $x_i$ whose influence on $f$ is at least…
I survey, for a general scientific audience, three decades of research into which sorts of problems admit exponential speedups via quantum computers -- from the classics (like the algorithms of Simon and Shor), to the breakthrough of…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
Optimal decision tree (\odt) is a fundamental problem arising in applications such as active learning, entity identification, and medical diagnosis. An instance of \odt is given by $m$ hypotheses, out of which an unknown ``true'' hypothesis…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…
Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key…
This paper tightens the best known analysis of Hein's 1989 algorithm to infer the topology of a weighted tree based on the lengths of paths between its leaves. It shows that the number of length queries required for a degree-$k$ tree of $n$…
It is found that Grover's quantum search algorithm is not robust against phase inversion and Hadmard transformation inaccuracies. Imperfect phase inversions and Hadmard-Walsh transformations in Grover's quantum search algorithm lead to…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
The rate of the trace distance is used to evaluate quantum speed-up for arbitrary mixed states. Compared with some present methods, the approach based on trace distance can provide an optimal bound to the speed of the evolution. The…
We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…
Different sources of information might tell different stories about the evolutionary history of a given set of species. This leads to (rooted) phylogenetic trees that "disagree" on triples of species, which we call "conflict triples". An…
We propose an approach for quantifying a quantum circuit's quantumness as a means to understand the nature of quantum algorithmic speedups. Since quantum gates that do not preserve the computational basis are necessary for achieving quantum…