Sampling isometric tensor network states with monitored quantum circuits

@misc{rong2026sampling,
  title = {{Sampling isometric tensor network states with monitored quantum circuits}},
  author = {Yuqing Rong and Huan-Hai Zhou and Guo-Yi Zhu and Jinguo Liu},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.18511},
  eprint = {2608.18511},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.18511},
}

TY  - UNPB
TI  - Sampling isometric tensor network states with monitored quantum circuits
AU  - Yuqing Rong
AU  - Huan-Hai Zhou
AU  - Guo-Yi Zhu
AU  - Jinguo Liu
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.18511
UR  - https://arxiv.org/abs/2608.18511
AB  - Projected entangled pair states (PEPS) provide an efficient variational ansatz for two-dimensional quantum phases, but computing observables remains challenging because PEPS contraction is generally costly. Here, we parameterize two-dimensional quantum states using variational PEPS subject to isometric constraints and map the resulting ansatz onto monitored quantum circuits, replacing tensor-network contraction with circuit sampling. For infinite cylinders, the transfer matrix defines a quantum channel on the virtual boundary. We use a fixed-point treatment and a monitored-circuit unraveling of this channel to evaluate observables efficiently. Using a constant number of variational parameters and a number of qubits that scales only with the cylinder width, our method yields a phase diagram for the J_1-J_2 model in qualitative agreement with DMRG results. Because the monitored circuits are compatible with near-term quantum hardware, this approach provides a hybrid quantum-classical framework for simulating two-dimensional quantum many-body systems.
ER  -