aiqbench analysis
This paper gives an exact sign rule for the ground state of the PXP Hamiltonian, a model of Rydberg atom arrays. A diagonal unitary transform makes the Hamiltonian stoquastic, so positive-only neural network ansatzes can represent the true ground state without architecture-specific changes. For AI and quantum readers, the main point is a reduction in the modeling burden for neural quantum states on this system, though the reported gains across SineKAN, RBM, MLP, and LSTM will depend on how the benchmarks scale with chain length.
Implications of the PXP ground-state sign structure for neural-network variational Monte Carlo
arXiv:2611.00603v1 Announce Type: new Abstract: Positive-definite neural-network quantum states cannot directly represent the ground state of the PXP Hamiltonian, since the ground-state wavefunction carries a nontrivial relative-sign structure. Building on the chiral symmetry of the PXP Hamiltonian, we show that this sign structure is fixed exactly by the parity of the total up-spin number: a diagonal unitary transformation that assigns a sign to each spin configuration according to this parity maps the PXP Hamiltonian to its negative, rendering the transformed Hamiltonian stoquastic on the Rydberg-blockaded Hilbert space. Since the configuration graph of allowed configurations is connected, the Perron-Frobenius theorem guarantees a unique, strictly positive ground state of the transformed Hamiltonian, yielding an exact sign rule for the ground state of the original Hamiltonian in terms of the parity of the up-spin number. Variational Monte Carlo performed directly on the transformed Hamiltonian with a positive-definite ansatz therefore requires no architecture-specific modification to represent the true ground state. We evaluate the performance of this formulation using five representative neural-network quantum state architectures, SineKAN, reflection-symmetrized SineKAN, RBM, MLP, and LSTM, for different chain lengths.
Abstract:Positive-definite neural-network quantum states cannot directly represent the ground state of the PXP Hamiltonian, since the ground-state wavefunction carries a nontrivial relative-sign structure. Building on the chiral symmetry of the PXP Hamiltonian, we show that this sign structure is fixed exactly by the parity of the total up-spin number: a diagonal unitary transformation that assigns a sign to each spin configuration according to this parity maps the PXP Hamiltonian to its negative, rendering the transformed Hamiltonian stoquastic on the Rydberg-blockaded Hilbert space. Since the configuration graph of allowed configurations is connected, the Perron-Frobenius theorem guarantees a unique, strictly positive ground state of the transformed Hamiltonian, yielding an exact sign rule for the ground state of the original Hamiltonian in terms of the parity of the up-spin number. Variational Monte Carlo performed directly on the transformed Hamiltonian with a positive-definite ansatz therefore requires no architecture-specific modification to represent the true ground state. We evaluate the performance of this formulation using five representative neural-network quantum state architectures, SineKAN, reflection-symmetrized SineKAN, RBM, MLP, and LSTM, for different chain lengths.
arXiv:2611.00603 [quant-ph]
(or arXiv:2611.00603v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2611.00603 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 267 words