Exploiting many-body localization for scalable variational quantum simulation

Chenfeng Cao; Yeqing Zhou; Swamit Tannu; Nic Shannon; Robert Joynt

doi:10.22331/q-2025-12-12-1942

Exploiting many-body localization for scalable variational quantum simulation

Chenfeng Cao^1,2, Yeqing Zhou³, Swamit Tannu⁴, Nic Shannon⁵, and Robert Joynt^3,6

¹HK Institute of Quantum Science $\&$ Technology, The University of Hong Kong, Hong Kong, China
²Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
³Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
⁴Department of Computer Science, University of Wisconsin-Madison, Madison, WI 53706, USA
⁵Theory of Quantum Matter Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0412, Japan
⁶Theoretical Sciences Visiting Program (TSVP), Okinawa Institute of Science and Technology Graduate University, Onna, 904-0495, Japan

Published:	2025-12-12, volume 9, page 1942
Editor:	Marco Cerezo
Eprint:	arXiv:2404.17560v6
Doi:	https://doi.org/10.22331/q-2025-12-12-1942
Citation:	Quantum 9, 1942 (2025).

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Updated after initial publication: This publication was updated to version v6 after the initial publication. The authors left the following comment on the arXiv:

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Abstract

Variational quantum algorithms (VQAs) represent a promising pathway toward achieving practical quantum advantage on near-term hardware. Despite this promise, for generic, expressive ansätze, their scalability is critically hindered by barren plateaus—regimes of exponentially vanishing gradients. We demonstrate that initializing a hardware-efficient, Floquet-structured ansatz within the many-body localized (MBL) phase mitigates barren plateaus and enhances algorithmic trainability. Through analysis of the inverse participation ratio, entanglement entropy, and a novel low-weight stabilizer Rényi entropy, we characterize a distinct MBL--thermalization transition. Below a critical kick strength, the circuit avoids forming a unitary 2-design, exhibits robust area-law entanglement, and maintains non-vanishing gradients. Leveraging this MBL regime facilitates the efficient variational preparation of ground states for several model Hamiltonians with significantly reduced computational resources. Crucially, experiments on a 127-qubit superconducting processor provide evidence for the preservation of trainable gradients in the MBL phase for a kicked Heisenberg chain, validating our approach on contemporary noisy hardware. Our findings position MBL-based initialization as a viable strategy for developing scalable VQAs and motivate broader integration of localization into quantum algorithm design.

Featured image: Exploiting the MBL phase for scalable quantum optimization. The top panel illustrates the transition controlled by the kick strength W: weak kicks keep the circuit in a many-body localized (MBL) phase with area-law entanglement, while strong kicks drive it into a thermal phase with volume-law entanglement and barren plateaus. The bottom panel depicts the corresponding optimization landscape. A low-complexity trial state captures essential structure of the target ground state; initializing the Floquet circuit within the MBL regime preserves this physical information, ensuring that the optimizer starts in a gradient-rich region and can efficiently converge to the solution.

Popular summary

Variational quantum algorithms (VQAs) are a leading strategy for extracting useful results from today’s noisy quantum processors. Yet as circuits become deeper and more expressive, training can suddenly fail: the optimization landscape flattens and the gradients needed for learning all but vanish—a notorious “barren plateau.”

We turn a phenomenon from many-body physics into a practical cure. We design a hardware-efficient, periodically driven (“Floquet”) ansatz whose behaviour is controlled by a single “kick strength.” For weak kicks, the circuit lives in a many-body localized (MBL) regime: quantum information stays local, entanglement follows an area law and the dynamics avoid scrambling into effectively random states. In this localized regime we find that gradients remain sizable, so the VQA is actually trainable. As the kick strength increases, the same circuit crosses sharply into a thermalizing phase with volume-law entanglement, rapid approach to unitary 2-design behaviour and the onset of barren plateaus.

We diagnose this localization–thermalization transition using the inverse participation ratio and entanglement entropy, and we introduce a new low-weight stabilizer Rényi entropy that reveals higher-order randomness using only local Pauli measurements. We use the MBL regime only for initialization; subsequent optimization moves the circuit away from strict localization while still avoiding the fully random 2-design regime where plateaus dominate. Initializing Variational Quantum Eigensolver (VQE) runs inside the MBL regime enables efficient preparation of ground states for several model Hamiltonians, substantially outperforming standard random initialization. Experiments on a 127-qubit superconducting processor observe the predicted restoration of gradients in a kicked Heisenberg chain of up to 31 qubits. Together, these results establish localization-based initialization as a robust and scalable route to training VQAs.

► BibTeX data

@article{Cao2025exploitingmanybody,
  doi = {10.22331/q-2025-12-12-1942},
  url = {https://doi.org/10.22331/q-2025-12-12-1942},
  title = {Exploiting many-body localization for scalable variational quantum simulation},
  author = {Cao, Chenfeng and Zhou, Yeqing and Tannu, Swamit and Shannon, Nic and Joynt, Robert},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1942},
  month = dec,
  year = {2025}
}

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[16] Kasidit Srimahajariyapong, Supanut Thanasilp, and Thiparat Chotibut, "Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithms", arXiv:2506.13865, (2025).

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