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.
This work introduces Matrix Product Evolution (MPE), a tensor-train representation of quantum circuits constructed along the circuit depth rather than along the qubit index, and develops an efficient contraction strategy based on a zip-up procedure to carry out this contraction in practice.
Haruyuki Kawabe, Minoru Nagai, Tsuyoshi Okubo et al.· 0 citations
A protocol for approximating the measurement distributions of quantum states, extending beyond standard observable estimation is introduced, and tightened gate complexity bounds for practically relevant systems, including those with k-local interactions, long-tailed matrix ensembles, and conserved quantities are provid...
Arul Rhik Mazumder, James D. Watson, Samson Wang· 0 citations
This work constructs a native 2D pairwise ansatz and compares its expressibility and trainability with representative 1D ansatze at identical layer depths, despite their different circuit depths.
Quantum phase transitions in many-body systems give rise to highly entangled states, and understanding their quantum correlations is crucial for characterizing quantum materials. However, traditional entanglement measures such as entanglement entropy are difficult to interpret for noisy or mixed states and require comp...
Anshumitra Baul, Xiao Xiao, Phillip C. Lotshaw· 1 citation
This paper provides a detailed comparison of the performance of separable and entangled Quantum Physics-Informed Neural Networks (QPINNs) to solve coupled nonlinear differential equations, with the multi-generator power system swing equation serving as a test application. Previous studies focused on single-layer circui...
L. Kavisankar, Sayak Das, Prashoon Mishra· 2026 International Conferenc...· 0 citations
Characterizing the Hamiltonian that a quantum processor actually implements is central to calibrating and validating current quantum hardware. Many devices, however, operate with generators that are time dependent by design. Here we develop a rigorous and experimentally friendly protocol for learning time-dependent man...
Jesús Jiménez-Rodríguez, Giacomo Franceschetto, Antonio Ac'in et al.· 0 citations
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