Related papers: Entanglement renormalization
Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly…
We construct entanglement renormalization schemes which provably approximate the ground states of non-interacting fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice.…
As a quantum-informative window into quantum many-body physics, the concept and application of entanglement renormalization group (ERG) have been playing a vital role in the study of novel quantum phases of matter, especially long-range…
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is…
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…
Numerical simulations of critical lattice systems are fundamentally limited by critical slowing down, as long-range correlations are typically established through slow temporal equilibration. A physically constrained generative framework…
We investigate the role of entanglement in quantum phase transitions, and show that the success of the density matrix renormalization group (DMRG) in understanding such phase transitions is due to the way it preserves entanglement under…
In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop…
We present an infinite lattice DMRG sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct…
A generalization of matrix product states (MPS) is introduced which is suitable for describing interacting quantum systems in two and three dimensions. These scale-renormalized matrix-product states (SR-MPS) are based on a course-graining…
We implement an algorithm which is aimed to reduce the number of basis states spanning the Hilbert space of quantum many-body systems. We test the efficiency of the procedure by working out and analyzing the spectral properties of strongly…
The low-lying bound states of a microscopic quantum many-body system of $n$ particles and the related physical observables can be worked out in a truncated $n$--particle Hilbert space. We present here a non-perturbative analysis of this…
We demonstrate, in the context of quadratic fermion lattice models in one and two spatial dimensions, the potential of entanglement renormalization (ER) to define a proper real-space renormalization group transformation. Our results show,…
Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. By contrast, complex networks defy the usual techniques, due to their small-world character and…
We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement…
Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science. Here we…
We present a quantum cluster solver for spin-$S$ Heisenberg model on a two-dimensional lattice. The formalism is based on the real-space renormalization procedure and uses the lattice point group-theoretical analysis and nonabelian SU(2)…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence…
In this article a comparative study of the renormalization of entanglement in one, two and three dimensional space and its relation with quantum phase transition (QPT) near the critical point is presented by implementing the Quantum…