Fast quantum gates with first-order transitions via frequency-modulated tunable coupling element

1. A method of operating a quantum processing device, the method comprising:

modulating a frequency of a tunable coupler to drive two first-order energy transitions, wherein the quantum processing device comprises at least two fixed frequency quantum circuits coupled to the tunable coupler; and

causing an excitation of one of the at least two fixed frequency quantum circuits such that the excitation is at least partly transferred to at least another one of the at least two fixed frequency quantum circuits, via the tunable coupler, wherein the frequency of the tunable coupler is modulated to implement a quantum gate operating on at least one of the at least two fixed frequency quantum circuits, wherein modulating the frequency of the tunable coupler is associated with a first frequency to drive a first transition associated with a first excitation of the one of the at least two fixed frequency quantum circuits and is associated with at least one second frequency distinct from the first frequency to drive at least one second transition.

2. The method according to claim 1 , wherein the frequency of the tunable coupler is operable to be modulated to drive at least two selectively addressable energy transitions in the quantum processing device; and

wherein the frequency of the tunable coupler is modulated at:

the first frequency, so as to drive the first transition and thereby transfer, at least partly, the first excitation of the one of the at least two fixed frequency quantum circuits to the tunable coupler; and

the at least one second frequency, so as to drive the at least one second transition and thereby further transfer, at least partly, the first excitation from the tunable coupler to the at least another one of the at least two fixed frequency quantum circuits, each of the first transition and the at least one second transition being a first-order energy transition.

3. The method according to claim 2 , wherein the frequency of the tunable coupler is modulated at the first frequency to drive the first transition and is modulated at the at least one second frequency to drive the at least one second transition responsive to the first transition.

4. The method according to claim 2 , wherein the frequency of the tunable coupler is concomitantly modulated at the first frequency and the at least one second frequency, so as to concomitantly drive the first transition and the at least one second transition.

5. The method according to claim 4 , wherein modulating the frequency of the tunable coupler further comprises switching on drives at the first frequency and the at least one second frequency to generate an adiabatic holonomic gate transformation.

6. The method according to claim 2 , wherein, to modulate the frequency of the tunable coupler, each of the first frequency and the at least one second frequency corresponds to a difference of energy between a pair of excited states of the quantum processing device, respectively, the pair of excited states involving a reference excited state which is representable as a tensor product of an excited state of the tunable coupler and a ground state of each of the at least two fixed frequency quantum circuits.

7. The method according to claim 6 , wherein each of the first frequency and the at least one second frequency corresponds to a difference of energy between the reference excited state and another excited state, the another excited state representable as a tensor product involving a ground state of the tunable coupler and a state of the at least two fixed frequency quantum circuits, where the state is representable as a tensor product involving an excited state of only one of the at least two fixed frequency quantum circuits and a ground state of each of the remaining at least two fixed frequency quantum circuits.

8. The method according to claim 2 , wherein the first-order energy transition is driven by applying harmonic microwave signals to the tunable coupler, the harmonic microwave signals modulated so as to modulate the frequency of the tunable coupler, in order to drive the first transition and the at least one second transition.

9. The method according to claim 2 , wherein the quantum processing device further comprises at least three fixed frequency quantum circuits, each coupled to the tunable coupler; and

wherein the frequency of the tunable coupler is concomitantly modulated at the first frequency, so as to drive the first transition, and at two or more second frequencies, so as to concomitantly drive two or more second transitions, respectively, whereby excitations are transferred, at least partly, from the tunable coupler to two or more other ones of the at least three fixed frequency quantum circuits, each of the two or more second transitions being a first-order energy transition.

10. The method according to claim 9 , further comprising setting amplitudes and phases of signals applied to the tunable coupler, so as to achieve a multipartite entangled state of the at least three fixed frequency quantum circuits.

11. The method according to claim 1 , wherein the quantum gate does not operate, effectively, on the tunable coupler.

12. A method of operating a quantum processing device, the method comprising:

modulating a frequency of a tunable coupler to drive two first-order energy transitions, the quantum processing device comprising at least two fixed frequency quantum circuits coupled to the tunable coupler; and

causing an excitation of one of the at least two fixed frequency quantum circuits such that the excitation is at least partly transferred to at least another one of the at least two fixed frequency quantum circuits, via the tunable coupler, wherein the frequency of the tunable coupler is modulated to implement a universal set of gates based on states of the at least two fixed frequency quantum circuits, wherein the frequency of the tunable coupler is operable to be modulated so as to drive at least two selectively addressable energy transitions in the quantum processing device.

13. The method according to claim 12 , wherein the universal set of gates are not based on states of the tunable coupler.

14. The method according to claim 12 , further comprising setting amplitudes and phases of signals applied to the tunable coupler, so as to achieve one or more selected from the group consisting of: an iSWAP gate, a c-Phase gate, a Fredkin gate, and a square root of SWAP gate.

15. The method according to claim 12 , wherein the frequency of the tunable coupler is modulated at:

a first frequency, so as to drive a first transition and thereby transfer, at least partly, a first excitation of the one of the at least two fixed frequency quantum circuits to the tunable coupler; and

at least one second frequency distinct from the first frequency, so as to drive at least one second transition, respectively, and thereby further transfer, at least partly, the first excitation from the tunable coupler to the at least another one of the at least two fixed frequency quantum circuits, each of the first transition and the at least one second transition being a first-order energy transition.

16. A method of operating a quantum processing device, the method comprising:

modulating a frequency of a tunable coupler to drive two first-order energy transitions, wherein the quantum processing device comprises at least two fixed frequency quantum circuits capacitively coupled to the tunable coupler; and

causing an excitation of one of the at least two fixed frequency quantum circuits such that the excitation is at least partly transferred to at least another one of the at least two fixed frequency quantum circuits, via the tunable coupler;

wherein the frequency of the tunable coupler is modulated to implement a quantum gate operating on at least one of the at least two fixed frequency quantum circuits;

wherein the frequency of the tunable coupler is modulated at a first frequency, so as to drive a first transition and thereby transfer, at least partly, a first excitation of the one of the at least two fixed frequency quantum circuits to the tunable coupler;

wherein the frequency of the tunable coupler is modulated at at least one second frequency distinct from the first frequency, so as to drive at least one second transition.

17. The method according to claim 16 , wherein the frequency of the tunable coupler modulated at the at least one second frequency distinct from the first frequency, so as to drive the at least one second transition further transfers, at least partly, the first excitation from the tunable coupler to the at least another one of the at least two fixed frequency quantum circuits.

18. The method according to claim 17 , wherein each of the first transition and the at least one second transition is a first-order energy transition.

19. The method according to claim 16 , wherein the frequency of the tunable coupler is operable to be modulated to drive at least two selectively addressable energy transitions in the quantum processing device.