Secure quantum swap

1. A computer implemented method for implementing a quantum swap operation on a first qubit and a second qubit, the method comprising:

establishing, by a first party and with a second party, an agreement to use a secure swap protocol to perform the quantum swap operation;

performing, by the first party and with the second party, the quantum swap operation, comprising, for each two-qubit gate included in the quantum swap operation:

performing, by the first party and according to the secure swap protocol, a respective preceding quantum gate cipher on the first qubit, wherein the preceding quantum gate cipher comprises a computational basis that anti-commutes with a computational basis of the two-qubit gate across a first axis of a Bloch sphere;

performing, by the first party and the second party, the two-qubit gate on the first qubit and the second qubit; and

performing, by the first party and according to the secure swap protocol, a respective succeeding quantum gate cipher on the first qubit, wherein the succeeding quantum gate cipher comprises a computational basis that anti-commutes with a computational basis of the two-qubit gate across a second axis of the Bloch sphere.

2. The method of claim 1 , wherein the method further comprises, after establishing the agreement to use the secure swap protocol to perform the quantum swap operation, performing, by the first party, a first commutation correction quantum operation to the first qubit, wherein the first commutation correction quantum operation corrects erroneous rotations of the first qubit.

3. The method of claim 1 , wherein the method further comprises, after performing the quantum swap operation, performing, by the first party, a second commutation correction quantum operation to the first qubit, wherein the second commutation correction quantum operation corrects erroneous rotations of the first qubit.

4. The method of claim 1 , further comprising, prior to implementing the quantum swap operation:

defining an initial quantum circuit with initial quantum gate ciphers;

adding quantum gates to the initial quantum gate ciphers to define an intermediate quantum circuit, wherein the intermediate quantum circuit is represented by a matrix with one of multiple acceptable forms, wherein a matrix has an acceptable form if the matrix i) includes four non-zero unitary-valued elements and twelve zero elements and ii) each row and column of the matrix includes one non-zero unitary-valued element.

5. The method of claim 4 , further comprising adding correction quantum operations to the intermediate quantum circuit to produce a correct quantum circuit, wherein performing the correct quantum circuit implements a correct quantum swap operation.

6. The method of claim 1 , wherein performing, by the first party, the two-qubit gate, comprises synchronizing with the second party to perform the two-qubit gate.

7. The method of claim 1 , wherein the preceding quantum gate ciphers and the succeeding quantum gate ciphers performed by the first party are unknown to the second party.

8. The method of claim 1 , wherein the preceding quantum gate ciphers and the succeeding quantum gate ciphers each comprise quantum gates that implement 120 degree and 180 degree rotations.

9. The method of claim 1 , wherein the preceding quantum gate ciphers and the succeeding quantum gate ciphers vary for each two-qubit gate included in the quantum swap operation.

10. The method of claim 1 , further comprising:

performing, by the second party and with the first party, the quantum swap operation, comprising, for each two-qubit gate included in the quantum swap operation:

performing, by the second party and according to the secure swap protocol, a respective preceding quantum gate cipher on the second qubit, wherein the preceding quantum gate cipher comprises a computational basis that anti-commutes with a computational basis of the two-qubit gate across a first axis of the Bloch sphere;

performing, by the second party and with the first party, the two-qubit gate; and

performing, by the second party and according to the secure swap protocol, a respective succeeding quantum gate cipher on the second qubit, wherein the succeeding quantum gate cipher comprises a computational basis that anti-commutes with a computational basis of the two-qubit gate across a second axis of the Bloch sphere.

11. The method of claim 1 , wherein the agreement to use a secure swap protocol to perform the quantum swap operation is established using a secure private channel.

12. The method of claim 1 , wherein the quantum swap operation comprises a SWAP gate or an iSWAP gate.

13. A system comprising:

one or more classical processors; and

quantum computing hardware;

wherein the system is configured to perform operations comprising:

establishing, by a first party and with a second party, an agreement to use a secure swap protocol to perform a quantum swap operation;

performing, by the first party and with the second party, the quantum swap operation, comprising, for each two-qubit gate included in the quantum swap operation:

performing, by the first party and according to the secure swap protocol, a respective preceding quantum gate cipher on a first qubit, wherein the preceding quantum gate cipher comprises a computational basis that anti-commutes with a computational basis of the two-qubit gate across a first axis of a Bloch sphere;

performing, by the first party and the second party, the two-qubit gate on the first qubit and a second qubit; and

performing, by the first party and according to the secure swap protocol, a respective succeeding quantum gate cipher on the first qubit, wherein the succeeding quantum gate cipher comprises a computational basis that anti-commutes with a computational basis of the two-qubit gate across a second axis of the Bloch sphere.

14. The system of claim 13 , wherein the operations further comprise, after establishing the agreement to use the secure swap protocol to perform the quantum swap operation, performing, by the first party, a first commutation correction quantum operation to the first qubit, wherein the first commutation correction quantum operation corrects erroneous rotations of the first qubit.

15. The system of claim 13 , wherein the operations further comprise, after performing the quantum swap operation, performing, by the first party, a second commutation correction quantum operation to the first qubit, wherein the second commutation correction quantum operation corrects erroneous rotations of the first qubit.

16. The system of claim 13 , wherein the preceding quantum gate ciphers and the succeeding quantum gate ciphers each comprise quantum gates that implement 120 degree and 180 degree rotations.

17. The system of claim 13 , wherein the preceding quantum gate ciphers and the succeeding quantum gate ciphers vary for each two-qubit gate included in the quantum swap operation.

18. The system of claim 13 , wherein the agreement to use a secure swap protocol to perform the quantum swap operation is established using a secure private channel.

19. The system of claim 13 , wherein the quantum swap operation comprises a SWAP gate or an iSWAP gate.

20. The system of claim 13 , wherein the operations further comprise, prior to implementing the quantum swap operation:

defining an initial quantum circuit with initial quantum gate ciphers;

adding quantum gates to the initial quantum gate ciphers to define an intermediate quantum circuit, wherein the intermediate quantum circuit is represented by a matrix with one of multiple acceptable forms, wherein a matrix has an acceptable form if the matrix i) includes four non-zero unitary-valued elements and twelve zero elements and ii) each row and column of the matrix includes one non-zero unitary-valued element; and

adding correction quantum operations to the intermediate quantum circuit to produce a correct quantum circuit, wherein performing the correct quantum circuit implements a correct quantum swap operation.