Sampling isometric tensor network states with monitored quantum circuits

• URL: http://arxiv.org/abs/2608.18511v1
• Date: Wed, 19 Aug 2026 03:57:05 GMT
• Title: Sampling isometric tensor network states with monitored quantum circuits
• Abstract summary: We parameterize two-dimensional quantum states using variational PEPS subject to constraints.<n>We map the resulting ansatz onto monitored quantum contraction circuits.<n>This approach provides a hybrid quantum-classical framework for two-dimensional quantum-body systems.
• Score: 1.137457877869062
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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