Simulation of time evolution with the MERA

Abstract

We describe an algorithm to simulate time evolution using the Multi-scale Entanglement Renormalization Ansatz (MERA) and test it by studying a critical Ising chain with periodic boundary conditions and with up to L ~ 10^6 quantum spins. The cost of a simulation, which scales as L log(L), is reduced to log(L) when the system is invariant under translations. By simulating an evolution in imaginary time, we compute the ground state of the system. The errors in the ground state energy display no evident dependence on the system size. The algorithm can be extended to lattice systems in higher spatial dimensions.

final version with data improvement (precision and size), 4.1 pages, 4 figures + extra on XY

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Cited by in corpus (43)

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• A positive tensor network approach for simulating open quantum many-body systems
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• Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
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• Lattice Gauge Tensor Networks
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• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Causal structure of the entanglement renormalization ansatz
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• Time Dependent Variational Principle for Tree Tensor Networks
• Critical properties of homogeneous binary trees
• Concatenated tensor network states
• Further developments in correlator product states: deterministic optimization and energy evaluation
• Improving the efficiency of variational tensor network algorithms
• Critical exponents of one-dimensional quantum critical models by means of MERA tensor network
• Renormalization algorithm with graph enhancement
• Homogeneous MERA states: an information theoretical analysis
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• Entanglement, Tensor Networks and Black Hole Horizons
• Entanglement renormalization and boundary critical phenomena
• Hybrid Tree Tensor Networks for quantum simulation
• Parameterized Hamiltonian simulation using quantum optimal control
• Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz
• Simulation of Anyons Using Symmetric Tensor Network Algorithms
• Simulating quantum circuits using the multi-scale entanglement renormalization ansatz
• Entanglement renormalization for chiral topological phases
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• Entanglement renormalization of fractonic anisotropic ${\mathbb{Z}}_N$ Laplacian models
• Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
• Optimal sampling of tensor networks targeting wave function's fast decaying tails