Optimal control of nanomechanical quantum memory coupled to superconducting qubit

Quantum memory coupled to a single non-linear element such as superconducting qubit can serve as a promising quantum information processing platform with advantages in lifetime and hardware-efficiency. However, naïve implementation of this quantum computing architecture requires two additional SWAP gates between the memory resonator and the processing qubit per each gate operation, which can cause longer gate time and larger error. In this work we explore the optimal control for performing high-fidelity state preparation and unitary gates on quantum memory by using a power- and bandwidth-limited pulse optimization method. Specifically, we apply our method to a hybrid system of nanomechanical resonators coupled to tunable-frequency transmon qubit and find the optimal pulse for generating entangled states of mechanical resonators as well as implementing phonon-phonon CNOT gate. We test the pulse's robustness to experimental imperfections, such as pulse noise, parameter uncertainties, and decoherence. Finally, we find the optimal pulse length and gate fidelity as a function of the qubit-resonator coupling strength and frequency spacing of resonators, suggesting the experimental parameter regime for achieving scalable quantum computing.