2024/10/24 by Grzegorz Czelusta, Czelusta, Grzegorz, Jakub Mielczarek +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2410.18812
openalex publication_date 2024/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which correspond to SU(2) gauge-invariant discrete field theories. Importantly, the spin network states play a central role in the Loop Quantum Gravity (LQG) approach to the Planck scale physics. Our focus is on the Ising-type spin networks, which provide a basic model of quantum space in LQG. It is shown that the tensor network approach improves the previously introduced methods of constructing quantum circuits for the Ising spin networks by reducing the number of qubits involved. It is also shown that the tensor network approach is convenient for implementing holographic states involving the bulk-boundary conjecture, which contributes to establishing a link between LQG and holographic duality.