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This study demonstrates that continuous-time quantum walk algorithms can be effectively implemented on current analog neutral-atom processors, achieving super-quadratic convergence at low circuit depths. By deriving closed-form control parameters for unentangled targets and optimizing for entangled states, the research bridges the gap between theoretical quantum speedups and practical hardware execution. These findings validate the accessibility of advanced quantum dynamics on near-term devices, offering a scalable pathway for leveraging spectral gap advantages over traditional adiabatic protocols.
Continuous-time quantum walk-based ans\"atze on neutral atom hardware
arXiv:2509.00386v3 Announce Type: replace Abstract: Continuous-time quantum walks offer provable speedups for certain computational problems, yet translating these advantages to near-term hardware remains challenging. We realize variational ans\"atze based on continuous-time quantum walks on an analog neutral-atom processor. For unentangled targets, we derive closed-form expressions for near-optimal control parameters that transfer directly to hardware with minimal calibration. On QuEra's Aquila processor we observe the super-quadratic convergence characteristic of efficient quantum walk algorithms, visible at low circuit depth, with theory predicting stronger speedups as hardware improves. For entangled targets, specifically symmetric superpositions in the Rydberg-blockaded subspace, we introduce an optimization protocol exploiting spectral properties of the walk dynamics. The required evolution time scales inversely with the spectral gap, offering an advantage over adiabatic protocols, whose evolution time scales as the inverse square of the spectral gap. We verify this scaling behavior on Aquila and confirm that the prepared states are coherent superpositions via quench dynamics. Our results establish a practical pathway from abstract quantum walk algorithms to analog quantum processors, demonstrating that the dynamics underlying their potential for super-quadratic quantum speedup are accessible on current devices.
Abstract:Continuous-time quantum walks offer provable speedups for certain computational problems, yet translating these advantages to near-term hardware remains challenging. We realize variational ansätze based on continuous-time quantum walks on an analog neutral-atom processor. For unentangled targets, we derive closed-form expressions for near-optimal control parameters that transfer directly to hardware with minimal calibration. On QuEra's Aquila processor we observe the super-quadratic convergence characteristic of efficient quantum walk algorithms, visible at low circuit depth, with theory predicting stronger speedups as hardware improves. For entangled targets, specifically symmetric superpositions in the Rydberg-blockaded subspace, we introduce an optimization protocol exploiting spectral properties of the walk dynamics. The required evolution time scales inversely with the spectral gap, offering an advantage over adiabatic protocols, whose evolution time scales as the inverse square of the spectral gap. We verify this scaling behavior on Aquila and confirm that the prepared states are coherent superpositions via quench dynamics. Our results establish a practical pathway from abstract quantum walk algorithms to analog quantum processors, demonstrating that the dynamics underlying their potential for super-quadratic quantum speedup are accessible on current devices.
arXiv:2509.00386 [quant-ph]
(or arXiv:2509.00386v3 [quant-ph] for this version)
https://doi.org/10.1103/cbd2-635q DOI(s) linking to related resources
From: Edric Matwiejew Mr. [view email] [v1] Sat, 30 Aug 2025 06:53:03 UTC (494 KB) [v2] Thu, 12 Feb 2026 09:23:18 UTC (495 KB) [v3] Wed, 3 Jun 2026 07:18:33 UTC (1,940 KB)
Full text under the publisher's open licence · 227 words
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