Directly observing replica symmetry breaking in a vector quantum-optical spin glass

Ronen M. Kroeze; Brendan P. Marsh; David Atri Schuller; Henry S. Hunt; Alexander N. Bourzutschky; Michael Winer; Sarang Gopalakrishnan; Jonathan Keeling; Benjamin L. Lev

doi:10.1126/science.adu7710

Directly observing replica symmetry breaking in a vector quantum-optical spin glass

Ronen M. Kroeze, Brendan P. Marsh, David Atri Schuller, Henry S. Hunt, Alexander N. Bourzutschky, Michael Winer, Sarang Gopalakrishnan, Jonathan Keeling, Benjamin L. Lev^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Spin glasses are quintessential examples of complex matter. Although their ordering lacks complete theoretical understanding, abstract models of spin glasses inform problems in other fields, such as combinatorial optimization and artificial intelligence—where they form a mathematical basis for neural network computing. We demonstrate the ability to realize a spin glass of a distinct driven-dissipative and vector form. By microscopically visualizing its glassy spin states, the technique allows us to directly measure replica symmetry breaking and the resulting ultrametric hierarchical structure. Ultrametricity is known to be emergent in models of evolution, protein folding, and climate change; this work shows it to be directly observable in a physically realized system.

Original language	English
Article number	eadu7710
Number of pages	11
Journal	Science
Volume	First Release
Early online date	14 Aug 2025
DOIs	https://doi.org/10.1126/science.adu7710
Publication status	E-pub ahead of print - 14 Aug 2025

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10.1126/science.adu7710

Kroeze_2025_Science_Directly-observing-replica-symmetry-breaking-AAM_CCBY
Copyright © 2025 the Authors. This work has been made available online in accordance with the University of St Andrews Open Access policy. This accepted manuscript is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The final published version of this work is available at https://doi.org/10.1126/science.adu7710
Accepted author manuscript, 1.07 MBLicence: CC BY

Cite this

@article{c08d3ae46f9a4f41bb634521ac4f1491,

title = "Directly observing replica symmetry breaking in a vector quantum-optical spin glass",

abstract = "Spin glasses are quintessential examples of complex matter. Although their ordering lacks complete theoretical understanding, abstract models of spin glasses inform problems in other fields, such as combinatorial optimization and artificial intelligence—where they form a mathematical basis for neural network computing. We demonstrate the ability to realize a spin glass of a distinct driven-dissipative and vector form. By microscopically visualizing its glassy spin states, the technique allows us to directly measure replica symmetry breaking and the resulting ultrametric hierarchical structure. Ultrametricity is known to be emergent in models of evolution, protein folding, and climate change; this work shows it to be directly observable in a physically realized system.",

author = "Kroeze, \{Ronen M.\} and Marsh, \{Brendan P.\} and Schuller, \{David Atri\} and Hunt, \{Henry S.\} and Bourzutschky, \{Alexander N.\} and Michael Winer and Sarang Gopalakrishnan and Jonathan Keeling and Lev, \{Benjamin L.\}",

note = "Funding: The authors are grateful for funding support from the Army Research Office (Grant \#W911NF2210261), NTT Research, and the Q-NEXT DOE National Quantum Information Science Research Center. J.K. and S.G. were supported in part by the International Centre for Theoretical Sciences (ICTS) through participating in the program, Periodically and quasi-periodically driven complex systems (code: ICTS/pdcs2023/6). B.M. acknowledges funding from the Stanford QFARM Initiative and the NSF Graduate Research Fellowship. A.B. and M.W. thank the Stanford Graduate Fellowship and the Joint Quantum Institute Fellowship for support, resp. ",

year = "2025",

month = aug,

day = "14",

doi = "10.1126/science.adu7710",

language = "English",

volume = "First Release",

journal = "Science",

issn = "0036-8075",

publisher = "American Association for the Advancement of Science",

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TY - JOUR

T1 - Directly observing replica symmetry breaking in a vector quantum-optical spin glass

AU - Kroeze, Ronen M.

AU - Marsh, Brendan P.

AU - Schuller, David Atri

AU - Hunt, Henry S.

AU - Bourzutschky, Alexander N.

AU - Winer, Michael

AU - Gopalakrishnan, Sarang

AU - Keeling, Jonathan

AU - Lev, Benjamin L.

N1 - Funding: The authors are grateful for funding support from the Army Research Office (Grant #W911NF2210261), NTT Research, and the Q-NEXT DOE National Quantum Information Science Research Center. J.K. and S.G. were supported in part by the International Centre for Theoretical Sciences (ICTS) through participating in the program, Periodically and quasi-periodically driven complex systems (code: ICTS/pdcs2023/6). B.M. acknowledges funding from the Stanford QFARM Initiative and the NSF Graduate Research Fellowship. A.B. and M.W. thank the Stanford Graduate Fellowship and the Joint Quantum Institute Fellowship for support, resp.

PY - 2025/8/14

Y1 - 2025/8/14

N2 - Spin glasses are quintessential examples of complex matter. Although their ordering lacks complete theoretical understanding, abstract models of spin glasses inform problems in other fields, such as combinatorial optimization and artificial intelligence—where they form a mathematical basis for neural network computing. We demonstrate the ability to realize a spin glass of a distinct driven-dissipative and vector form. By microscopically visualizing its glassy spin states, the technique allows us to directly measure replica symmetry breaking and the resulting ultrametric hierarchical structure. Ultrametricity is known to be emergent in models of evolution, protein folding, and climate change; this work shows it to be directly observable in a physically realized system.

AB - Spin glasses are quintessential examples of complex matter. Although their ordering lacks complete theoretical understanding, abstract models of spin glasses inform problems in other fields, such as combinatorial optimization and artificial intelligence—where they form a mathematical basis for neural network computing. We demonstrate the ability to realize a spin glass of a distinct driven-dissipative and vector form. By microscopically visualizing its glassy spin states, the technique allows us to directly measure replica symmetry breaking and the resulting ultrametric hierarchical structure. Ultrametricity is known to be emergent in models of evolution, protein folding, and climate change; this work shows it to be directly observable in a physically realized system.

UR - https://www.scopus.com/pages/publications/105015376054

U2 - 10.1126/science.adu7710

DO - 10.1126/science.adu7710

M3 - Article

SN - 0036-8075

VL - First Release

JO - Science

JF - Science

M1 - eadu7710

ER -

Directly observing replica symmetry breaking in a vector quantum-optical spin glass

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