Automatic Structural Search of Tensor Network States including Entanglement Renormalization

Abstract

Tensor network (TN) states, including entanglement renormalization (ER), can encompass a wider variety of entangled states. When the entanglement structure of the quantum state of interest is non-uniform in real space, accurately representing the state with a limited number of degrees of freedom hinges on appropriately configuring the TN to align with the entanglement pattern. However, a proposal has yet to show a structural search of ER due to its high computational cost and the lack of flexibility in its algorithm. In this study, we conducted an optimal structural search of TN, including ER, based on the reconstruction of their local structures with respect to variational energy. Firstly, we demonstrated that our algorithm for the spin-$1/2$ tetramer singlets model could calculate exact ground energy using the multi-scale entanglement renormalization ansatz (MERA) structure as an initial TN structure. Subsequently, we applied our algorithm to the random XY models with the two initial structures: MERA and the suitable structure underlying the strong disordered renormalization group. We found that, in both cases, our algorithm achieves improvements in variational energy, fidelity, and entanglement entropy. The degree of improvement in these quantities is superior in the latter case compared to the former, suggesting that utilizing an existing TN design method as a preprocessing step is important for maximizing our algorithm's performance.

12 pages, 10 figures

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• A class of quantum many-body states that can be efficiently simulated
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
• Efficient tensor network simulation of IBM's Eagle kicked Ising experiment
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Real-Space Parallel Density Matrix Renormalization Group
• Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance
• Gauging tensor networks with belief propagation
• Entanglement renormalization for disordered systems
• Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation

Cited by in corpus (3)

• Optimal Symbolic Construction of Matrix Product Operators and Tree Tensor Network Operators
• Improving accuracy of tree-tensor network approach by optimization of network structure
• TTNOpt: Tree tensor network package for high-rank tensor compression