Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

By J. Hauschild, Frank Pollmann. SciPost Physics Lecture Notes, 2018

461 citations recorded by the source corpus.

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [1]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/d2074c0faaaf2edb8a72e4e9ebc114975c6f6448

How researchers see this paper

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

In Atomic and Molecular Physics, and Optics

1. M. Fishman
2. S. White
3. E. Stoudenmire
4. R. Ma
5. Kristan Temme
6. Chong Wang
7. M. Zaletel
8. Ewout van den Berg

In Computational Mathematics

1. R. Ma
2. Chong Wang
3. S. White
4. M. Fishman
5. E. Stoudenmire

In Materials Chemistry

1. R. Ma
2. Chong Wang
3. S. White
4. M. Fishman
5. E. Stoudenmire

Citations in the corpus

• Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification (2021, unknown): “Future work will be interesting to explore more optimization techniques for tensor network[8], tricks to improve performance[15] and accelerating training and inference time[18].”
• Evidence for the utility of quantum computing before fault tolerance (2023, methodology): “Tensor networks have been widely used to approximate and compress quantum state vectors that arise in the study of the low-energy eigenstates of and time evolution by local Hamiltonians 2,32,33 and, more recently, have been successfully used to simulate low-depth noisy quantum circuits 34–36 .”
• The ITensor Software Library for Tensor Network Calculations (2020, methodology): “For this purpose, we have performed benchmarks comparing the Julia version of ITensor to the TeNPy high-performance tensor network library, which is implemented in a combination of Python and C++ with a Python interface [73].”
• Average Symmetry-Protected Topological Phases (2022, methodology): “[78] Johannes Hauschild and Frank Pollmann, “Effi-”