Use of topological charge measurements to change between different qubit encodings
A method for changing qubit encoding for implementation of a quantum computational gate is disclosed. Such a method may include providing first and second qubits encoded in a plurality of non-abelian anyons according to a first encoding scheme. The first encoding scheme may not be suitable for implementing a certain topologically protected quantum computational gate, such as an entangling gate, for example. Successive topological charge measurements may be performed on at least a subset of the anyons until the qubits are encoded according to a second encoding scheme. The second encoding scheme may be different from the first encoding scheme, and may be suitable for implementing the gate.
1. A method for implementing a quantum computational gate, the method comprising:
encoding first and second qubits in accordance with a first encoding scheme that utilizes a first cardinal number of a plurality of non-abelian quasiparticles;
changing, via performance of at least one topological charge measurement, the encoding of the first and second qubits to a second encoding scheme that utilizes a second cardinal number of the plurality of non-abelian quasiparticles, wherein the first and the second cardinal numbers are different; and
implementing a quantum computational gate with the qubits after the encoding is changed.
2. The method of claim 1 , wherein the qubits are unsuitable for implementing the gate before the encoding is changed, and suitable for implementing the gate after the encoding is changed.
3. The method of claim 2 , wherein the gate is a topologically protected quantum computational gate.
4. The method of claim 3 , wherein the gate is an entangling gate.
5. The method of claim 1 , wherein the non-abelian quasiparticles are Ising quasiparticles.
6. The method of claim 1 , wherein the non-abelian quasiparticles are disposed in a υ=5/2 fractional quantum Hall fluid.
7. The method of claim 1 , wherein the first cardinal number is eight, and before the encoding is changed, each of the first and second qubits is encoded in a respective subset of four of the non-abelian quasiparticles.
8. The method of claim 7 , wherein the second cardinal number is six, after the encoding is changed, the first and second qubits are encoded in a subset of six of the non-abelian quasiparticles.
9. A method for changing qubit encoding for implementation of a quantum computational gate, the method comprising:
providing first and second qubits, wherein the first and second qubits are encoded in a first cardinal number of non-abelian quasiparticles of a plurality of non-abelian quasiparticles according to a first encoding scheme; and
performing successive topological charge measurements on at least a subset of the plurality of non-abelian quasiparticles until the first and second qubits are encoded in a second cardinal number of non-abelian quasiparticles of the plurality of non-abelian quasiparticles according to a second encoding scheme that is different from the first encoding scheme, wherein the first and second cardinal numbers are different.
10. The method of claim 9 , wherein the second encoding scheme is suitable for implementing a topologically protected quantum computational gate, and the first encoding scheme is not suitable for implementing the gate.
11. The method of claim 10 , wherein the first cardinal number is eight, and according to the first encoding scheme, each of the first and second qubits is encoded in a respective subset of four of the non-abelian quasiparticles.
12. The method of claim 11 , wherein the first cardinal number is eight, and according to the second encoding scheme, the first and second qubits are encoded in a subset of six of the non-abelian quasiparticles.
13. A method for implementing a quantum computational gate, the method comprising:
providing first and second qubits, wherein each of the first and second qubits is encoded in a respective set of four non-abelian quasiparticles disposed in a fractional quantum Hall fluid;
performing successive topological charge measurements on at least a subset of the non-abelian quasiparticles until the first and second qubits are encoded in a set of six non-abelian quasiparticles; and
implementing a quantum computational gate while the first and second qubits are encoded in the set of six non-abelian quasiparticles.
14. The method of claim 13 , wherein the quantum computational gate is a topologically protected gate.
15. The method of claim 13 , wherein the quantum computational gate is an entangling gate.
16. The method of claim 15 , wherein the quantum computational gate is a Control(Z) gate.
17. The method of claim 15 , wherein the quantum computational gate is a Control(NOT) gate.
18. The method of claim 13 , wherein the non-abelian quasiparticles are Ising quasiparticles.
19. The method of claim 13 , wherein the fractional quantum Hall fluid is in a υ=5/2 fractional quantum Hall state.
20. The method of claim 13 , further comprising:
performing successive topological charge measurements on at least a subset of the non-abelian quasiparticles, after the quantum computational gate is implemented, to encode each of the first and second qubits in respective sets of four non-abelian quasiparticles.