Detection of quasiparticle poisoning at Majorana island

1 . A computing system comprising:

a quantum computing device including:

a Majorana island at which a plurality of Majorana zero modes (MZMs) are instantiated;

a quantum dot electrically connectable to an MZM of the plurality of MZMs; and

a capacitance sensor capacitively coupled to the quantum dot; and

a controller configured to:

for each of one or more candidate resonance regions corresponding to one or more candidate quasiparticle poisoning values:

determine whether resonance occurs at that candidate resonance region at least in part by:

setting a Majorana island gate voltage of the Majorana island and a quantum dot gate voltage of the quantum dot to a candidate resonance Majorana island voltage and a candidate resonance quantum dot voltage of the candidate resonance region, respectively;

via the capacitance sensor, receiving a capacitance measurement of the quantum dot and the Majorana island at the candidate resonance region; and

determining whether resonance occurs at the candidate resonance region based at least in part on the capacitance measurement; and

reset the Majorana island gate voltage and the quantum dot gate voltage to a Coulomb valley Majorana island gate voltage and a Coulomb valley quantum dot gate voltage, respectively; and

output a quasiparticle poisoning value selected from among the candidate quasiparticle poisoning values as indicated by the one or more determinations of whether resonance occurs at the one or more candidate resonance regions.

2 . The computing system of claim 1 , wherein the Majorana island is a coherent link, a Majorana tetron, or a Majorana hexon.

3 . The computing system of claim 1 , wherein the quasiparticle poisoning value is a change in a fermion number of the Majorana island.

4 . The computing system of claim 3 , wherein the one or more candidate resonance regions correspond to a set of values of the change in the fermion number selected from the group consisting of:

−2, −1, 0, 1, and 2;

−1, 0, and 1; and

0.

5 . The computing system of claim 3 , wherein the controller is further configured to:

determine, based at least in part on the one or more capacitance measurements, that resonance does not occur in an initial resonance domain within which the candidate resonance regions are located;

in response to determining that resonance does not occur at any of the candidate resonance regions, determine whether resonance occurs at one or more additional candidate resonance regions located within an extended resonance domain.

6 . The computing system of claim 1 , wherein the quasiparticle poisoning value is a change in a fermion parity of the Majorana island.

7 . The computing system of claim 1 , wherein the controller is further configured to:

electrically couple the Majorana island to the quantum dot prior to performing the capacitance measurement; and

electrically decouple the Majorana island from the quantum dot subsequently to performing the capacitance measurement.

8 . The computing system of claim 1 , wherein the controller is further configured to estimate the one or more candidate resonance regions during a calibration phase at least in part by, for each of one or more values of a change in a fermion number of the Majorana island:

initializing the fermion number of the Majorana island and a fermion number of the quantum dot at zero;

setting the fermion number of the Majorana island to the value of the change in the fermion number;

electrically coupling the Majorana island to the quantum dot;

approximating, as the candidate resonance region corresponding to the change in the fermion number, one or more respective values of the Majorana island gate voltage and the quantum dot gate voltage at which resonance occurs at least in part by searching over respective ranges of the values of the Majorana island gate voltage and the quantum dot gate voltage;

resetting the Majorana island gate voltage and the quantum dot gate voltage to the Coulomb valley Majorana island gate voltage and the Coulomb valley quantum dot gate voltage, respectively; and

electrically decoupling the Majorana island from the quantum dot.

9 . The computing system of claim 8 , wherein, for each of the one or more values of the change in the fermion number, subsequently to approximating the candidate resonance region, the calibration phase further includes resetting the fermion number of the Majorana island and the fermion number of the quantum dot to zero at least in part by electrically coupling the quantum dot or Majorana island to a fermion reservoir.

10 . The computing system of claim 1 , wherein, via the quantum dot, the quantum computing device is further configured to perform a fermion parity measurement of a plurality of MZMs that includes the MZM to which the quantum dot is electrically coupled.

11 . The computing system of claim 1 , wherein, via an additional quantum dot, the quantum computing device is further configured to perform a fermion parity measurement of a plurality of MZMs that includes the MZM to which the quantum dot is electrically coupled.

12 . The computing system of claim 1 , wherein the controller is further configured to:

determine the quasiparticle poisoning value subsequently to a fermion parity measurement performed at the quantum computing device;

select an error correction protocol from among a plurality of error correction protocols based at least in part on the quasiparticle poisoning value; and

perform the selected error correction protocol at the quantum computing device.

13 . The computing system of claim 1 , wherein the capacitance sensor includes a microwave readout circuit configured to generate a microwave signal based at least in part on a capacitance of the quantum dot and the Majorana island.

14 . A method for use with a computing system, the method comprising:

for each of one or more candidate resonance regions corresponding to one or more candidate quasiparticle poisoning values of a Majorana island included in a quantum computing device:

determining whether resonance occurs at that candidate resonance region at least in part by:

setting a Majorana island gate voltage of the Majorana island and a quantum dot gate voltage of the quantum dot to a candidate resonance Majorana island voltage and a candidate resonance quantum dot voltage of the candidate resonance region, respectively;

via a capacitance sensor included in the quantum computing device, receiving a capacitance measurement of the quantum dot and the Majorana island at the candidate resonance region; and

determining whether resonance occurs at the candidate resonance region based at least in part on the capacitance measurement; and

resetting the Majorana island gate voltage and the quantum dot gate voltage to a Coulomb valley Majorana island gate voltage and a Coulomb valley quantum dot gate voltage, respectively; and

outputting a quasiparticle poisoning value selected from among the candidate quasiparticle poisoning values as indicated by the one or more determinations of whether resonance occurs at the one or more candidate resonance regions.

15 . The method of claim 14 , wherein the Majorana island is a coherent link, a Majorana tetron, or a Majorana hexon.

16 . The method of claim 14 , wherein the quasiparticle poisoning value is a change in a fermion number of the Majorana island.

17 . The method of claim 16 , wherein the one or more candidate resonance regions correspond to a set of values of the change in the fermion number selected from the group consisting of:

−2, −1, 0, 1, and 2;

−1, 0, and 1; and

0.

18 . The method of claim 14 , further comprising:

electrically coupling the Majorana island to the quantum dot prior to performing the capacitance measurement; and

electrically decoupling the Majorana island from the quantum dot subsequently to performing the capacitance measurement.

19 . The method of claim 14 , further comprising estimating the one or more candidate resonance regions during a calibration phase at least in part by, for each of one or more values of a change in a fermion number of the Majorana island:

initializing the fermion number of the Majorana island and a fermion number of the quantum dot at zero;

setting the fermion number of the Majorana island to the value of the change in the fermion number;

electrically coupling the Majorana island to the quantum dot;

approximating, as the candidate resonance region corresponding to the change in the fermion number, one or more respective values of the Majorana island gate voltage and the quantum dot gate voltage at which resonance occurs at least in part by searching over respective ranges of the values of the Majorana island gate voltage and the quantum dot gate voltage;

resetting the Majorana island gate voltage and the quantum dot gate voltage to the Coulomb valley Majorana island gate voltage and the Coulomb valley quantum dot gate voltage, respectively; and

electrically decoupling the Majorana island from the quantum dot.

20 . A computing system comprising:

a quantum computing device including:

a Majorana island at which a plurality of Majorana zero modes (MZMs) are instantiated;

a quantum dot electrically connectable to an MZM of the plurality of MZMs; and

a capacitance sensor capacitively coupled to the quantum dot; and

a controller configured to, for each of one or more candidate resonance regions corresponding to one or more candidate values of a change in a fermion number of the Majorana island:

set a Majorana island gate voltage of the Majorana island and a quantum dot gate voltage of the quantum dot to a candidate resonance Majorana island voltage and a candidate resonance quantum dot voltage of the candidate resonance region, respectively;

via the capacitance sensor, receive a capacitance measurement of the quantum dot and the Majorana island at the candidate resonance region; and

determine whether resonance occurs at the candidate resonance region based at least in part on the capacitance measurement; and

output the determination of whether resonance occurs at the candidate resonance region.