An Algorithm for Fast Assembling Large-Scale Defect-Free Atom Arrays
Authors: Tao Zhang, Xiaodi Li, Hui Zhai, Linghui Chen
Organizations: Institute for Advanced Study, Tsinghua University, Beijing, 100084, China · Intelligent Quantum Inception Inc., Haidian, Beijing, 100085, China · iFLYTEK Research, Hefei 230088, China
It is widely believed that tens of thousands of physical qubits are needed to build a practically useful quantum computer. Atom arrays formed by optical tweezers are among the most promising platforms for achieving this goal, owing to the excellent scalability and mobility of atomic qubits. However, assembling a defect-free atom array with ~ 10^4 qubits remains algorithmically challenging, alongside other hardware limitations. This is due to the computationally hard path-planning problems and the time-consuming generation of suffciently smooth trajectories for optical tweezer potentials by spatial light modulators (SLM). Here, we present a unified framework comprising two innovative components to fully address these algorithmic challenges: (1) a path-planning module that employs a supervised learning approach using a graph neural network combined with a modified auction decoder, and (2) a potential-generation module called the phase and profile-aware Weighted Gerchberg-Saxton algorithm. The inference time for the first module is nearly a size-independent constant overhead of ~ 5 ms, and the second module generates a potential frame with about 0.5 ms, a timescale shorter than the current commercial SLM refresh time. Altogether, our algorithm enables the assembly of an atom array with 10^4 qubits on a timescale much shorter than the typical vacuum lifetime of the trapped atoms.
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Figure 1: Decomposition of the task. The entire process for assembling a large-scale atom array is divided into two stages. (a) The path planning task. The initial configuration is an array of atoms with randomly distributed vacancies. The final target configuration is a defect-free atom array. The goal of path planning is to find collision-free trajectories that simultaneously move all atoms while optimizing the maximum travel distance. (b) The potential generation task. The SLM hologram plane and the tweezer potential plane are conjugate Fourier planes. This task involves solving an inverse problem: given the planned paths, we need to compute the corresponding phase-only hologram sequence that, when applied to the input laser beams, generates the intended optical potentials and determines the required trajectories of the optical tweezers.
Figure 2: Algorithm for two tasks. (a) The GNN-based path planning module. The initial and target atom sites are modeled as vertices of the graph processed by the GNN. The edges (not shown in the figure) are defined by a rule described in the main text in detail. A parallel decoder then extracts the optimal, collision-free movement vectors from the GNN’s output. (b) The P2WGS -based potential generation module. A sequence of SLM holograms is generated via the proposed P2WGS algorithm. Unlike the traditional WGS algorithm that only constrains amplitudes, our algorithm explicitly enforces both amplitude and phase constraints in the tweezer plane during the iterations, thereby ensuring coherent and smooth transport of the atoms.
Figure 3: GNN-based Path Planner Performance. We benchmark our method on 1024 random instances of rearranging a stochastically loaded 127×127 initial array to a 101×101 target lattice. The initial lattice spacing is normalized to 1.0 for simplicity. (a) Distribution of the maximum move distance. Our method (green) yields a mean of 1.93 , compared to the optimal value of 1.82 achieved by the Hungarian algorithm (red). (b) Distribution of the average move distance. Our method (orange) achieves a mean distance of 0.5120 , which is nearly identical to the global optimum of 0.5112 provided by the Hungarian algorithm (blue).
Figure 4: Continuity of Optical Potentials. The phase continuity (top) and intensity continuity (bottom) between consecutive frames along the atomic trajectories. The metrics are evaluated on an array assembling task for N=10201 ( T=101 ) across different numbers of P2WGS iterations (iter = 3, 5, 8, and 10). Error bars represent the standard deviation across multiple independent stochastic loading realizations.
Figure 5: Inference Time and Pipelined Assembly Performance. (a) Computational time of the path planning and potential generation tasks across varying array sizes, evaluated on a single NVIDIA RTX 5090 GPU. The path planning (blue bars) achieves a nearly constant overhead of ∼5 ms. The potential generation time (orange/red bars) remains strictly below 1 ms per frame for N=10,201 . (b) Total assembly time versus the hardware SLM refresh time for N=10,201 atoms using a 20-frame trajectory. The pipelined execution model assumes a 3 ms constant data transfer delay. A kink occurs when the SLM refresh time matches the algorithm’s per-frame generation time. To the left of this kink, the system is compute-bound (plateau region), whereas to the right, the algorithm overhead is covered, rendering the total time strictly hardware-bound (linear region).
Indian Institute of Technology Jodhpur · Inter-Disciplinary Research Platform, Quantum Information and Computation, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan 342037, India