The Haar measure plays a vital role in quantum information, but its study often requires a
deep understanding of representation theory, posing a challenge for beginners. This tutorial …

Quantum randomness is an essential key to understanding the dynamics of complex many-
body systems and also a powerful tool for quantum engineering. However, exact realizations …

The complexity of quantum states has become a key quantity of interest across various
subfields of physics, from quantum computing to the theory of black holes. The evolution of …

The entanglement entropy of subsystems of typical eigenstates of quantum many-body
Hamiltonians has recently been conjectured to be a diagnostic of quantum chaos and …

Producing quantum states at random has become increasingly important in modern
quantum science, with applications being both theoretical and practical. In particular …

The applications of random quantum circuits range from quantum computing and quantum
many-body systems to the physics of black holes. Many of these applications are related to …

The concept of quantum complexity has far-reaching implications spanning theoretical
computer science, quantum many-body physics, and high-energy physics. The quantum …

A bstract The fine grained energy spectrum of quantum chaotic systems is widely believed to
be described by random matrix statistics. A basic scale in such a system is the energy range …

Random reversible and quantum circuits form random walks on the alternating group
$\mathrm {Alt}(2^ n) $ and unitary group $\mathrm {SU}(2^ n) $, respectively. Known bounds …

We study the distribution over measurement outcomes of noisy random quantum circuits in
the regime of low fidelity, which corresponds to the setting where the computation …