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 …

We introduce a novel measure for the quantum property of “nonstabilizerness”—commonly
known as “magic”—by considering the Rényi entropy of the probability distribution …

Recent work has explored using the stabilizer formalism to classically simulate quantum
circuits containing a few non-Clifford gates. The computational cost of such methods is …

The precise control of complex quantum systems promises numerous technological
applications including digital quantum computing. The complexity of such devices renders …

Measurements with randomly chosen settings determine many important properties of
quantum states without the need for a shared reference frame or calibration. They naturally …

Nonstabilizerness, also colloquially referred to as magic, is a resource for advantage in
quantum computing and lies in the access to non-Clifford operations. Developing a …

The classical shadows protocol, recently introduced by Huang, Kueng, and Preskill [Nat.
Phys. 16, 1050 (2020)], is a quantum-classical protocol to estimate properties of an unknown …

Unitary t-designs are a ubiquitous tool in many research areas, including randomized
benchmarking, quantum process tomography, and scrambling. Despite the intensive efforts …

In chaotic quantum systems, the entanglement of a region A can be described in terms of the
surface tension of a spacetime membrane pinned to the boundary of A. Here, we interpret …