Identifying minimum-energy resonance region at Majorana island

A method for use with a computing system including a quantum computing device and a controller, wherein:

• the quantum computing device includes:
• a Majorana island at which a plurality of Majorana zero modes (MZMs) are instantiated;
• a quantum dot (QD) configured to be electrically connectable to the Majorana island via an MZM of the plurality of MZMs;
• an electrical ground;
• and
• a capacitance sensor;
• and
• the method comprises:
• at the quantum computing device, in each of a plurality of sampling iterations:
• electrically coupling the Majorana island to the electrical ground while a first plunger gate located proximate to the Majorana island is set to an idle voltage;
• disconnecting the Majorana island from the electrical ground;
• electrically coupling the Majorana island to the QD;
• via the capacitance sensor, scanning over a plurality of values of a first plunger gate voltage of a first plunger gate located proximate to the Majorana island and a second plunger gate voltage applied to a second plunger gate located proximate to the QD;
• and
• outputting, to the controller, respective quantum capacitance measurements obtained at the plurality of values of the first plunger gate voltage and the second plunger gate voltage;
• and
• at the controller:
• receiving the quantum capacitance measurements;
• based at least in part on the quantum capacitance measurements, determining a measured distribution of a respective plurality of resonance regions associated with the sampling iterations;
• based at least in part on the measured distribution, identifying a minimum-energy resonance region of the plurality of resonance regions that corresponds to a minimum energy value of the Majorana island;
• and
• outputting the minimum-energy resonance region identification.

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 (QD) configured to be electrically connectable to the Majorana island via an MZM of the plurality of MZMs;
• an electrical ground;
• and
• a capacitance sensor;
• and
• a controller configured to initialize a fermion number of the Majorana island at least in part by, in each of one or more initialization iterations performed until the controller determines that a current-iteration resonance region is a minimum-energy resonance region of the Majorana island:
• controlling the quantum computing device to:
• electrically couple the Majorana island to the electrical ground while a first plunger gate located proximate to the Majorana island is set to an idle voltage;
• disconnect the Majorana island from the electrical ground;
• and
• via the capacitance sensor, scan over a plurality of current-iteration values of a first plunger gate voltage applied to the first plunger gate and a second plunger gate voltage of a second plunger gate located proximate to the QD;
• and
• output, to the controller, respective quantum capacitance measurements obtained at the plurality of values of the first plunger gate voltage and the second plunger gate voltage;
• receiving the quantum capacitance measurements;
• based at least in part on the quantum capacitance measurements, identifying a current-iteration resonance region;
• and
• determining whether the current-iteration resonance region is the minimum-energy resonance region.