Comparative Analysis of Direct and Indirect Coupling in Superconducting Two-Qubit Circuits

Details

Supervisors

Melinte, Sorin

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil électricien, à finalité spécialisée

Abstract

enIn a superconducting processor, a coupler is the circuit element through which two qubits ex change excitations. It sets the interaction strength g, hence the rate at which the two qubits exchange excitations and the timescale on which a two-qubit gate can be performed: a gate must be fast compared to the coherence time for its error to stay low, so a strong coupling is wanted, up to the point where the residual interaction it leaves on between gates becomes the limiting factor. A coupler may be a capacitance drawn directly between the two qubit islands, a resonator shared by both and detuned from them, or a tunable element switching the interaction on and off. The choice is a determining factor for processor performance, because the same metal that produces the coupling also loads the qubits it connects, shifting the frequency and the anharmonicity they were designed for. Starting from Yohan Burignat’s Master thesis, which designed and validated a single-transmon chip, this work extends that layout to two qubits, a transmon pocket and an Xmon, each carrying its own quarter-wave readout resonator and charge line. Two configurations are compared: a reference layout with no coupler, in which the qubits interact only through the shared readout network, and a direct capacitive coupler formed by extending one Xmon arm until it faces a capacitor pad of the pocket. Both are built in Qiskit Metal and simulated by finite elements in the Ansys Quasi-static 3D Extractor, whose capacitance matrix feeds a two qubit lumped oscillator quantisation, and in the Ansys High-Frequency Structure Simulator, whose eigenmodes are post-processed through energy participation ratios. No parameter is fitted, and the two branches agree to better than 7 % on the frequencies and anharmonicities of the converged modes. The direct coupler yields g=25.9 MHz, a coupling rate corresponding to about 10 ns, against 0.034 MHz for the reference layout, which corresponds to some 7 μs and leaves no usable interaction. The coupler therefore does its job, but not for free. It leaves the transmon pocket untouched, its island capacitance moving by 0.5 %, while tripling that of the Xmon, from 111.7 to 374.2 fF, driving the ratio of Josephson to charging energy EJ/EC from 94 to 316 and the qubit frequency from 4.6 down to 2.6 GHz, 3.3 GHz below its neighbour, a detuning large enough for the interaction to be suppressed rather than used. Only 5.63 fF of the 262 fF added actually face the neighbouring qubit, so this penalty follows from the geometry of the coupler rather than from the coupling itself. A direct coupler cannot be inserted into an already validated single-qubit layout without re-optimising the qubit that carries it.