Simulating and sampling from quantum circuits with 2D tensor networks
- 1Center for Computational Quantum Physics, Flatiron Institute, New York, NY, USA
- 2Centre for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
- 3Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
Abstract
Classical simulations of quantum circuits play a vital role in the development of quantum computers and in taking the temperature of the field. Here, we classically simulate various physically-motivated circuits using 2D tensor network ansätze for the many-body wavefunction, which match the geometry of the underlying quantum processor. We employ a generalized boundary Matrix Product State contraction algorithm to controllably generate samples from the resultant tensor network states. Our approach systematically converges both the quality of the final state and the samples drawn from it to the true distribution defined by the circuit, with GPU hardware providing significant speedups over CPU hardware. Using these methods, we simulate the largest local unitary Jastrow ansatz circuit from recent IBM experiments to numerical precision. We also study a domain-wall quench in a 2D discrete-time Heisenberg model on large heavy-hex and rotated square lattices, reflecting IBM’s and Google’s latest processors, respectively. We observe a rapid buildup of complex loop correlations on the Google Willow geometry, which significantly impacts local properties of the system. Meanwhile, loop correlations build up extremely slowly on heavy-hex processors, with almost negligible impact even at large circuit depths. Our results underscore the role processor geometry plays in classical simulability.
Related
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BibTeX
@article{rudolph2026simulating,
title = {{Simulating and sampling from quantum circuits with 2D tensor networks}},
author = {Manuel S. Rudolph and Joseph Tindall},
journal = {npj Quantum Information},
year = {2026},
month = sep,
doi = {10.1038/s41534-026-01372-2},
url = {https://doi.org/10.1038/s41534-026-01372-2},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - Simulating and sampling from quantum circuits with 2D tensor networks
AU - Manuel S. Rudolph
AU - Joseph Tindall
PY - 2026
DA - 2026/09/24
JO - npj Quantum Information
DO - 10.1038/s41534-026-01372-2
UR - https://doi.org/10.1038/s41534-026-01372-2
AB - Classical simulations of quantum circuits play a vital role in the development of quantum computers and in taking the temperature of the field. Here, we classically simulate various physically-motivated circuits using 2D tensor network ansätze for the many-body wavefunction, which match the geometry of the underlying quantum processor. We employ a generalized boundary Matrix Product State contraction algorithm to controllably generate samples from the resultant tensor network states. Our approach systematically converges both the quality of the final state and the samples drawn from it to the true distribution defined by the circuit, with GPU hardware providing significant speedups over CPU hardware. Using these methods, we simulate the largest local unitary Jastrow ansatz circuit from recent IBM experiments to numerical precision. We also study a domain-wall quench in a 2D discrete-time Heisenberg model on large heavy-hex and rotated square lattices, reflecting IBM’s and Google’s latest processors, respectively. We observe a rapid buildup of complex loop correlations on the Google Willow geometry, which significantly impacts local properties of the system. Meanwhile, loop correlations build up extremely slowly on heavy-hex processors, with almost negligible impact even at large circuit depths. Our results underscore the role processor geometry plays in classical simulability.
SN - 2056-6387
ER -