Quasi-particle interferometry for logical gates
View Patent ↗A quantum computer can only function stably if it can execute gates with extreme accuracy. “Topological protection” is a road to such accuracies. Quasi-particle interferometry is a tool for constructing topologically protected gates. Assuming the corrections of the Moore-Read Model for ν=5/2's FQHE (Nucl. Phys. B 360, 362 (1991)) we show how to manipulate the collective state of two e/4-charge anti-dots in order to switch said collective state from one carrying trivial SU(2) charge, |1>, to one carrying a fermionic SU(2) charge |∈>. This is a NOT gate on the {|1>, |∈>} qubit and is effected by braiding of an electrically charged quasi particle a which carries an additional SU(2)-charge. Read-out is accomplished by σ-particle interferometry.
1. A method for implementing a NOT gate in a quantum computer, the method comprising:
providing a logical gate for a quantum computer, said logical gate comprising first and second electrically-conductive gates disposed within a fractional quantum Hall effect (FQHE) fluid, the FQHE fluid having one or more anti-dots disposed therein; and
affecting a collective state of the one or more anti-dots by adjusting a voltage between the first and second gates to cause a quasi-particle to tunnel between the first and second gates.
2. The method of claim 1 , wherein the FQHE fluid is a ν=5/2 quantum Hall effect fluid.
3. The method of claim 1 , wherein the quasi-particle is an anyon.
4. The method of claim 1 , wherein affecting the collective state of the one or more anti-dots comprises converting the collective state from a state carrying trivial SU(2)−charge |1> to a state carrying a fermionic SU(2) charge |∈>.
5. The method of claim 1 , wherein affecting the collective state of the one or more anti-dots comprises converting the collective state from a state carrying a fermionic SU(2)−charge |∈> to a state carrying trivial SU(2) charge | 1 >.
6. A method for read out of a logical gate in a quantum computer, the method comprising:
providing a fractional quantum Hall effect (FQHE) fluid having one or more anti-dots disposed therein;
injecting an input current into a first edge of the FQHE fluid such that the input current forms at least two tunneling current paths, the anti-dots being disposed between the tunneling current paths;
removing from a second edge of the FQHE fluid an output current that represents a combination of the tunneling currents; and
determining from the output current a collective state of the one or more anti-dots.
7. The method of claim 6 , further comprising:
determining whether the collective state of the one or more anti-dots corresponds to a state carrying trivial SU(2)−charge |1>.
8. The method of claim 6 , further comprising:
determining whether the collective state of the one or more anti-dots corresponds to a state carrying a fermionic SU(2) charge |∈>.