Co-Designed Multimode Quantum Optimal Control: Mitigating Crosstalk in Neutral Atom Arrays with Programmable Photonics

Quantum optimal control (QOC) has evolved significantly over the years, particularly its mathematical formulation and algorithm development. An emerging challenge lies in its integration into practical quantum devices, which is essential for real-world quantum engineering.

We present a multimode QOC framework that bridges its theory with practical hardware via a co-design approach, incorporating a programmable photonic control engine into a neutral atom array platform. The control hardware is mathematically represented as a unitary transformation matrix based on a multichannel atomic photonic integrated circuit (APIC). The matrix is parameterized by time-varying constrained voltages applied to ring modulators in APIC, which serve as control signals to locally manipulate the fields at qubit locations. The atom-field interaction follows the Jaynes-Cummings model. For high-fidelity time-optimal gate implementation, we utilized a hybrid optimization approach, combining Self-adaptive Differential Evolution for global search with Adam for local fine-tuning.

Our co-designed QOC approach demonstrates the ability to implement high-fidelity single-qubit and two-qubit gates (above 99.999%) with limited control signals, despite the presence of crosstalk, which arises from overlapping control beams between neighboring atoms or closely spaced waveguides in APIC channels.