Scaling and Qubit Addressability via Driven Superconducting Left-Handed Metamaterials

Transmission lines made of capacitors in series and inductors to the ground form so called metamaterials with inverse dispersion relations. These Left-Handed materials allow for a multi-mode interaction of transmons coupled to the resonator [1]. We demonstrate the effect of applying a microwave drive to the resonator. Depending on its frequency we are able to excite different modes of the resonator into coherent states and calculate the resulting ac Stark shift of the qubit. This shift depends on the coupling strength to the resonator mode and by extension on the position of the qubit along the transmission line. By placing multiple qubits along the transmission line and applying a multi-frequency microwave drive one can target a specific ac Stark shift of individual qubits or a combination of them. This would allow a hardware efficient way of implementing single- and multi-qubit gates by using control pulses that are only resonant with a qubit, if a specific ac Stark shift is present [2].