Programmable quantum simulators and quantum computers are opening unprecedented
opportunities for exploring and exploiting the properties of highly entangled complex …

The future development of quantum technologies relies on creating and manipulating
quantum systems of increasing complexity, with key applications in computation, simulation …

Predicting the properties of complex, large-scale quantum systems is essential for
developing quantum technologies. We present an efficient method for constructing an …

Substantial progress has been made recently on developing provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

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 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 …

We study the power of quantum memory for learning properties of quantum systems and
dynamics, which is of great importance in physics and chemistry. Many state-of-the-art …

The operator entanglement (OE) is a key quantifier of the complexity of a reduced density
matrix. In out-of-equilibrium situations, eg, after a quantum quench of a product state, it is …

We show that the gradient descent algorithm provides an implicit regularization effect in the
learning of over-parameterized matrix factorization models and one-hidden-layer neural …

Low-rank matrices play a fundamental role in modeling and computational methods for
signal processing and machine learning. In many applications where low-rank matrices …