Method to access fibonacci anyons for topologicial quantum computation in a correlated two-dimensional electron system
A method is provided for operating a fractional quantum Hall apparatus including a set of interferometers, each having a cell and a set of gate electrodes located around the cell. The method includes calibrating each one of the interferometers to confine a droplet of a 2D charge carrier gas in a fractional quantum Hall effect state of filling factor 17/5 or 12/5, while a reentrant phase of integer quantum Hall effect states of the 2D charge carrier gas is located between the area of the droplet in a fractional quantum Hall effect state and the interferometer electrodes. The calibrating includes setting a value of a magnetic field across the apparatus such that the reentrant phase and the droplet of the 2D charge carrier gas are present in at least one of the interferometers based on interference measurements on at least one of the interferometers for different values of the magnetic field.
1. A method for operating an apparatus including a set of interferometers located along a surface of a substrate, the substrate having a quantum well operable to trap a 2D charge carrier gas such that the trapped 2D charge carrier gas extends along the surface, each interferometer having a cell and a set of gate electrodes located around the cell, the method comprising:
calibrating each one of the interferometers to confine a droplet of the 2D charge carrier gas in a fractional quantum Hall effect state of filling factor 17/5 or 12/5 in an area of the cell thereof while a reentrant phase of integer quantum Hall effect states of the 2D charge carrier gas is located between the area of the droplet of the 2D charge carrier gas in a fractional quantum Hall effect state and the electrodes of the one of the interferometers;
wherein the calibrating includes setting a value of a magnetic field across the substrate such that the reentrant phase and the droplet of the 2D charge carrier gas are present in at least one of the interferometers based on interference measurements on the at least one of the interferometers for different values of the magnetic field; and
illuminating the substrate to increase a density of the charge carriers in the 2D charge carrier gas, stopping the illuminating, and then, applying voltages to the gate electrodes to form the droplets in the interferometers.
2. The method of claim 1 , further comprising:
measuring or varying a topological property of the droplet of the 2D charge carrier gas confined in one or more of the interferometers of the set while maintaining the calibration of the interferometers.
3. The method of claim 1 , further comprising:
manipulating the 2D charge carrier gas while maintaining the calibration of the interferometers to perform at least one of:
read a qubit value stored in a selected one of the calibrated interferometers,
store a qubit value to the selected one of the calibrated interferometers, and
perform a braid operation of qubit states confined to two or more selected ones of the calibrated interferometers.
4. The method of claim 1 , wherein the substrate includes a group III-V semiconductor heterostructure comprising:
a primary quantum well having an InGaAs or GaAs well layer between AlGaAs barrier layers, each AlGaAs barrier layer including a shielding quantum well; and
at least one silicon dopant layer located such that one of the shielding quantum wells is between the silicon dopant layer and the InGaAs or GaAs well layer.
5. The method of claim 1 , wherein the calibrating comprises using the interference measurements to determine whether a reentrant phase of integer quantum Hall effect states of the 2D charge carrier gas is present in the at least one of the interferometers.
6. The method of claim 1 , wherein the calibrating further comprises, in response to determining that a reentrant phase is not present in the at least one of the interferometers:
re-illuminating the substrate; and
after stopping the re-illuminating, using interference measurements to determine whether a reentrant phase of integer quantum Hall effect states of the 2D charge carrier gas is present in the at least one of the interferometers.
7. The method of claim 6 , wherein the calibration further comprises, while varying the magnetic field, measuring oscillations in the interference measurements due to some or all of: Aharonov-Bohm oscillations, statistical phase oscillations, and oscillations due to a quasiparticle number change of a non-abelian state for the filling factor 12/5 or the filling factor 17/5.
8. The method of claim 7 , wherein the calibration further comprises, in the event of a failure to observe oscillations of a type selected from the set consisting of Aharonov-Bohm oscillations, statistical phase oscillations, and oscillations due to quasiparticle number change in non-abelian states associated with the filling factor 12/5 or the filling factor 17/5:
re-illuminating the substrate; and
after stopping the re-illuminating, repeating the varying the magnetic field and, while varying the magnetic field, measuring oscillations in the interference measurements due to some or all of: Aharonov-Bohm oscillations, statistical phase oscillations, and oscillations due to quasiparticle number change of a non-abelian state for the filling factor 12/5 or the filling factor 17/5.
9. The method of claim 1 , wherein the charge carriers of the 2D charge carrier gas are electrons and the illuminating causes a bulk density of the electrons in the 2D charge carrier gas to be greater than, substantially, 4×10 11 per square centimeter of the surface.
10. The method of claim 1 , wherein each one of the interferometers includes a set of side electrodes and a set of backscattering electrodes, and the method further comprises:
applying voltages to the side electrodes of a specific one of the interferometers to deplete an area around the cell of the specific one of the interferometers of the 2D charge carrier gas; and
adjusting voltages applied across the backscattering electrodes of the specific one of the interferometers to change a backscattering of edge excitations of the droplet in the specific one of the interferometers.
11. The method of claim 10 , wherein a pattern comprising one or more dot electrodes overlies the cell of the specific one of the interferometers, the one or more dot electrodes being electrically isolated from the side and backscattering electrodes of the specific one of the interferometers; and
the method further comprises applying a voltage to a selected one of the dot electrodes of the dot pattern such that a charge becomes localized in the 2D charge carrier gas near the selected dot electrode.
12. The method of claim 11 , further comprising:
varying a voltage applied to the selected dot electrode such that a charge becomes localized in the 2D charge carrier gas near a different one of the one or more dot electrodes.
13. The method of claim 11 , further comprising:
varying a voltage applied to the selected dot electrode such that a charge moves between adjacent facing backscattering electrodes.
14. The method of claim 10 , further comprising:
varying a voltage applied to the selected dot electrode such that a charge is shifted from a localized position at the selected dot electrode to one of the side electrodes or one of the backscattering electrodes of the specific one of the interferometers.