Qubit-to-qubit interactions mediated by pairs of resonators with tunable inductive coupling

A method for tuning a qubit interaction circuit, the method comprising:

• providing a qubit interaction circuit, the qubit interaction circuit comprising:
• a first qubit device;
• a second qubit device;
• a first resonator comprising a first terminal and a second terminal;
• a second resonator comprising a first terminal and a second terminal;
• a first capacitor coupling the first qubit device to the first terminal of the first resonator;
• a second capacitor coupling the second qubit device to the first terminal of the second resonator;
• an rf-SQUID circuit comprising an rf-SQUID loop, an rf-SQUID controller, and a dc-SQUID loop, the rf-SQUID controller configured to influence a first flux of the rf-SQUID loop and the dc-SQUID loop, the rf-SQUID circuit coupling the second terminal of the first resonator with the second terminal of the second resonator;
• and
• a dc-SQUID controller configured to influence a second flux of the rf-SQUID loop and the dc-SQUID loop;
• iteratively tuning a flux of the dc-SQUID loop and tuning a flux of the rf-SQUID loop to half of a magnetic flux quantum such that an inductance of the rf-SQUID loop is cancelled out by an inductance of the dc-SQUID loop and such that an Off state between two qubit devices is attained with a non-hysteretic regime, the dc-SQUID loop and the rf-SQUID loop being coupled to the two qubit devices via corresponding resonators;
• and
• performing an additional tuning of the flux of the rf-SQUID loop such that the corresponding resonators couple and hybridize with each other, and such that an On state between the two qubit devices is attained.

A hardware description language (HDL) design structure encoded on a non-transitory machine-readable data storage medium, the HDL design structure comprising elements that when processed in a computer-aided design system generates a machine-executable representation of a semiconductor structure, wherein the HDL design structure comprises:

• a first qubit device;
• a second qubit device;
• a first resonator comprising a first terminal and a second terminal;
• a second resonator comprising a first terminal and a second terminal;
• a first capacitor coupling the first qubit device to the first resonator;
• a second capacitor coupling the second qubit device to the second resonator;
• an rf-SQUID circuit comprising an rf-SQUID loop, an rf-SQUID controller, and a dc-SQUID loop, the rf-SQUID controller configured to influence a first flux of the rf-SQUID loop and the dc-SQUID loop, the rf-SQUID circuit coupling the second terminal of the first resonator with the second terminal of the second resonator;
• and
• a dc-SQUID controller configured to influence a second flux of the rf-SQUID loop and the dc-SQUID loop.