Inductively-shunted transmon qubit for superconducting circuits
Techniques for modifying the Josephson potential of a transmon qubit by shunting the transmon with an inductance are described. The inclusion of this inductance may increase the confined potential of the qubit system compared with the conventional transmon, which may lead to a transmon qubit that is stable at much higher drive energies. The inductive shunt may serve the purpose of blocking some or all phase-slips between the electrodes of the qubit. As a result, the inductively shunted transmon may offer an advantage over conventional devices when used for applications involving high energy drives, whilst offering few to no drawbacks in comparison to conventional devices when used at lower drive energies.
1. A circuit quantum electrodynamics system comprising:
a charge qubit, the charge qubit comprising an island of superconducting material coupled to a superconducting reservoir via a Josephson junction and coupled to at least one capacitor; and
a series array of Josephson junctions coupled to the charge qubit such that the series array is coupled in parallel to the Josephson junction of the charge qubit and in parallel to the at least one capacitor of the charge qubit.
2. The circuit quantum electrodynamics system of claim 1 , wherein each Josephson junction in the series array of Josephson junctions has a Josephson coupling energy K J ′, wherein the Josephson junction of the charge qubit has a Josephson coupling energy K J , and wherein K J ′ is greater than K J .
3. The circuit quantum electrodynamics system of claim 1 , wherein the series array of Josephson junctions has a combined inductive energy E L that is between 0.8×E J and 1.2×E J , where E J is the Josephson energy of the Josephson junction of the charge qubit.
4. The circuit quantum electrodynamics system of claim 3 , wherein E L is between 0.9×E J and 1.1×E J .
5. The circuit quantum electrodynamics system of claim 1 , wherein the Josephson junction of the charge qubit has a Josephson coupling energy K J , wherein the at least one capacitor of the charge qubit has a charging energy E C , and wherein the ratio E J /E C is at least 5.
6. The circuit quantum electrodynamics system of claim 5 , wherein the ratio E J /E C is at least 25.
7. The circuit quantum electrodynamics system of claim 1 , wherein a dc magnetic flux threaded through an inductive loop formed by the series array of Josephson junctions and the charge qubit is less than 10 −15 weber.
8. The circuit quantum electrodynamics system of claim 1 , further comprising an oscillator coupled to the charge qubit and the series array of Josephson junctions.
9. The circuit quantum electrodynamics system of claim 8 , wherein the oscillator is a microwave cavity.
10. The circuit quantum electrodynamics system of claim 1 , further comprising a transmission line coupled to the charge qubit and the series array of Josephson junctions.
11. The circuit quantum electrodynamics system of claim 1 , wherein the series array of Josephson junctions is M Josephson junctions coupled in series, and wherein M is greater or equal to 3 and M is less than or equal to 20.
12. The circuit quantum electrodynamics system of claim 11 , wherein M is greater or equal to 5 and M is less than or equal to 10.
13. A circuit quantum electrodynamics system comprising:
a charge qubit, the charge qubit comprising an island of superconducting material coupled to a superconducting reservoir via a Josephson junction and coupled to at least one capacitor; and
a superinductor coupled in parallel to the Josephson junction of the charge qubit and in parallel to the at least one capacitor of the charge qubit.
14. The circuit quantum electrodynamics system of claim 13 , wherein the superinductor has an inductive energy E L that is between 0.8×E J and 1.2×E J , where E J is the Josephson energy of the Josephson junction of the charge qubit.
15. The circuit quantum electrodynamics system of claim 13 , wherein the Josephson junction of the charge qubit has a Josephson coupling energy K J , wherein the at least one capacitor of the charge qubit has a charging energy E C , and wherein the ratio E J /E C is at least 5.
16. The circuit quantum electrodynamics system of claim 13 , wherein a dc magnetic flux threaded through an inductive loop formed by the superinductor and the charge qubit is less than 10 −15 weber.
17. The circuit quantum electrodynamics system of claim 13 , wherein the superinductor comprises granular aluminum.
18. A method of operating a circuit quantum electrodynamics (cQED) system, the cQED system comprising an inductively shunted transmon qubit coupled to a transmission line, the method comprising:
applying a pump of frequency ω p to the inductively shunted transmon qubit via the transmission line; and
adjusting ω p , thereby causing a coupling strength between a Floquet mode of the inductively shunted transmon qubit |Φ n ) and a Floquet mode of the inductively shunted transmon qubit |Φ m > to fall below a selected threshold,
wherein n is 0 or 1, and wherein m is between 1 and 20.
19. The method of claim 18 , wherein ω p is selected so that the coupling strength remains below the selected threshold irrespective of the amplitude of the pump.
20. The method of claim 18 , wherein the threshold is 0.1 MHz.
21. The method of claim 20 , wherein the threshold is 0.01 MHz.
22. The method of claim 18 , wherein the inductively shunted transmon qubit has a characteristic frequency ω q , and wherein ω p is between 0.5ω q and 3.0ω q .
23. The method of claim 22 , wherein the inductively shunted transmon qubit has a characteristic frequency ω q , and wherein ω p is between 1.4ω q and 1.8ω q .
24. The method of claim 18 , wherein n is 0 and m is 4.
25. The method of claim 18 , wherein n is 1 and m is 5.
26. A circuit quantum electrodynamics system comprising:
a charge qubit, the charge qubit comprising a Josephson junction coupled to at least one capacitor; and
an inductor coupled in parallel to the Josephson junction of the charge qubit and in parallel to the at least one capacitor of the charge qubit,
wherein the inductor has an inductive energy E L , the Josephson junction has a Josephson energy E J , and wherein E L /E J is at least 3 and no greater than 6.
27. The circuit quantum electrodynamics system of claim 26 , wherein the Josephson junction of the charge qubit has a Josephson coupling energy K J , wherein the at least one capacitor of the charge qubit has a charging energy E C , and wherein the ratio E J /E C is at least 5.
28. The circuit quantum electrodynamics system of claim 26 , wherein a dc magnetic flux threaded through an inductive loop formed by the series array of Josephson junctions and the charge qubit is less than 10 −15 weber.
29. The circuit quantum electrodynamics system of claim 26 , wherein E L /E J is at least 4 and no greater than 5.