During the last ten years, superconducting circuits have passed from being interesting
physical devices to becoming contenders for near-future useful and scalable quantum …

We review the mathematical speed limits on quantum information processing in many-body
systems. After the proof of the Lieb–Robinson Theorem in 1972, the past two decades have …

Variational quantum algorithms are proposed to solve relevant computational problems on
near term quantum devices. Popular versions are variational quantum eigensolvers and …

Classical machine learning (ML) provides a potentially powerful approach to solving
challenging quantum many-body problems in physics and chemistry. However, the …

Quantum learning theory is a new and very active area of research at the intersection of
quantum computing and machine learning. Important breakthroughs in the past two years …

Differentiable programming is a fresh programming paradigm which composes
parameterized algorithmic components and optimizes them using gradient search. The …

Generative modeling, which learns joint probability distribution from data and generates
samples according to it, is an important task in machine learning and artificial intelligence …

The curse of dimensionality associated with the Hilbert space of spin systems provides a
significant obstruction to the study of condensed matter systems. Tensor networks have …

Adiabatic quantum computing (AQC) started as an approach to solving optimization
problems and has evolved into an important universal alternative to the standard circuit …

The spectral gap—the energy difference between the ground state and first excited state of a
system—is central to quantum many-body physics. Many challenging open problems, such …