Classical simulation of quantum many-body systems with a tree tensor network

By Yaoyun Shi, Luming Duan, Guifré Vidal. 2005

535 citations recorded by the source corpus.

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. B. Skinner
2. A. Nahum
3. J. Ruhman
4. R. Krems
5. Jun Ye
6. Sthitadhi Roy
7. Lincoln D. Carr
8. David Gross

In Atomic and Molecular Physics, and Optics

1. B. Skinner
2. A. Nahum
3. J. Ruhman
4. R. Krems
5. Sthitadhi Roy
6. Lincoln D. Carr
7. Jun Ye
8. D. DeMille

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Such tensor tree networks had already been discussed in [238] (without the basis matrices at the leafs).”
• Information–theoretic implications of quantum causal structures (2014, methodology): “In the third line of (26) we used strong subadditivity, and in the last line we used that the entropy of a classical state conditioned on a quantum state is positive.”
• Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “The tree tensor network state (TTNS) model, whereby all nodes are of 3rdorder or higher, can be considered as a generalization of the Hierarchical Tucker (HT) decomposition, as illustrated by two examples in Figure 23 (see [194, 233] and references therein).”
• Cold and ultracold molecules: science, technology and applications (2009, background): “However, higher dimensional extensions of TEBD such as the projected entangled pair state algorithm (PEPS) [472, 473] are still under development.”
• Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, background): “Tree tensor networks are also interesting quite apart from the connection to the all-to-all circuit [56–65].”
• Synthesis and optimization of reversible circuits—a survey (2011, methodology): “To improve runtime and memory usage, algorithmic techniques have been developed for high-performance simulation of quantum circuits [Shi et al. 2006; Viamontes et al. 2009].”