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版本更新 · v2arXiv:2610.16733

TheoPhysEval: Assessing AI agents at autonomous theoretical physics problem solving

A. Ramesh Chandra, Aaghaz Mahajan, Ainesh Sanyal, Mianqi Wang, Shubhadeep Chakraborty, Sudip Chakraborty, Shailesh Chandrasekharan, Rama Govindarajan 等 35 位作者

原文摘要

We present a suite of 50 unpublished research-level theoretical physics problems with verifiable answers. Without AI assistance, a typical problem in our collection could be solved by a world expert in about a day or less but would take considerably longer for experts in adjacent specialties. We test the ability of off-the-shelf AI agents to tackle these problems autonomously, without human hints. When given access to tools available in a realistic setting, including the ability to search the literature and write scripts for numerical and symbolic work, the best-performing agent, GPT-6-Astra harnessed in Codex, obtains the final answers with a near-perfect accuracy of 98% at an average cost under USD 3 per problem. On average, agents show only small changes in accuracy when denied web search and access to background research papers, suggesting significant memorization of the literature. These results suggest that state-of-the-art agents can accurately perform concrete calculations required across theoretical physics research. We comment on the broader implications of these findings and discuss possible explanations for the current lack of agent-led breakthroughs in theoretical physics despite their outstanding problem-solving abilities.

hep-th · cond-mat.stat-mech · cond-mat.str-el · cs.AI · gr-qc

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2509.13423

Computational complexity of Berry phase estimation in topological phases of matter

Ryu Hayakawa, Kazuki Sakamoto, Chusei Kiumi

原文摘要

The Berry phase is a fundamental quantity in the classification of topological phases of matter. In this paper, we present a new quantum algorithm and several complexity-theoretical results for the Berry phase estimation (BPE) problems. Our new quantum algorithm achieves BPE in a more general setting than previously known quantum algorithms, with a theoretical guarantee. For the complexity-theoretic results, we consider two main cases. First, we prove $\mathsf{BQP}$-completeness when we are given a guiding state that has a large overlap with the ground state. This result establishes an exponential quantum speedup for estimating the Berry phase. Second, we prove $\mathsf{UQMA} \cap \mathsf{co}$-$\mathsf{UQMA}$-completeness when we have an $\textit{a priori}$ bound for the ground-state energy. Here, $\mathsf{UQMA}$ is the unique witness version of $\mathsf{QMA}$, and $\mathsf{UQMA} \cap \mathsf{co}$-$\mathsf{UQMA}$ precisely captures the complexity of BPE without the known guiding state. Remarkably, this problem is, to our knowledge, the first natural problem complete for $\mathsf{UQMA} \cap \mathsf{co}$-$\mathsf{UQMA}$. These results advance the role of quantum computing in the study of topological phases of matter and provide a pathway for clarifying the connection between topological phases of matter and computational complexity.

quant-ph · cond-mat.str-el · cs.CC

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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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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.11935

AI-Driven Discovery of Entanglement Witness in Spin Hamiltonians

Jiwei Tian, Mouyang Cheng, Mingda Li

原文摘要

Entanglement is a crucial resource in quantum science and engineering, but detecting it in many-body states from experimentally accessible observables remains challenging. Here we introduce EntNet, an AI-driven framework to discover compact combinations of spin observables that accurately distinguish entangled from fully separable many-body mixed states in one-dimensional spin-$1/2$ chains governed by short-range Hamiltonians. We construct local-unitary-invariant representations of measurable Pauli correlators up to four-body order, sparsely select 16 candidate invariant feature channels, and learn their spatial structure using a Transformer architecture with rotary positional embeddings. Using only expectation values of these low-order observables, EntNet achieves $>98\%$ recall on certified entangled states with near-zero false-positive rates on separable states. Remarkably, it exhibits transferability across system sizes and distinct Hamiltonian families, including frustrated and disordered spin models, with minimal loss of accuracy. Beyond detection, EntNet provides physical insight into entanglement detection by revealing a selective spatial organization of pair correlations, while its finite-temperature decision boundary tracks the excitation gap of Jordan-Wigner quasiparticles. These results establish a transferable and physically interpretable framework for data-driven discovery of entanglement witnesses from local correlation functions.

quant-ph · cond-mat.str-el · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2603.18205

Tackling the Sign Problem in the Doped Hubbard Model with Normalizing Flows

Dominic Schuh, Lena Funcke, Janik Kreit, Thomas Luu, Simran Singh

原文摘要

The Hubbard model at finite chemical potential is a cornerstone for understanding doped correlated systems, but simulations are severely limited by the sign problem. In the auxiliary-field formulation, the spin basis mitigates the sign problem, yet severe ergodicity issues have limited its use. We extend recent advances with normalizing flows at half-filling to finite chemical potential by introducing an annealing scheme enabling ergodic sampling. Compared to state-of-the-art hybrid Monte Carlo in the charge basis, our approach accurately reproduces exact diagonalization results while reducing statistical uncertainties by an order of magnitude, opening a new path for simulations of doped correlated systems.

cond-mat.str-el · cs.LG · hep-lat

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.10039

Efficient classical simulation of Fermi-Hubbard models with Kramers symmetry

Chaithanya Rayudu, Jun Takahashi, Ojas Parekh, Andrew Zhao

原文摘要

Quantum Monte Carlo methods are widely used to solve quantum many-body problems. However, rigorous guarantees for their performance are poorly understood, especially for simulating interacting fermions. In this work, we develop a quantum Monte Carlo algorithm for a broad family of fermionic systems exhibiting Kramers time-reversal symmetry, and prove that their partition functions can be estimated in polynomial time. This family, which contains many important classes of Hubbard-type models, is known to both avoid the sign problem and obey a Lee-Yang zero-freeness theorem. Thus our results suggest that these two properties together may enable efficient classical algorithms for quantum many-body systems more broadly.

cs.DS · cond-mat.stat-mech · cond-mat.str-el · quant-ph

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2609.23942

费米子的李-杨定理

Lee-Yang theorem for fermions

Chaithanya Rayudu, Takahiro Misawa, Andrew Zhao, Jun Takahashi

AI 速读 基于摘要

作者证明了一类广泛相互作用的费米子模型配分函数的李-杨零点不存在定理，并据此给出估计基态能量的可证明高效量子算法。

quant-ph · cond-mat.stat-mech · cond-mat.str-el · cs.CC · math-ph

arXiv ↗PDF ↗
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Lee-Yang theorems are a powerful tool for studying many-body systems, with applications ranging from analyzing phase transitions to proving the efficiency of certain classical and quantum algorithms. In this work, we prove a Lee-Yang zero-freeness theorem for the partition function of a broad class of interacting fermion models, implying the existence of a provably efficient quantum algorithm for estimating their ground-state energies. This class includes several well-known models such as the attractive Hubbard model, repulsive Hubbard model on bipartite graphs, and the interacting Hofstadter model. Our results also rigorously establish the nonexistence of phase transitions in these models in the presence of a nonzero local external field.

新论文 · v1arXiv:2611.07337

Frustration-freeness is decidable but unprovable

Naoto Shiraishi

原文摘要

The frustration-free property is valuable in quantum many-body systems, which states that its ground states simultaneously minimize all local interaction terms, even when these terms act on overlapping degrees of freedom. Prominent examples include the AKLT model and Kitaev's toric code model, which serve as paradigmatic models of symmetry-protected topological phases and topological order, respectively. A fundamental question is whether a given Hamiltonian is frustration-free for all system sizes. Here we establish two seemingly contradictory results concerning this decision problem. First, we prove that frustration-freeness is decidable for any fixed local Hilbert space dimension. Specifically, there exists a finite, Hamiltonian-independent system-size cutoff such that frustration-freeness at this cutoff size guarantees frustration-freeness at all system sizes. Second, on the other hand, we also show that there exists a frustration-free Hamiltonian whose frustration-freeness cannot be proved within the standard axioms of mathematics (ZFC). We reconcile these seemingly contradictory results by showing that the cutoff, although finite for each local Hilbert space dimension, is uncomputable as a function of that dimension. Our findings reveal an unexpected fundamental distinction between decidability and provability arising in quantum many-body physics.

quant-ph · cond-mat.stat-mech · cond-mat.str-el · cs.LO

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2601.04104

Point-Group Equivariant Neural Networks for Local Dynamics in Lattice Systems

Yunhao Fan, Gia-Wei Chern

原文摘要

We develop point-group equivariant neural networks for learning local mappings used in dynamical simulations of lattice systems. The same network acts on a finite neighborhood around each site, respecting lattice translations through shared parameters. The local configuration is decomposed into features that transform according to irreducible representations of the point group, and hidden features retain this organization throughout the network. Equivariant linear maps and symmetry-allowed tensor products then learn nonlinear spatial correlations while preserving the required transformation laws. This approach avoids constructing a fixed set of hand-crafted invariant descriptors, whose selection requires choices about which local correlations to retain. It also allows the complexity of the learned mapping to grow without enlarging its spatial cutoff. We demonstrate the construction by learning the forces governing adiabatic dynamics in the square-lattice Holstein model. Comparisons with exact diagonalization test the accuracy of the predicted forces and the evolution of spatial correlations. Force evaluation scales linearly with system size, allowing the trained model to simulate charge-density-wave ordering on large lattices. These simulations reproduce anomalously slow coarsening of the charge-density-wave domains, illustrating the use of the learned local mapping for collective dynamics.

cond-mat.str-el · cs.LG · physics.comp-ph

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arXiv ↗PDF ↗