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

1 . 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 de-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.

2 . The qubit interaction circuit of claim 1 , wherein the rf-SQUID controller is configured to:

iteratively tune a flux of an rf-SQUID loop to ½Φ 0 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 a corresponding one of the first resonator and the second resonator; and

perform 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.

3 . The qubit interaction circuit of claim 1 , wherein the dc-SQUID controller is configured to iteratively tune a flux of a dc-SQUID loop 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 a corresponding one of the first resonator and the second resonator.

4 . The qubit interaction circuit of claim 1 , wherein the qubit devices are transmon qubits.

5 . The qubit interaction circuit of claim 1 , wherein the qubit devices are fluxonium qubits.

6 . The qubit interaction circuit of claim 1 , wherein the qubit devices are capacitively shunted flux qubit (CSFQ) qubits.

7 . The qubit interaction circuit of claim 1 , further comprising:

a third qubit device;

a third resonator;

a fourth resonator;

a third capacitor coupling the second qubit device to the third resonator;

a fourth capacitor coupling the third qubit device to the fourth resonator;

a second rf-SQUID circuit comprising a second rf-SQUID loop, a second rf-SQUID controller, and a second dc-SQUID loop, the second rf-SQUID controller being configured to influence a first flux of the second rf-SQUID loop and the second dc-SQUID loop, the rf-SQUID circuit coupling the third resonator with the fourth resonator; and

a second dc-SQUID controller configured to influence a second flux of the rf-SQUID loop and the second dc-SQUID loop.

8 . The qubit interaction circuit of claim 1 , further comprising a controller, the controller being coupled to the rf-SQUID flux control and the de-SQUID flux control and configured to:

iteratively tune a flux of a dc-SQUID loop and tuning a flux of an 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

perform 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.

9 . The qubit interaction circuit of claim 8 , the controller further configured to select a sign of a dc-SQUID controller and a sign of an rf-SQUID controller such that the flux in the rf-SQUID loop reverts to the non-hysteretic regime in response to the additional tuning of the flux of the rf-SQUID loop changing the flux in the dc-SQUID loop and thereby causing the flux in the rf-SQUID loop to revert to the hysteretic regime.

10 . The qubit interaction circuit of claim 9 , wherein the selection of the signs causes a magnitude of the flux in the dc-SQUID loop to increase and causes a further reduction of a screening parameter that is indicative of the non-hysteretic regime.

11 . The qubit interaction circuit of claim 8 , wherein the controller is further configured to tune a coupling between the corresponding resonators to zero.

12 . The qubit interaction circuit of claim 8 , wherein the hybridized resonators are configured such that one of a plurality of normal modes of the hybridized resonators moves up in frequency, close to that of a frequency of the two qubit devices, increasing an exchange coupling between the two qubit devices and turning on ZZ coupling between the two qubit devices.

13 . The qubit interaction circuit of claim 12 , wherein the controller is further configured to control ZZ between the first qubit device and the second qubit device to enable a CPHASE gate.

14 . 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.

15 . The method of claim 14 , further comprising selecting a sign of the dc-SQUID controller and a sign of the rf-SQUID controller such that the flux in the rf-SQUID loop reverts to the non-hysteretic regime in response to the additional tuning of the flux of the rf-SQUID loop changing the flux in the dc-SQUID loop and thereby causing the flux in the rf-SQUID loop to revert to the hysteretic regime.

16 . The method of claim 15 , wherein the selection of the signs causes a magnitude of the flux in the dc-SQUID loop to increase and causes a further reduction of a screening parameter that is indicative of the non-hysteretic regime.

17 . The method of claim 14 , further comprising tuning a coupling between the corresponding resonators to zero.

18 . The method of claim 14 , wherein one of a plurality of normal modes of the hybridized resonators moves up in frequency, close to that of a frequency of the two qubit devices, increasing an exchange coupling between the two qubit devices and turning on ZZ coupling between the two qubit devices.

19 . The method of claim 18 , further comprising controlling ZZ between the first qubit device and the second qubit device to enable a CPHASE gate.

20 . 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.