Methods for single qubit gate teleportation
View Patent ↗A method for performing a single-qubit gate on an arbitrary quantum state. An ancillary qubit is set to an initial state |I>. The data qubit is coupled to an ancillary qubit. The state of the ancillary qubit is measured, and the data qubit and the ancillary qubit are coupled for a first period of time. A method for applying a single-qubit gate to an arbitrary quantum state. A state of a first and second ancillary qubit are set to an entangled initial state |I>. A state of a data qubit and the first ancillary qubit are measured thereby potentially performing a single qubit operation on the arbitrary quantum state. A first result is determined. The first result indicates whether the single qubit operation applied the single qubit gate to the arbitrary quantum state.
1. A method for performing a single-qubit gate on the state of a data qubit, the method comprising:
setting an ancillary qubit to a predetermined initial state |I>;
coupling said data qubit and said ancillary qubit for a first period of time to apply said single-qubit gate to said data qubit; and
measuring a state of said ancillary qubit, thereby collapsing the quantum state of the ancillary qubit to a classical result |0> or |1>, and wherein the classical result, |0> or |1>, indicates whether said single-qubit gate has been applied to said data qiubit.
2. The method of claim 1 , wherein, when said measuring indicates that said single-qubit gate was not successfully applied to said data qubit, the method further comprises coupling said data qubit and said ancillary qubit for a second period of time.
3. The method of claim 1 , wherein said predetermined initial state |I> comprises a superposition of basis states of said ancillary qubit.
4. The method of claim 3 , wherein said predetermined initial state has the form
I
〉
=
a
0
〉
+
b
1
〉
2
,
wherein,
|0> is a first basis state for said ancillary qubit;
|1> is a second basis state for said ancillary qubit;
a is a first probability amplitude;
b is a second probability amplitude; and
the magnitude of a and b are about the same.
5. The method of claim 4 , wherein said predetermined initial state is obtained by applying a single-qubit Pauli X gate for a phase π/2 to said ancillary qubit for a predetermined period of time.
6. The method of claim 5 , wherein said predetermined period of time is about
h
Δ
π
2
,
wherein h is Planck's constant and Δ is the tunneling amplitude of said ancillary qubit.
7. The method of claim 1 , wherein said data qubit is a superconducting qubit.
8. The method of claim 7 , wherein said superconducting qubit is a superconducting phase qubit.
9. The method of claim 8 , wherein said superconducting phase qubit is comprised of an unconventional superconducting material.
10. The method of claim 8 , wherein said superconducting phase qubit is a permanent readout superconducting qubit or a two-junction flux qubit.
11. The method of claim 7 , wherein the superconducting qubit is a superconducting charge qubit.
12. The method of claim 1 , wherein said coupling of said data qubit and said ancillary qubit for a first period of time comprises applying a Josephson gate between said data qubit and said ancillary qubit.
13. The method of claim 1 , wherein said single-qubit gate is a single-qubit Pauli Z gate.
14. The method of claim 1 , wherein said first period of time is about
h
J
1
·
π
2
,
wherein,
J 1 is a coupling term between said ancillary qubit and said data qubit during said coupling; and
h is Planck's constant.
15. The method of claim 3 , wherein said second period of time is about
h
J
2
·
π
wherein,
J 2 is a coupling term between said ancillary qubit and said data qubit during said second coupling; and
h is Planck's constant.
16. The method of claim 2 , wherein said second time period is about equal to said first time period and wherein a coupling term between said ancillary qubit and said data qubit during said first coupling is about double a coupling term between said ancillary qubit and said data qubit during said second coupling.
17. The method of claim 1 , wherein said coupling of said data qubit and said ancillary qubit for said first period of time comprises an XX gate.
18. The method of claim 1 , wherein said single-qubit gate is an X gate or a bit-flip gate.
19. The method of claim 1 , wherein said coupling of said data qubit and said ancillary qubit is a YY gate.
20. The method of claim 1 , wherein said single-qubit gate is a Y gate.
21. A method for applying a single-qubit gate to an arbitrary quantum state, wherein said arbitrary quantum state is initially on a data qubit, the method comprising:
setting a state of a first and second ancillary qubit to an entangled initial state |I>;
weakly measuring a state of said data qubit and said first ancillary qubit thereby performing said single qubit gate on said arbitrary quantum state with a probability; and
determining a first result from said weakly measuring step.
22. The method of claim 21 , wherein said arbitrary quantum state is present on said second ancillary qubit after said weakly measuring step and said first result indicates that said single-qubit gate has been applied to said arbitrary quantum state.
23. The method of claim 21 , wherein said arbitrary quantum state is present on said second ancillary qubit after said weakly measuring step and said first result indicates that said single-qubit gate was not applied on said second ancillary qubit, the method further comprising:
applying a first correction, wherein said first correction comprises weakly measuring the state of said data qubit and said first ancillary qubit; and
determining a second result.
24. The method of claim 23 , wherein said second result indicates that said first correction applied the Hermitian conjugate of said single-qubit gate on said arbitrary quantum state that is present on said second ancillary qubit after said first correction.
25. The method of claim 24 , the method further comprising correcting the state of said second ancillary qubit for said Hermitian conjugate of said single-qubit gate.
26. The method of claim 25 , wherein correcting the state of said second ancillary qubit for said Hermitian conjugate of said single-qubit gate comprises coupling said first ancillary qubit and said second ancillary qubit with an exchange two-qubit unitary operator:
U EX 3,2 (π/2,0).
27. The method of claim 23 , wherein, when said second result indicates that the Hermitian conjugate of said single-qubit gate was not applied on said arbitrary quantum state, now present on said second ancillary qubit, the method further comprises:
applying a second correction, wherein said second correction comprises weakly measuring the state of said first ancillary qubit and said second ancillary qubit; and
determining a third result.
28. The method of claim 27 , wherein said arbitrary quantum state is present on said data qubit after applying said second correction and said third result indicates that said single-qubit gate was applied on said arbitrary quantum state.
29. The method of claim 27 , wherein said arbitrary quantum state is present on said data qubit after applying said second correction and said third result indicates that the Hermitian conjugate of said single-qubit gate was applied on said arbitrary quantum state.
30. The method of claim 29 , the method further comprising correcting the state of said data qubit for said Hermitian conjugate of said single-qubit gate.
31. The method of claim 30 , wherein the correction for said Hermitian conjugate of said single-qubit gate comprises coupling said data qubit and said first ancillary qubit via an exchange two-qubit unitary operator:
U EX 3,2 (π/2,0).
32. The method of claim 21 , wherein said entangled initial state comprises a superposition of basis states of said first ancillary qubit and said second ancillary qubit.
33. The method of claim 32 , wherein said initial state |I> has the form:
I
〉
≈
1
2
(
a
01
〉
-
ⅈ
b
10
〉
)
,
wherein,
|0> is a first state for said first ancillary qubit and said second ancillary qubit;
|0> is a second state for said first ancillary qubit and said second ancillary qubit;
a is a first probability amplitude;
b is a second probability amplitude;
the magnitude of a and b are about the same; and
i=√{square root over (−1)}.
34. The method of claim 33 , wherein said setting said state of said first ancillary qubit and said state of said second ancillary qubit to said entangled initial state |I> comprises:
a first coupling of said first and second ancillary qubits for a duration t 1 ;
measuring the state of at least one of said first and second ancillary qubits; and
a second coupling of said first and second ancillary qubits for a second duration t β .
35. The method of claim 34 , wherein said first coupling allows the entangled state of said first and second ancillary qubits to relax to their respective ground states.
36. The method of claim 35 , wherein said duration , is one microsecond or less.
37. The method of claim 34 , wherein said measuring results in an overall state of either |10> or |01>.
38. The method of claim 34 , wherein said second coupling creates a phase difference that is about π radians between the respective basis states of the entangled pair wherein the overall entangled state satisfies |I>.
39. The method of claim 34 , wherein said second duration t β is about
h
J
α
·
π
8
wherein J α is a coupling term of an exchange Hamiltonian H ex between the first ancillary qubit and the second ancillary qubit and h is Planck's constant.
40. The method of claim 34 , wherein said second duration t β is one microsecond or less.
41. The method of claim 21 , wherein said data qubit is a superconducting qubit.
42. The method of claim 41 , wherein said superconducting qubit is a superconducting phase qubit.
43. The method of claim 42 , wherein said superconducting phase qubit is comprised of an unconventional superconducting material.
44. The method of claim 42 , wherein said superconducting phase qubit is a permanent readout superconducting qubit or a two junction flux qubit.
45. The method of claim 41 , wherein said superconducting qubit is a superconducting charge qubit.
46. The method of claim 21 , wherein said data qubit is a quantum dot, a donor atom in silicon, a photon, a resonant cavity, an atom, or an electron.
47. The method of claim 21 , wherein said first and second ancillary qubits are of the same type of qubit as said data qubit.
48. The method of claim 21 , wherein said first and second ancillary qubits are not the same type of qubit as said data quibit.
49. The method of claim 21 , wherein said single-qubit gate is a Z gate, a phase gate, an X gate, a bit-flip gate, or a Y gate.
50. The method of claim 21 , further comprising creating a universal set of gates using a plurality of applications of said single qubit gate in order to create a plurality of composite gates that form said universal set of gates.
51. A method for applying a single-qubit gate to an arbitrary quantum state that is initially present on a data qubit, the method comprising:
setting a state of a first and second ancillary qubit to an entangled initial state |I>;
performing a weak measurement on a state of said data qubit and said first ancillary qubit;
determining whether said weak measurement indicates said data qubit and said first ancillary qubit were in a singlet or triplet state; wherein
when the data qubit and said first ancillary qubit are in the singlet state, said single-qubit gate was applied on said arbitrary quantum state, and
when the data qubit and said first ancillary qubit are in the triplet state, the Hermitian conjugate of said single-qubit gate was applied on said arbitrary quantum state; and
performing a corrective operation when the data qubit and said first ancillary qubit are in the triplet state to convert the Hermitian conjugate of said single-qubit gate to said single-qubit gate.