This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

We propose a tomographic protocol for estimating any k-body reduced density matrix (k-
RDM) of an n-mode fermionic state, a ubiquitous step in near-term quantum algorithms for …

Algebraic combinatorics is the study of combinatorial objects as an extension of the study of
finite permutation groups, or, in other words, group theory without groups. In the spirit of …

The neural collapse (NC) phenomenon describes an underlying geometric symmetry for
deep neural networks, where both deeply learned features and classifiers converge to a …

As with classical computers, quantum computers require error-correction schemes to reliably
perform useful large-scale calculations. The nature and frequency of errors depends on the …

We propose a construction of $ d^ 2$ complex equiangular lines in $\mathbb {C}^ d $, also
known as SICPOVMs, which were conjectured by Zauner to exist for all d. The construction …

Flexible characterization techniques that provide a detailed picture of the experimental
imperfections under realistic assumptions are crucial to gain actionable advice in the …

Properties of quantum systems can be estimated using classical shadows, which implement
measurements based on random ensembles of unitaries. Originally derived for global …

We develop a method to synthesize a class of entangling multi-qubit gates for a quantum
computing platform with fixed Ising-type interaction with all-to-all connectivity. The only …