Gradient-free pulse optimization for adiabatic control in open few-body quantum systems

TL;DR

This work develops a gradient-free adiabatic quantum-optimal-control framework using CMA-ES to minimize diabatic leakage while enforcing ground-state adherence in open few-body quantum systems. By parameterizing control pulses on top of a reference, and by employing basis expansions (Gaussian, sine, Chebyshev) together with Lindblad dynamics, the method delivers robust, high-fidelity adiabatic protocols for RAP, STIRAP, and MIS problems. The approach outperforms ensemble optimization in computational efficiency, while maintaining comparable robustness to parameter fluctuations, and is validated with both classical simulations and digitized pulses on IBM Quantum hardware. The results offer a scalable pathway to accelerate adiabatic quantum computation and adiabatic control in noisy, multi-qubit settings, with practical implications for Rydberg-based MIS and superconducting-qubit architectures.

Abstract

We present a robust pulse optimization method for adiabatic population transfer and adiabatic quantum computation. The approach relies on identifying control pulses that keep the evolving quantum system close to its instantaneous ground state. By combining advanced gradient-free optimization tools with specialized cost functions for adiabatic control, it achieves both efficiency and robustness. To demonstrate its generality, we apply the method to three examples involving both atomic and superconducting qubits. We test different optimization cost functions and discretization bases, showing that the approach outperforms ensemble optimization. Finally, to verify its performance on real quantum hardware, we implement digitized adiabatic qubit control using the optimized pulses on the IBM Quantum cloud.

Figures (11)

• Figure 1: Three RAP Pulses for adiabatic excitation in a two-level system with Rabi frequency $\Omega$ and detuning $\Delta$: (a) An unoptimized polynomial pulse, (b) a pulse obtained with traditional QOC, and (c) a pulse obtained with adiabatic QOC. (d,e,f) State trajectories on the Bloch sphere under pulses from (a,b,c). Purple curve is the ground-state trajectory.
• Figure 2: Flow chart of iterative adiabatic QOC algorithm. In each iteration ($k$), generate random samples of expansion coefficients ($w_i^k$). For each sample ($i$), construct pulse, evolve system, and evaluate cost using Eq. (\ref{['eq:cost-functions']}) (including the adiabatic infidelity cost $C_2$). Select best samples and update the distribution to lower the cost.
• Figure 3: Robustness of optimized RAP pulses. (a--c) Python simulations showing infidelity of state transfer [Eq. (\ref{['eq:traditional-QOC']})] (colorbar) for the three pulses from Fig. \ref{['fig:RAP-fig1']} under variations in pulse amplitude, $\int_0^{t_f} \varepsilon \Omega(t) dt$ and frequency shifts, $\Delta(t)+\delta_\mathrm{dopp}$. (d--f) Infidelity of a trotterized RAP protocol under variations in the controls pulse area and detuning, obtained from quantum simulations on the IBM quantum cloud IBMQuantum.
• Figure 4: (a) Single-excitation subspace of two qubits coupled to a multimode waveguide with couplings $g_{ac}^{(n)}$ and $g_{ab}^{(n)}$ and FSR $\Delta_c$. Decay rates $\gamma_1, \gamma_{\phi}, \gamma_c$ representing qubit relaxation, dephasing, and waveguide decay. (b) Coupling amplitudes $g_{ac}(t)$ and $g_{ab}(t)$ of SATD pulses and pulses obtained with $C_1$, $C_1 + \tfrac{1}{2}C_2$ (labeled as $C_2$) and $C_3$ [Eq. (\ref{['eq:cost-functions']})]. (c,d) State-transfer infidelity for varying $T_\varphi = 1/\gamma_\phi$ (where $C_1$ is optimal) and pulse areas of the qubit-waveguide couplings (where $C_2$ is optimal) for pulses from (b) and assuming $Q_c = 10^5$ where $Q_c = \omega_c / \gamma_c$ and $\omega_c = 5$ GHz and $\Delta_c = 500$ MHz.
• Figure 5: (a) Rydberg qubits with levels $|\!\left.{g}\right>$ and $|\!\left.{r}\right>$. $V_r$ is the Rydberg interaction, while $\Omega$ and $\Delta$ are the Rabi frequency and detuning of the control. (b) An 8-node ring graph and one of its MIS solutions. (c) Rabi frequency $\Omega(t)$ of a constant field (green), a squared sine pulse (blue), and pulses obtained with adiabatic QOC for rings containing $N = 2, 6, 10$ atoms (orange). (d) Fidelity defined as the overlap of the final state and MIS solution, $1- \mathcal{C}_1$, versus ring length for the pulses from (c).