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 provided.
A. 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 complex circuits to evaluate. Therefore, we explore the Positive Partial Transpose (PPT) criterion, coupled with overlapping state tomography, as an efficient and scalable spin-spin entanglement witness. It detects pairwise entanglement from reduced density matrices, distinguishes quantum from classical correlations, and applies to both pure and mixed states. It is ideal for studying condensed matter systems prepared on noisy quantum devices as well as future extensions to finite temperatures. We demonstrate the approach on quantum hardware, using variational circuits to prepare quantum critical states with up to 20 qubits and completely map their two-spin entanglement across various quantum phase transitions.
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 circuits not enforcing initial conditions, while the work here implements multi-layer variational circuits that include explicit initial condition loss. All models are tested against both a high-accuracy RK45 numerical baseline and iso-parameter classical PINNs. An ablation study considering qubit count and circuit depth shows that entanglement is the most important architectural property because it provides approximately 10× lower physics residuals than separable QPINNs at equivalent parameter budgets for entangled QPINNs. An additional study of performance based on the number of generators shows the differential between performance of entangled QPINNs and classical PINNs becomes smaller as the system grows larger (40 machines for 2 machines and 27 machines for 4 machines). This supports the theory that a ring CNOT topology replicates physical connection between generators. This research demonstrates that entangled QPINNs are suitable candidates for power system stability analysis on NISQ hardware with 280× fewer parameters than classical PINNs with the same architecture.
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 many-body Hamiltonians from continuous weak measurement records. The key observation is that interaction sparsity reduces the global reconstruction to a set of local inverse problems, whose number is controlled by the interaction connectivity rather than by the system size. Pure separable probe states suffice to drive these inversions, and a graph-coloring construction embeds them into a small number of global product-state preparations. We derive explicit reconstruction-error bounds and a sample-complexity theorem that cleanly separates the finite-sampling statistical noise from the deterministic bias of the iterative state update, and we validate the protocol on time-dependent spin chains with up to $n=8$ qubits. Beyond these results, our analysis provides a rigorous foundation for time-dependent Hamiltonian learning from continuous monitoring in many-body systems, establishing a framework that extends naturally to many platforms and probe ensembles.
Jesús Jiménez-Rodríguez, Giacomo Franceschetto, Antonio Ac'in et al.· 0 citations
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