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From Architectures to Applications: A Review of Neural Quantum States

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arxiv 2402.09402 v3 pith:UHX6WD44 submitted 2024-02-14 cond-mat.dis-nn cond-mat.quant-gascond-mat.str-elquant-ph

classification cond-mat.dis-nncond-mat.quant-gascond-mat.str-elquant-ph
keywords statesquantumsimulationstateapplicationsarchitecturesexponentialneural
verification ladder T0 review T1 audit T2 compute T3 formal
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Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the simulation of such systems, namely neural quantum states (NQS), which overcome the exponential scaling by compressing the state in terms of the network parameters rather than storing all exponentially many coefficients needed for an exact parameterization of the state. We introduce the commonly used NQS architectures and their various applications for the simulation of ground and excited states, finite temperature and open system states as well as NQS approaches to simulate the dynamics of quantum states. Furthermore, we discuss NQS in the context of quantum state tomography.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Infinite temperature at zero energy

    quant-ph 2025-09 conditional novelty 8.0 of 10

    Periodic Feynman-Kitaev clocks built from linear feedback shift register circuits have provably volume-law-entangled ground states and almost all eigenstates.

  2. Unveiling Semiclassical Structures in Quantum Chaotic Eigenstates Using Neural Networks

    quant-ph 2026-07 conditional novelty 7.0 of 10

    Localization-constrained sparse quantum dictionaries trained on baker-map eigenstates spontaneously recover scar-like atoms aligned with classical periodic orbits.

  3. Odd Toric Code in a tilted field: Higgs-confinement multicriticality, spontaneous self-duality symmetry breaking, and valence bond solids

    cond-mat.str-el 2025-07 conditional novelty 7.0 of 10

    Numerics on the odd toric code reveal a continuous multicritical point on the self-dual line where confinement, Higgs condensation, VBS order, and self-duality breaking coincide. Hints of additional VBS phases at inte...

  4. MPStab: an hybrid stabilizers tensor-network quantum circuit simulator

    quant-ph 2026-07 accept novelty 4.0 of 10

    MPStab implements hybrid stabilizer–MPO circuit simulation and shows it outperforms pure tensor networks on Clifford-heavy circuits with moderate magic at matched bond dimension.

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