We apply the framework of block-encodings, introduced by Low and Chuang (under the
name standard-form), to the study of quantum machine learning algorithms and derive …

Graph sparsification underlies a large number of algorithms, ranging from approximation
algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its …

Analyzing large sparse electrical networks is a fundamental task in physics, electrical
engineering and computer science. We propose two classes of quantum algorithms for this …

We introduce a new quantum algorithm for computing the Betti numbers of a simplicial
complex. In contrast to previous quantum algorithms that work by estimating the eigenvalues …

We give a new upper bound on the quantum query complexity of deciding $ st $-connectivity
on certain classes of planar graphs, and show the bound is sometimes exponentially better …

Lin and Lin [16] have recently shown how starting with a classical query algorithm (decision
tree) for a function, we may find upper bounds on its quantum query complexity. More …

Span programs are an important model of quantum computation due to their tight
correspondence with quantum query complexity. For any decision problem $ f $, the …

An important family of span programs, st-connectivity span programs, have been used to
design quantum algorithms in various contexts, including a number of graph problems and …

Quantum span program algorithms for function evaluation sometimes have reduced query
complexity when promised that the input has a certain structure. We design a modified span …

We investigate quantum backtracking algorithms of the type introduced by Montanaro
(Montanaro, arXiv: 1509.02374). These algorithms explore trees of unknown structure and in …