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This study utilizes superconducting quantum processors to image wavefunction networks in 2D disordered systems, revealing a non-ergodic multifractal regime that rules out a direct transition to localization. By directly sampling the Hilbert space via bitstring return probabilities, the research provides critical empirical evidence on glassy relaxation dynamics previously inaccessible to traditional simulation methods. These findings advance our understanding of quantum many-body physics by demonstrating how wavefunction support saturates in finite fractions of configuration space under strong disorder.
Multifractal and Glassy Signatures of Non-Ergodic 2D Quantum Dynamics
arXiv:2601.01309v4 Announce Type: replace Abstract: The fate of ergodicity and localization in disordered, interacting quantum systems in two spatial dimensions remains an outstanding open problem in non-equilibrium physics. Theoretical and numerical approaches are severely constrained by exponential Hilbert space growth. Here, we leverage the high data-acquisition rates of superconducting quantum processors to extensively sample Hilbert space configurations, effectively imaging the state as a wavefunction network (WFN). Tracking the bitstring return probability across varied disorder strengths, we find heavy-tailed distributions and power-law typical decay characteristic of glassy relaxation. Furthermore, the distribution of bitstring probabilities transitions from a Porter-Thomas form at low disorder to an eight-decade power law at stronger disorder. In the reconstructed configuration space, WFN connectivity is compatible with a random geometric network at low disorder and becomes scale-free at stronger disorder. Finally, a multifractal analysis based on the binary intrinsic dimension (BID) reveals a non-ergodic regime where the wavefunction support saturates to a finite fraction of the total Hilbert space. Together, these results rule out a direct ergodic-to-localized transition, pointing instead to an extended multifractal regime. By visualizing wavefunction dynamics directly in configuration space, this work complements traditional real-space studies, showing the potential of quantum processors to resolve long-standing questions in non-equilibrium physics.
Authors:Aleksey Lunkin, Nicole S. Ticea, Michael T. Solomon, Riccardo Andreoni, Shashwat Kumar, Connie Miao, Jaehong Choi, Mohammed Alghadeer, Ilya Drozdov, Dmitry Abanin, Amira Abbas, Rajeev Acharya, Laleh Beni, Georg Aigeldinger, Ross Alcaraz, Sayra Alcaraz, Markus Ansmann, Frank Arute, Kunal Arya, Walt Askew, Nikita Astrakhantsev, Juan Atalaya, Ryan Babbush, Brian Ballard, Joseph C. Bardin, Hector Bates, Andreas Bengtsson, Majid Karimi, Alexander Bilmes, Simon Bilodeau, Felix Borjans, Alexandre Bourassa, Jenna Bovaird, Dylan Bowers, Leon Brill, Peter Brooks, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, Tim Burger, Brian Burkett, Nicholas Bushnell, Jamal Busnaina, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Silas Chen, Zijun Chen, Ben Chiaro, Liang-Ying Chih, Agnetta Y. Cleland, Bryan Cochrane, Matt Cockrell, Josh Cogan, Paul Conner, Harold Cook, Rodrigo G. Cortiñas, William Courtney, Alexander L. Crook, Ben Curtin, Martin Damyanov, Sayan Das, Dripto M. Debroy, Sean Demura, Paul Donohoe, Andrew Dunsworth, Valerie Ehimhen, Alec Eickbusch, Aviv Moshe Elbag, Lior Ella, Mahmoud Elzouka, David Enriquez, Catherine Erickson, Lara Faoro, Vinicius S. Ferreira, Marcos Flores, Leslie Burgos, Sam Fontes, Ebrahim Forati, Jeremiah Ford, Brooks Foxen, Masaya Fukami, Alan Wing Fung, Lenny Fuste, Suhas Ganjam, Gonzalo Garcia, Christopher Garrick, Robert Gasca, Helge Gehring, Robert Geiger, William Giang, Dar Gilboa, James E. Goeders, Edward C. Gonzales, Raja Gosula, Stijn J. Graaf, Alejandro Dau, Dietrich Graumann, Joel Grebel
et al. (199 additional authors not shown)
Abstract:The fate of ergodicity and localization in disordered, interacting quantum systems in two spatial dimensions remains an outstanding open problem in non-equilibrium physics. Theoretical and numerical approaches are severely constrained by exponential Hilbert space growth. Here, we leverage the high data-acquisition rates of superconducting quantum processors to extensively sample Hilbert space configurations, effectively imaging the state as a wavefunction network (WFN). Tracking the bitstring return probability across varied disorder strengths, we find heavy-tailed distributions and power-law typical decay characteristic of glassy relaxation. Furthermore, the distribution of bitstring probabilities transitions from a Porter-Thomas form at low disorder to an eight-decade power law at stronger disorder. In the reconstructed configuration space, WFN connectivity is compatible with a random geometric network at low disorder and becomes scale-free at stronger disorder. Finally, a multifractal analysis based on the binary intrinsic dimension (BID) reveals a non-ergodic regime where the wavefunction support saturates to a finite fraction of the total Hilbert space. Together, these results rule out a direct ergodic-to-localized transition, pointing instead to an extended multifractal regime. By visualizing wavefunction dynamics directly in configuration space, this work complements traditional real-space studies, showing the potential of quantum processors to resolve long-standing questions in non-equilibrium physics.
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)
arXiv:2601.01309 [quant-ph]
(or arXiv:2601.01309v4 [quant-ph] for this version)
Full text under the publisher's open licence · 438 words
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