Parametrically activated quantum logic gates
In a general aspect, a quantum logic gate is performed in a quantum computing system. In some cases, a pair of qubits are defined in a quantum processor; the pair of qubits can include a first qubit defined by a first qubit device in the quantum processor and a second qubit defined by a tunable qubit device in the quantum processor. A quantum logic gate can be applied to the pair of qubits by communicating a control signal to a control line coupled to the tunable qubit device. The control signal can be configured to modulate a transition frequency of the tunable qubit device at a modulation frequency, and the modulation frequency can be determined based on a transition frequency of the first qubit device.
1. A quantum information control method comprising:
generating a control signal configured to modulate, at a modulation frequency, a transition frequency of a tunable qubit device in a quantum processor, the modulation frequency being determined based on a transition frequency of a fixed-frequency qubit device in the quantum processor, the transition frequency of the fixed-frequency qubit device being independent of a magnetic flux experienced by the fixed-frequency qubit device; and
applying a two-qubit quantum logic gate to a pair of qubits in the quantum processor by communicating the control signal to a control line coupled to the tunable qubit device, the pair of qubits comprising a first qubit defined by the fixed-frequency qubit device and a second qubit defined by the tunable qubit device,
wherein applying the two-qubit quantum logic gate to the pair of qubits comprises one of the following:
applying an iSWAP gate to the pair of qubits;
applying a square-root-of-iSWAP gate to the pair of qubits;
applying a controlled-Z gate to the pair of qubits; or
applying a Bell-Rabi gate to the pair of qubits.
2. The method of claim 1 , comprising determining the modulation frequency based on the sum or the difference of:
the transition frequency of the tunable qubit device, and
the transition frequency of the fixed-frequency qubit device.
3. The method of claim 1 , wherein the modulation frequency is determined based on the transition frequency of the fixed-frequency qubit device and the transition frequency of the tunable qubit device.
4. The method of claim 1 , wherein the modulation frequency is determined based on the transition frequency of the fixed-frequency qubit device and the anharmonicity of the tunable qubit device.
5. The method of claim 1 , wherein the modulation frequency is determined based on the transition frequency between the ground state and first excited state of the fixed-frequency qubit device.
6. The method of claim 1 , wherein the modulation frequency is determined based on the transition frequency between the first excited state and second excited state of the fixed-frequency qubit device.
7. The method of claim 1 , wherein applying the two-qubit quantum logic gate to the pair of qubits comprises applying an iSWAP gate to the pair of qubits.
8. The method of claim 7 , wherein the control signal is configured to modulate the transition frequency of the tunable qubit device at the modulation frequency with a modulation amplitude ow, and the control signal is configured to produce an interaction between the tunable qubit device and the fixed-frequency qubit device for a total interaction time
t
i
S
W
A
P
(
1
)
=
π
2
1
g
|
J
1
(
δ
ω
/
ω
m
)
|
,
where g represents a capacitive coupling strength between the tunable qubit device and the fixed-frequency qubit device, J 1 represents a first-order Bessel function of the first kind, and ω m represents the modulation frequency.
9. The method of claim 1 , wherein applying the two-qubit quantum logic gate to the pair of qubits comprises applying a square-root-of-iSWAP gate to the pair of qubits.
10. The method of claim 9 , wherein the control signal is configured to modulate the transition frequency of the tunable qubit device at the modulation frequency with a modulation amplitude ow, and the control signal is configured to produce an interaction between the tunable qubit device and the fixed-frequency qubit device for a total interaction time
t
i
S
W
A
P
(
1
)
=
π
4
1
g
J
1
(
δ
ω
/
ω
m
,
)
,
where g represents a capacitive coupling strength between the tunable qubit device and the fixed-frequency qubit device, J 1 represents a first-order Bessel function of the first kind, and ω m represents the modulation frequency.
11. The method of claim 1 , comprising generating the control signal to modulate the transition frequency of the tunable qubit device about a reference frequency ω T 01 at the modulation frequency ω m =| ω T 01 −ω F 01 |, where ω F 01 represents the transition frequency of the fixed-frequency qubit device.
12. The method of claim 1 , wherein applying the two-qubit quantum logic gate to the pair of qubits comprises applying a controlled-Z gate to the pair of qubits.
13. The method of claim 12 , wherein the control signal is configured to modulate the transition frequency of the tunable qubit device at the modulation frequency with a modulation amplitude δω, and the control signal is configured to produce an interaction between the tunable qubit device and the fixed-frequency qubit device for a total interaction time
t
C
Z
(
1
)
=
π
2
1
g
|
J
1
(
δ
ω
/
ω
m
)
|
,
where g represents a capacitive coupling strength between the tunable qubit device and the fixed-frequency qubit device, J 1 represents a first-order Bessel function of the first kind, and ω m represents the modulation frequency.
14. The method of claim 1 , comprising generating the control signal to modulate the transition frequency of the tunable qubit device about a reference frequency ω T 01 at the modulation frequency ω m =| ω T 01 −ω F 01 − η T |, where ω F 01 represents the transition frequency of the fixed-frequency qubit device and η T represents an average anharmonicity of the tunable qubit device.
15. The method of claim 1 , comprising generating the control signal to modulate the transition frequency of the tunable qubit device about a reference frequency ω T 01 at the modulation frequency ω m =| ω T 01 −ω F 01 + η T |, where ω F 01 represents the transition frequency of the fixed-frequency qubit device and η F represents the anharmonicity of the fixed-frequency qubit device.
16. The method of claim 1 , wherein applying the two-qubit quantum logic gate to the pair of qubits comprises applying a Bell-Rabi gate to the pair of qubits.
17. The method of claim 16 , wherein the control signal is configured to produce an interaction between the tunable qubit device and the fixed-frequency qubit device for a total interaction time
t
B
R
(
1
)
=
π
g
|
J
1
(
δ
ω
/
ω
m
)
|
,
where g represents a capacitive coupling strength between the tunable qubit device and the fixed-frequency qubit device, J 1 represents a first-order Bessel function of the first kind, and ω m represents the modulation frequency.
18. The method of claim 1 , comprising generating the control signal to modulate the transition frequency of the tunable qubit device about a reference frequency ω T 01 at the modulation frequency ω m = ω T 01 +ω F 01 , where ω F 01 represents the transition frequency of the fixed-frequency qubit device.
19. The method of claim 1 , wherein communicating the control signal to the control line produces, between the tunable qubit device and the fixed-frequency qubit device, an interaction having an effective coupling strength that is based on the modulation frequency.
20. A quantum information control method comprising:
generating a control signal configured to modulate, at a modulation frequency, a transition frequency of a tunable qubit device in a quantum processor, the modulation frequency being determined based on a transition frequency of a fixed-frequency qubit device in the quantum processor, the transition frequency of the fixed-frequency qubit device being independent of a magnetic flux experienced by the fixed-frequency qubit device, wherein the control signal is configured to modulate the transition frequency of the tunable qubit device about a reference frequency ω T 01 of the tunable qubit device at the modulation frequency with a modulation amplitude δω, and communicating the control signal to the control line produces, between the tunable qubit device and the fixed-frequency qubit device, an interaction having an effective coupling strength
g
1
0
↔
0
1
(
n
)
=
g
|
J
n
(
n
δ
ω
Δ
)
|
where g represents a capacitive coupling strength between the tunable qubit device and the fixed-frequency qubit device, J n represents a Bessel function of the first kind, n represents a non-zero integer, and Δ represents the difference between the reference frequency ω T 01 and the transition frequency of the fixed-frequency qubit device ω F 01 ; and
applying a two-qubit quantum logic gate to a pair of qubits in the quantum processor by communicating the control signal to a control line coupled to the tunable qubit device, the pair of qubits comprising a first qubit defined by the fixed-frequency qubit device and a second qubit defined by the tunable qubit device.
21. The method of claim 20 , comprising generating the control signal to modulate the transition frequency of the tunable qubit device about the reference frequency ω T 01 at the modulation frequency ω m =| ω T 01 −ω F 01 |.
22. The method of claim 21 , wherein applying the two-qubit quantum logic gate to the pair of qubits comprises applying an iSWAP gate to the pair of qubits, and in response to n=1, the control signal is configured to produce an interaction between the tunable qubit device and the fixed-frequency qubit device for a total interaction time
t
iSWAP
(
1
)
=
π
2
1
g
❘
"\[LeftBracketingBar]"
J
1
(
δω
/
ω
m
)
|
,
where J 1 represents a first-order Bessel function of the first kind.
23. The method of claim 21 , wherein applying the two-qubit quantum logic gate to the pair of qubits comprises applying a square-root-of-iSWAP gate to the pair of qubits and in response to n=1, the control signal is configured to produce an interaction between the tunable qubit device and the fixed-frequency qubit device for a total interaction time
t
iSWAP
(
1
)
=
π
4
1
g
❘
"\[LeftBracketingBar]"
J
1
(
δω
/
ω
m
)
|
,
where J 1 represents a first-order Bessel function of the first kind.