Flux control of qubit under resonant excitation
Systems and methods are provided for flux control of a qubit. A quantum system includes a microwave transmitter configured to provide a continuous microwave tone, and a qubit configured such that a portion of an energy spectrum of the qubit is responsive to an applied flux. The qubit also has an inductive element responsive to the continuous microwave tone to produce a Rabi oscillation within the qubit. A flux source is configured to apply a flux to the qubit.
1. A method for performing a Y rotation of a qubit configured such that the qubit is responsive to the continuous microwave tone to produce a Rabi oscillation within the qubit and a portion of an energy spectrum of the qubit is responsive to an applied flux, the method comprising:
providing a continuous microwave tone to the qubit;
providing a flux pulse to the qubit as to detune the energy spectrum of the qubit from a frequency of the Rabi oscillation by a first predetermined amount for a predetermined time; and
adjusting the flux pulse to the qubit as to detune the energy spectrum of the qubit from a frequency of the Rabi oscillation by a second predetermined amount for the predetermined time, wherein the second predetermined amount is the additive inverse of the first predetermined amount.
2. The method of claim 1 , wherein the predetermined time is equal to
ϕcos
(
ϕ
4
)
Ω
and the first amount is equal to
Ωtan
(
ϕ
4
)
,
where ϕ is a desired angle of the Y rotation, and Ω is the frequency of the Rabi oscillation.
3. The method of claim 1 , wherein the predetermined time is a first predetermined time and the method further comprises adjusting the flux pulse to the qubit as to tune the energy spectrum of the qubit to the frequency of the Rabi oscillation for a second predetermined time.
4. The method of claim 3 , wherein the flux pulse is adjusted to the qubit as to tune the energy spectrum of the qubit to the frequency of the Rabi oscillation after the flux pulse is provided to the qubit and before the flux pulse is adjusted as to detune the energy spectrum of the qubit from a frequency of the Rabi oscillation by a second predetermined amount.
5. The method of claim 3 , wherein the first predetermined time is equal to
ϕcos
(
ϕ
2
)
Ω
,
the first amount is equal to
Ωtan
(
ϕ
2
)
,
and the second predetermined time is equal to
π
Ω
,
where ϕ is a desired angle of the Y rotation, and Ω is the frequency of the Rabi oscillation.
6. A quantum system comprising:
a microwave transmitter configured to provide a continuous microwave tone;
a qubit configured such that a portion of an energy spectrum of the qubit is linearly dependent on an applied flux, the qubit having an inductive element responsive to the continuous microwave tone to produce a Rabi oscillation within the qubit;
a flux source configured to apply a flux to the qubit; and
a system control configured to control the flux source as to selectively apply flux to the qubit, such that a qubit resonance frequency associated with the energy spectrum of the qubit can be selectively tuned to a frequency of the Rabi oscillation, the system control being configured to tune the qubit resonance frequency such that the detuning is pulsed symmetrically around a zero point, such that the qubit resonant frequency is detuned from the frequency of the Rabi oscillation by a first amount for a predetermined period of time and then detuned from the frequency of the Rabi oscillation by a second amount for the predetermined period of time, where the second amount is the additive inverse of the first amount.
7. The quantum system of claim 6 , wherein the system control is configured such that the predetermined time is equal to
ϕcos
(
ϕ
4
)
Ω
,
where ϕ is a desired angle of the Y rotation, and Ω is the frequency of the Rabi oscillation.
8. The quantum system of claim 6 , wherein the system control is configured such that the first amount is equal to
Ωtan
(
ϕ
4
)
,
where ϕ is a desired angle of the Y rotation, and Ω is the frequency of the Rabi oscillation.