Mapping functions on bits to Hamiltonians acting on qubits has many applications in
quantum computing. In particular, Hamiltonians representing Boolean functions are required …

Common information is ubiquitous in information theory and related areas such as
theoretical computer science and discrete probability. However, because there are multiple …

The approximate degree of a Boolean function f is the least degree of a real polynomial that
approximates f pointwise to error at most 1/3. The approximate degree of f is known to be a …

Abstract The $\textit {stabilizer rank} $ of a quantum state $\psi $ is the minimal $ r $ such
that $\left|\psi\right\rangle=\sum_ {j= 1}^ r c_j\left|\varphi_j\right\rangle $ for $ c_j\in\mathbb …

We consider the problem of representing Boolean functions exactly by" sparse" linear
combinations (over $\mathbb {R} $) of functions from some" simple" class ${\cal C} $. In …

We give new quantum algorithms for evaluating composed functions whose inputs may be
shared between bottom-level gates. Let $ f $ be an $ m $-bit Boolean function and consider …

Abstract Let (X, ‖ ⋅ ‖ _X)(X,‖·‖ X) be a Banach space. The purpose of this article is to
systematically investigate dimension independent properties of vector valued functions f:{-1 …

These are notes from a course I gave at MIT on the Fall of 2015 entitled:“18. S096: Topics in
Mathematics of Data Science”. These notes are not in final form and will be continuously …

We establish a link between stabilizer states, stabilizer rank, and higher-order Fourier
analysis–a still-developing area of mathematics that grew out of Gowers's celebrated Fourier …

The entropy method originates from information theory, and has found a mass of
applications therein. This monograph illustrates the power of the entropy method in …