Tensor network methods with graph enhancement

Abstract

We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)] to other tensor-network states such as the tensor tree states (TTS) and projected entangled pair states (PEPS). We investigate the suitability of the bare TTS to describe ground states, showing that the description of certain graph states and condensed matter models improves. We investigate graph-enhanced tensor-network states, demonstrating that in some cases (disturbed graph states and for certain quantum circuits) the combination of weighted graph states with tensor tree states can greatly improve the accuracy of the description of ground states and time evolved states. We comment on delineating the boundary of the classically efficiently simulatable states of quantum many-body systems.

26 pages, 14 figures, final version

References in corpus (21)

• Multi-party entanglement in graph states
• Area laws in quantum systems: mutual information and correlations
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• DMRG and periodic boundary conditions: a quantum information perspective
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Quantum information analysis of electronic states at different molecular structures
• General entanglement scaling laws from time evolution
• On entropy growth and the hardness of simulating time evolution
• Classical simulation versus universality in measurement based quantum computation
• Fundamentals of universality in one-way quantum computation
• Ground state approximation for strongly interacting systems in arbitrary dimension
• Unifying variational methods for simulating quantum many-body systems
• The computational difficulty of finding MPS ground states
• Efficient classical simulation of the approximate quantum Fourier transform
• Concatenated tensor network states
• Real-space renormalization yields finite correlations
• Renormalization algorithm with graph enhancement
• Spin gases as microscopic models for non-Markovian decoherence
• Density-matrix-renormalization-group study of excitons in poly-diacetylene chains

Cited by in corpus (8)

• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Entanglement negativity in the critical Ising chain
• A measurement-based variational quantum eigensolver
• Towards adiabatic quantum computing using compressed quantum circuits
• Entanglement negativity and conformal field theory: a Monte Carlo study
• Variational Monte Carlo simulations using tensor-product projected states
• Measurement-based infused circuits for variational quantum eigensolvers
• Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits