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新论文 · v1arXiv:2611.14006

Normalizing Flows for Classical Simulation of Quantum Circuits in Phase Space

Edward Jiang, Timothy Heightman, Marcin Płodzień

原文摘要

We present a novel framework to learn a representation of quantum circuits based on the phase space formulation of many-body systems. Given that $N$-qubit states can be represented as probability distributions on a smooth $2N$-dimensional manifold, we show how unitary gates can be parameterized as normalizing flows between these distributions, opening a new avenue for quantum circuit simulation using generative models. We evaluate our method on three common families of quantum circuits, and show that its accuracy exceeds that of current state-of-the-art neural network methods for large system sizes.

quant-ph · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2609.07591

Topology Obstructs Pure Foundation Neural Quantum States

Timothy Heightman, Elena Orlova, Philip Mantrov, Aleksei Ustimenko

原文摘要

Foundation models for ground states in spin-1/2 systems are a promising method for problems ranging from quantum chemistry to identifying new phase diagrams. Nearly all such models are currently pure-states that condition on the Hamiltonian's parameters, whose Monte Carlo samples give energy estimates according to the variational principle. In this contribution, we show that this representation is topologically obstructed. For any gapped Hamiltonian family whose ground-state bundle is non-trivial, every continuous normalized state-vector model has zero fidelity with the ground state at some parameter value in the Hamiltonian family. For that value, the energy is at least one spectral gap, $Δ$, with an $O(Δ)$ gap in an open-neighbourhood of that point. We show that this is a sufficient no-go also in the case of degenerate ground-state manifolds, time dynamics, and periodic systems with mixed space-time topology, demonstrating these obstructions on one- and two-qubit systems. We discuss how this causes a spike in the fidelity susceptibility, giving a numerical signature of a phase-transition where there is none. Finally, we show that operator-valued models canonically avoid these obstructions and preserve topological information, implying a structural necessity in representation for foundation neural quantum states.

quant-ph · cond-mat.dis-nn · cond-mat.str-el · cs.AI · math-ph

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