Aug 2026· 2 citations· ⚡ 1 influential· 25 references
PhysicsComputer Science
Abstract
Under mild assumptions, any quantum mechanical (QM) model or quantum field theory (QFT) admits a representation in terms of an ensemble of neural networks with countably many random parameters. We investigate the features of NN-QM and NN-FT models with finitely many parameters, such as a feedforward network of width $N<\infty$. We find that, generically, such models must violate one of the properties of conventional Euclidean QFTs, such as reflection positivity or cluster decomposition. We present several complementary ways of understanding which features can and cannot be preserved at finite $N$, both in QM and in QFT.
A no-go theorem is used to separate four versions of neural network field theory, according to whether the defining object is the finite width ensemble or its infinite width limit, and whether the target the authors want to compute is a quantum or an effective field theory.
This work proves that, for sufficiently large circuit width, the nonlinear gradient flow is quantitatively approximated by a linearized NTK model, with explicit bounds depending on the number of qubits, circuit depth, circuit light-cone geometry, and the dimension of the domain of the solution to the PDE.
This work extends the notion of quantum neural network, using random sampling and classical data processing to enlarge the optimization space in a way that includes linear combinations of completely positive maps and leverages its enlarged optimization space to achieve increased expressivity and improved noise robustne...
Ben-Chi Zhao, Xuanqiang Zhao, Yi-Nan Li et al.· 0 citations
Neural quantum states (NQS) have emerged as powerful representations of quantum states with rapidly expanding applications across quantum many-body physics. Yet our understanding of when neural networks can efficiently represent physical quantum states remains limited, in part due to the nonlinear parameterization of N...
Nisarga Paul, Ke-Huang Chen, J. Jiang et al.· 0 citations
This work furnishes a proof-of-concept demonstrating that hyperbolic non-autoregressive NQS ansatze, thanks to the exponential volume of the hyperbolic geometry underlying their constructions, might be more natural at representing volume-law quantum systems than conventional Euclidean NQS.
It is demonstrated that this problem can be effectively amortized across an arbitrary and universal set of Hamiltonians by a foundation model with $\sim0.5$B variational parameters, trained with contemporary techniques from large language models and deep reinforcement learning.
Timothy Heightman, Elena Orlova, Philip Mantrov et al.· 1 citation· ⚡1
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