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Hardware Co-Designed Optimal Control for Programmable Atomic Quantum Processors via Reinforcement Learning

Qian Ding, Dirk Englund

Abstract

Developing scalable, fault-tolerant atomic quantum processors requires precise control over large arrays of optical beams. This remains a major challenge due to inherent imperfections in classical control hardware, such as inter-channel crosstalk and beam leakage. In this work, we introduce a hardware co-designed intelligent quantum control framework to address these limitations. We construct a mathematical model of the photonic control hardware, integrate it into the quantum optimal control (QOC) framework, and apply reinforcement learning (RL) techniques to discover optimal control strategies. We demonstrate that the proposed framework enables robust, high-fidelity parallel single-qubit gate operations under realistic control conditions, where each atom is individually addressed by an optical beam. Specifically, we implement and benchmark three optimization strategies: a classical hybrid Self-Adaptive Differential Evolution-Adam (SADE-Adam) optimizer, a conventional RL approach based on Proximal Policy Optimization (PPO), and a novel end-to-end differentiable RL method. Using SADE-Adam as a baseline, we find that while PPO performance degrades as system complexity increases, the end-to-end differentiable RL consistently achieves gate fidelities above 99.9$\%$, exhibits faster convergence, and maintains robustness under varied channel crosstalk strength and randomized dynamic control imperfections.

Hardware Co-Designed Optimal Control for Programmable Atomic Quantum Processors via Reinforcement Learning

Abstract

Developing scalable, fault-tolerant atomic quantum processors requires precise control over large arrays of optical beams. This remains a major challenge due to inherent imperfections in classical control hardware, such as inter-channel crosstalk and beam leakage. In this work, we introduce a hardware co-designed intelligent quantum control framework to address these limitations. We construct a mathematical model of the photonic control hardware, integrate it into the quantum optimal control (QOC) framework, and apply reinforcement learning (RL) techniques to discover optimal control strategies. We demonstrate that the proposed framework enables robust, high-fidelity parallel single-qubit gate operations under realistic control conditions, where each atom is individually addressed by an optical beam. Specifically, we implement and benchmark three optimization strategies: a classical hybrid Self-Adaptive Differential Evolution-Adam (SADE-Adam) optimizer, a conventional RL approach based on Proximal Policy Optimization (PPO), and a novel end-to-end differentiable RL method. Using SADE-Adam as a baseline, we find that while PPO performance degrades as system complexity increases, the end-to-end differentiable RL consistently achieves gate fidelities above 99.9, exhibits faster convergence, and maintains robustness under varied channel crosstalk strength and randomized dynamic control imperfections.

Paper Structure

This paper contains 27 sections, 25 equations, 3 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Mathematical Models
  3. Formulating Co-designed Optimization Problem
  4. Physical System Model
  5. Control Hardware Model
  6. Qubit System Model
  7. Optimization Methods
  8. Hybrid SADE-Adam Approach
  9. PPO-Based RL Approach
  10. End-to-End Differentiable RL Approach
  11. Numerical Results and Discussions
  12. Necessity of QOC
  13. Performance Benchmarking
  14. Robustness Validation
  15. Conclusion and Outlook
  16. ...and 12 more sections

Figures (3)

  • Figure 1: (a) Workflow of the implemented hardware co-designed QOC framework. The process starts with defining system parameters and initial control pulses, then constructing mathematical model of control hardware and further system Hamiltonian, further simulating quantum evolution and computing cost function, and iteratively optimizing control pulses until the cost function is minimized under given constraints. (b) A conceptual sketch of the control system for neutral atom quantum processors: laser beams first get modulated via tunable units in programmable PICs and then dynamically steered by a SLM onto a neutral atom array (assuming a triangular lattice here) to implement target gate operations. (c) Mathematical model of the control hardware system using unitary transformation representation. The input modes $\{a_1, \dots, a_{N_{\mathrm{pic}}}\}$ are modes coupled from free space into the PIC, which is modeled as a unitary matrix $U_{\mathrm{PIC}}$, incorporating transformations induced by both programmed modulations and unintentional inter-channel crosstalk. Weak scattering effects are modeled by a slightly perturbed identity matrix $I'_{\mathrm{weak,1}}$. The output modes from the PIC further get transformed by a SLM, represented by another unitary matrix $U_{\mathrm{SLM}}$. Weak scattering effects in this stage are captured by $I'_{\mathrm{weak,2}}$. The output modes $\{b_1, \dots, b_{N_a}\}$ are steered to the target atoms to implement a desired gate operation by programming the control Hamiltonian.
  • Figure 2: (a) A 16-channel programmable atomic PIC control hardware fabricated using a 200 mm CMOS process Dong2022. Insets show SEM images of the piezo-actuated Si$_3$N$_4$ dual-ring Mach-Zehnder modulator (DRMZM). (b) Simulated inter-channel crosstalk arising from evanescent waveguide coupling in the PIC. Dotted curves represent data from 2D FDTD simulations using FlexCompute Tidy3D, assuming refractive indices of 2.0255 for Si$_3$N$_4$ and 1.45 for SiO$_2$ at a wavelength of 780 nm. Coupling coefficient $\kappa_0 = 10.145$ and decay factor $\alpha = 6.934$ are extracted from the fitted solid curve. (c, d) Heatmaps showing the amplitude (c) and phase (d) crosstalk matrices induced by waveguide coupling in a six-channel PIC. The matrices are generated using the fitted model from (b), assuming a coupling length of 600 $\mu$m and a channel pitch of 1.0 $\mu$m.
  • Figure 3: (a) Gaussian control pulse $V(t)$ applied only to channel 1 targeting atom 1, aiming to implement the gate $X_1/I_2/I_3$ on atoms 1, 2, and 3. (b) Optimized Gaussian control pulses $V(t)$ applied to all channels, mitigating beam leakage and inter-channel crosstalk to implement the same target gate as in (a). (c, d) Normalized amplitude (c) and phase (d) profiles of the optical field on the 2D atomic plane, taken at half the total gate operation time. Field profiles for cases (a), (b), and (c) are shown from left to right. The inter-atomic spacing is set to 3 $\mu$m, and the beam waist is 2 $\mu$m, resulting in significant leakage between atoms. (e) Histogram comparing gate fidelities achieved in cases (a), (b), and (c), highlighting the fidelity degradation due to beam leakage and crosstalk. (f) Gate error optimization progress curves for the same target gate $X_1/I_2/I_3$, using the classical hybrid SADE-Adam QOC optimizer. Each curve represents an independent test run initialized with a different random guess for the control pulses $V_{\text{ini}}(t)$. (g) Example of optimized control pulses $V(t)$ for channels 1–3 targeting atoms 1–3, from the first test run in (f). Control voltages are constrained within $[-15, +15]$ V, consistent with practical hardware limits.