Related papers: Tensor network state correspondence and holography
We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian $H$ by applying the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly and…
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors.…
Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called…
We describe a quantum circuit that produces a highly entangled state of N qubits from which one can efficiently compute expectation values of local observables. This construction yields a variational ansatz for quantum many-body states that…
The study of low-dimensional quantum systems has proven to be a particularly fertile field for discovering novel types of quantum matter. When studied numerically, low-energy states of low-dimensional quantum systems are often approximated…
The complexity of quantum many-body systems is manifested in the vast diversity of their correlations, making it challenging to distinguish the generic from the atypical features. This can be addressed by analyzing correlations through…
While standard approaches to quantum simulation require a number of qubits proportional to the number of simulated particles, current noisy quantum computers are limited to tens of qubits. With the technique of holographic quantum…
Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs and the system becomes topologically trivial. We show that…
The investigation of strongly-correlated quantum matter is difficult due to the curse of dimensionality and intricate entanglement structures. These challenges are particularly pronounced in the vicinity of continuous quantum phase…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of random tensor networks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
One of the main challenges of quantum many-body physics is that the dimensionality of the Hilbert space grows exponentially with the system size, which makes it extremely difficult to solve the Schr\"{o}dinger equations of the system. But…
Tensor network methods, most prominently matrix product states (MPS), have become fundamental tools in modern quantum many-body physics. While MPS and extensions like the multiscale entanglement renormalization ansatz (MERA) and tree tensor…
This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for…
Understanding the limiting capabilities of classical methods in simulating complex quantum systems is of paramount importance for quantum technologies. Although many advanced approaches have been proposed and recently used to challenge…
This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement…
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…
The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand such bulk-boundary…
The tensor network representation of the ground state of a Bethe chain is analytically obtained and studied in relation to its entanglement distribution. Block entanglement displays a maximum at the interplay between single- and…