[ { "id": "authors:rwezk-de264", "collection": "authors", "collection_id": "rwezk-de264", "cite_using_url": "https://authors.library.caltech.edu/records/rwezk-de264", "type": "article", "title": "Quantum Glassiness from Efficient Learning", "author": [ { "family_name": "Anschuetz", "given_name": "Eric R.", "orcid": "0000-0002-9825-3692", "clpid": "Anschuetz-Eric-R" } ], "abstract": "We show a relation between quantum learning theory and algorithmic hardness. We use the existence of efficient, local learning algorithms for energy estimation\u2014such as the classical shadows algorithm\u2014to prove that finding near-ground states of disordered quantum systems exhibiting a certain topological property is impossible in the average case for Lipschitz quantum algorithms. A corollary of our result is that many standard quantum algorithms fail to find near-ground states of these systems, including time-T Lindbladian dynamics from an arbitrary initial state, time-T quantum annealing, phase estimation to T bits of precision, and depth-T variational quantum algorithms, whenever T is less than some universal constant times the logarithm of the system size. To achieve this, we introduce a generalization of the overlap gap property (OGP) for quantum systems that we call the quantum overlap gap property (QOGP). This property is defined by a specific topological structure over representations of low-energy quantum states as output by an efficient local learning algorithm. We prove that preparing low-energy states of systems which exhibit the QOGP is intractable for quantum algorithms whose outputs are stable under perturbations of their inputs. We then prove that the QOGP is satisfied for a sparsified variant of the quantum p-spin model, giving the first known algorithmic hardness-of-approximation result for quantum algorithms in finding the ground state of a non-stoquastic, noncommuting quantum system. Our resulting lower bound for quantum algorithms optimizing this model using Lindbladian evolution matches (up to constant factors) the best-known time lower bound for classical Langevin dynamics optimizing classical p-spin models. For this reason we suspect that finding ground states of typical instances of these quantum spin models using quantum algorithms is, in practice, as intractable as the classical p-spin model is for classical algorithms. Inversely, we show that the Sachdev\u2013Ye\u2013Kitaev model does not exhibit the QOGP, consistent with previous evidence that the model is rapidly mixing at low temperatures.", "doi": "10.1007/s00220-025-05536-7", "issn": "0010-3616", "publisher": "Springer Science and Business Media LLC", "publication": "Communications in Mathematical Physics", "publication_date": "2026-02", "series_number": "2", "volume": "407", "issue": "2", "pages": "30" }, { "id": "authors:w86fw-6xs05", "collection": "authors", "collection_id": "w86fw-6xs05", "cite_using_url": "https://authors.library.caltech.edu/records/w86fw-6xs05", "type": "article", "title": "Does provable absence of barren plateaus imply classical simulability?", "author": [ { "family_name": "Cerezo", "given_name": "M.", "orcid": "0000-0002-2757-3170" }, { "family_name": "Larocca", "given_name": "Martin", "orcid": "0000-0002-8700-4308" }, { "family_name": "Garc\u00eda-Mart\u00edn", "given_name": "Diego", "orcid": "0000-0002-0693-1952" }, { "family_name": "Diaz", "given_name": "N. L." }, { "family_name": "Braccia", "given_name": "Paolo", "orcid": "0000-0003-0158-0943" }, { "family_name": "Fontana", "given_name": "Enrico" }, { "family_name": "Rudolph", "given_name": "Manuel S.", "orcid": "0000-0003-1261-1442" }, { "family_name": "Bermejo", "given_name": "Pablo" }, { "family_name": "Ijaz", "given_name": "Aroosa" }, { "family_name": "Thanasilp", "given_name": "Supanut", "orcid": "0000-0002-8252-4056" }, { "family_name": "Anschuetz", "given_name": "Eric R.", "orcid": "0000-0002-9825-3692", "clpid": "Anschuetz-Eric-R" }, { "family_name": "Holmes", "given_name": "Zo\u00eb" } ], "abstract": "A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective article, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We collect evidence-on a case-by-case basis-that many commonly used models whose loss landscapes avoid barren plateaus can also admit classical simulation, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. Thus, while stressing that quantum computers can be essential for collecting data, our analysis sheds doubt on the information processing capabilities of many parametrized quantum circuits with provably barren plateau-free landscapes. We end by discussing the (many) caveats in our arguments including the limitations of average case arguments, the role of smart initializations, models that fall outside our assumptions, the potential for provably superpolynomial advantages and the possibility that, once larger devices become available, parametrized quantum circuits could heuristically outperform our analytic expectations.", "doi": "10.1038/s41467-025-63099-6", "pmcid": "PMC12378457", "issn": "2041-1723", "publisher": "Nature Publishing Group", "publication": "Nature Communications", "publication_date": "2025-08-25", "series_number": "1", "volume": "16", "issue": "1", "pages": "7907" }, { "id": "authors:r0y54-eek49", "collection": "authors", "collection_id": "r0y54-eek49", "cite_using_url": "https://authors.library.caltech.edu/records/r0y54-eek49", "type": "article", "title": "Strongly Interacting Fermions Are Nontrivial yet Nonglassy", "author": [ { "family_name": "Anschuetz", "given_name": "Eric R.", "orcid": "0000-0002-9825-3692", "clpid": "Anschuetz-Eric-R" }, { "family_name": "Chen", "given_name": "Chi-Fang", "orcid": "0000-0001-5589-7896", "clpid": "Chen-Chi-Fang" }, { "family_name": "Kiani", "given_name": "Bobak T.", "orcid": "0000-0003-1477-0308" }, { "family_name": "King", "given_name": "Robbie", "orcid": "0000-0002-8152-6340", "clpid": "King-Robbie" } ], "abstract": "Random spin systems at low temperatures are glassy and feature computational hardness in finding low-energy states. We study the random all-to-all interacting fermionic Sachdev-Ye-Kitaev model and prove that, in contrast, the low-energy states have polynomial circuit depth, yet the annealed and quenched free energies agree to polynomially inverse low temperatures, ruling out a glassy phase transition in this sense. These results are derived by showing that fermionic and spin systems significantly differ in their \"commutation index,\" which quantifies the noncommutativity of Hamiltonian terms. Our results suggest that low-temperature strongly interacting fermions, unlike spins, belong in a classically nontrivial yet quantumly easy phase.", "doi": "10.1103/cbqf-d24r", "issn": "0031-9007", "publisher": "American Physical Society", "publication": "Physical Review Letters", "publication_date": "2025-07-17", "series_number": "3", "volume": "135", "issue": "3", "pages": "030602" } ]