Abstract Graph Neural Networks (GNN) are inherently limited in their expressive power.
Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler …

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 …

We propose a qubit efficient scheme to study ground-state properties of quantum many-body
systems on near-term noisy intermediate-scale quantum computers. One can obtain a tensor …

Tensor network methods are taking a central role in modern quantum physics and beyond.
They can provide an efficient approximation to certain classes of quantum states, and the …

We develop an algorithmic framework for contracting tensor networks and demonstrate its
power by classically simulating quantum computation of sizes previously deemed out of …

Effectively compressing and optimizing tensor networks requires reliable methods for fixing
the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new …

Tensor networks are efficient representations of high-dimensional tensors with widespread
applications in quantum many-body physics. Recently, they have been adapted to the field …

Ground state preparation is classically intractable for general Hamiltonians. On quantum
devices, shallow parametrized circuits can be effectively trained to obtain short-range …

We introduce a unified framework to compute the solution space properties of a broad class
of combinatorial optimization problems. These properties include finding one of the optimum …

Tensor network contraction is central to problems ranging from many-body physics to
computer science. We describe how to approximate tensor network contraction through …