Computable Rényi mutual information: Area laws and correlations

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on Rényi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

Quantum Machine Learning Tensor Network States

Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools—called tensor network methods—form the backbone of modern numerical methods used to simulate many-body physics and have a further range of applications in machine learning. Finding and contracting tensor network states is a computational task, which may be accelerated by quantum computing. We present a quantum algorithm that returns a classical description of a rank-r tensor network state satisfying an area law and approximating an eigenvector given black-box access to a unitary matrix. Our work creates a bridge between several contemporary approaches, including tensor networks, the variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA), and quantum computation.

The seniority quantum number in Tensor Network States

We employ tensor network methods for the study of the seniority quantum number – defined as the number of unpaired electrons in a many-body wave function – in molecular systems. Seniority-zero methods recently emerged as promising candidates to treat strong static correlations in molecular systems, but are prone to deficiencies related to dynamical correlation and dispersion. We systematically resolve these deficiencies by increasing the allowed seniority number using tensor network methods. In particular, we investigate the number of unpaired electrons needed to correctly describe the binding of the neon and nitrogen dimer and the \mathbf{D_{6h}}D6h symmetry of benzene.

Studying dynamics in two-dimensional quantum lattices using tree tensor network states

We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle in a manifold of binary and quaternary Tree Tensor Network States. The approach is found to be competitive with existing matrix product state approaches. We discuss issues related to the convergence of the method, which could be relevant to a broader set of numerical techniques used for the study of two-dimensional systems.