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 machine learning is often highlighted as one of the most promising practical
applications for which quantum computers could provide a computational advantage …

While quantum state tomography is notoriously hard, most states hold little interest to
practically minded tomographers. Given that states and unitaries appearing in nature are of …

We prove that random quantum circuits on any geometry, including a 1D line, can form
approximate unitary designs over $ n $ qubits in $\log n $ depth. In a similar manner, we …

Monitored quantum dynamics—unitary evolution interspersed with measurements—has
recently emerged as a rich domain for phase structure in quantum many-body systems away …

Learning about physical systems from quantum-enhanced experiments can outperform
learning from experiments in which only classical memory and processing are available …

Classical shadows enable us to learn many properties of a quantum state ρ with very few
measurements. However, near-term and early fault-tolerant quantum computers will only be …

Classical shadow tomography is a powerful randomized measurement protocol for
predicting many properties of a quantum state with few measurements. Two classical …

Classical shadows are a powerful method for learning many properties of quantum states in
a sample-efficient manner, by making use of randomized measurements. Here we study the …

Exploiting near-term quantum computers and achieving practical value is a considerable
and exciting challenge. Most prominent candidates as variational algorithms typically aim to …