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arXiv · 2404.17560

Exploiting many-body localization for scalable variational quantum simulation

Chenfeng Cao·Yeqing Zhou·Swamit Tannu·Nic Shannon·Robert Joynt
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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 ans\"atze, 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 R\'enyi 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.

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Chenfeng Cao, Yeqing Zhou, Swamit Tannu, Nic Shannon, Robert Joynt. 2024-04-26. Exploiting many-body localization for scalable variational quantum simulation. https://doi.org/10.22331/q-2025-12-12-1942

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