Implementation of quantum gates by Floquet analysis of kicked quantum system

This paper addresses the challenge of controlling multi-qubit operations in superconducting processors, specifically focusing on fixed-frequency transmon architectures with tunable couplers. The authors propose a framework based on Floquet theory to engineer high-fidelity quantum gates. By applying a periodic train of pulses to the coupler, they transform the time-dependent control problem into a time-independent effective Hamiltonian description. This allows them to identify resonance conditions where quasi-energy differences match the driving frequency, enabling selective state transfer. The researchers use a combination of analytical perturbative expansions and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to optimize driving parameters for high-fidelity gate synthesis.

In a three-qubit architecture, the protocol successfully synthesizes the iSWAP gate with near-unity fidelity. Extending this to a seven-site linear chain, the authors demonstrate the ability to perform complex multi-excitation transport—such as swapping excitations between non-adjacent qubits—with gate durations around 170 ns. This speed provides a critical scale separation from typical energy-relaxation (T1) and dephasing (Tφ) times, minimizing the impact of environmental decoherence. Spectral analysis confirms that these operations are driven by isolated Floquet resonances, effectively suppressing leakage into unwanted computational states.

As superconducting processors scale, the ability to perform high-fidelity multi-qubit operations without requiring individual control lines for every coupler becomes increasingly important. This global Floquet engineering approach offers a scalable, hardware-efficient method for quantum routing and state transfer. While the current linear topology is sensitive to static disorder, the authors suggest that moving to closed-loop (ring) architectures could provide topological protection, making this a promising path for robust, large-scale quantum gate engineering.