Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency

Autor: Vittorio Giovannetti, Giovanni Cataldi, Simone Montangero, Nicola Dalla Pozza, Simone Notarnicola, Giuseppe Magnifico, Ashkan Abedi
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Physics and Astronomy (miscellaneous)
QC1-999
Structure (category theory)
FOS: Physical sciences
Computer Science::Digital Libraries
01 natural sciences
010305 fluids & plasmas
symbols.namesake
Condensed Matter - Strongly Correlated Electrons
Fractal
0103 physical sciences
MATRIX RENORMALIZATION-GROUP
Tensor
010306 general physics
Condensed Matter - Statistical Mechanics
Mathematics
Quantum Physics
Statistical Mechanics (cond-mat.stat-mech)
Strongly Correlated Electrons (cond-mat.str-el)
Physics
Mathematical analysis
Hilbert space
Hilbert curve
Computational Physics (physics.comp-ph)
Atomic and Molecular Physics
and Optics
Matrix multiplication
Lattice (module)
STATES
Quantum Gases (cond-mat.quant-gas)
DENSITY
Computer Science::Mathematical Software
symbols
Ising model
Quantum Physics (quant-ph)
Condensed Matter - Quantum Gases
Physics - Computational Physics
Zdroj: Quantum, Vol 5, p 556 (2021)
Quantum (Vienna) 5 (2021):--–--. doi:10.22331/Q-2021-09-29-556
info:cnr-pdr/source/autori:Cataldi G.; Abedi A.; Magnifico G.; Notarnicola S.; Pozza N.D.; Giovannetti V.; Montangero S./titolo:Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency/doi:10.22331%2FQ-2021-09-29-556/rivista:Quantum (Vienna)/anno:2021/pagina_da:--/pagina_a:--/intervallo_pagine:--–--/volume:5
Quantum
DOI: 10.22331/Q-2021-09-29-556
Popis: We present a novel mapping for studying 2D many-body quantum systems by solving an effective, one-dimensional long-range model in place of the original two-dimensional short-range one. In particular, we address the problem of choosing an efficient mapping from the 2D lattice to a 1D chain that optimally preserves the locality of interactions within the TN structure. By using Matrix Product States (MPS) and Tree Tensor Network (TTN) algorithms, we compute the ground state of the 2D quantum Ising model in transverse field with lattice size up to $64\times64$, comparing the results obtained from different mappings based on two space-filling curves, the snake curve and the Hilbert curve. We show that the locality-preserving properties of the Hilbert curve leads to a clear improvement of numerical precision, especially for large sizes, and turns out to provide the best performances for the simulation of 2D lattice systems via 1D TN structures.
17 pages, 13 figures
Databáze: OpenAIRE
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