Measuring and manipulating states of non-abelian quasiparticles via quantum dot hybridization energy shifts

A quantum-dot-supported topological quantum device that is quasiparticle-poisoning-protected, wherein the quantum device comprises:

• a first superconducting island on which two or more first-island nanowires are located, the two or more first-island nanowires including a first first-island nanowire having a first end and a second end distal to the first end, and a second first-island nanowire having a first end and a second end distal to the first end;
• a second superconducting island on which two or more second-island nanowires are located, including a first second-island nanowire having a first end and a second end distal to the first end, and a second second-island nanowire having a first end and a second end distal to the first end;
• a first quantum dot having a first tunable quantum-tunneling coupling to the second end of the first first-island nanowire and a second tunable quantum-tunneling coupling to the first end of the first second-island nanowire;
• and
• a second quantum dot having a third tunable quantum-tunneling coupling to the second end of the second first-island nanowire and a fourth tunable quantum tunneling coupling to the first end of the second second-island nanowire.

A quantum-dot-supported topological quantum device that is quasiparticle-poisoning-protected, wherein the quantum device comprises:

• a first superconducting island on which one or more first-island nanowires are located, the one or more first-island nanowires including a first first-island nanowire having a first end and a second end distal to the first end;
• a second superconducting island on which two or more second-island nanowires are located, including a first second-island nanowire having a first end and a second end distal to the first end, and a second second-island nanowire having a first end and a second end distal to the first end;
• a first quantum dot having a first tunable quantum-tunneling coupling to the first end of the first first-island nanowire and a second tunable quantum-tunneling coupling to the first end of the second second-island nanowire;
• and
• a second quantum dot having a third tunable quantum-tunneling coupling to the second end of the first first-island nanowire and a fourth tunable quantum tunneling coupling to the second end of the first second-island nanowire.

A quantum-dot-supported topological quantum device that is quasiparticle-poisoning-protected, wherein the quantum device comprises:

• a first superconducting island on which two or more first-island Majorana zero modes are located;
• a second superconducting island on which two or more second-island Majorana zero modes are located;
• a first quantum dot comprising a first tunable quantum-tunneling coupling to any of the first-island Majorana zero modes and a second tunable quantum-tunneling coupling to any of the second-island Majorana zero modes;
• and
• a second quantum dot comprising a third tunable quantum-tunneling coupling to any of the first-island Majorana zero modes to which the first quantum dot is not also coupled and a fourth tunable quantum-tunneling coupling to any of the second-island Majorana zero modes to which the first quantum dot is not also coupled.

A method for operating a quantum device, comprising:

• measuring a collective topological charge of a plurality of non-Abelian quasiparticles using quantum dots;
• and
• using the measurement of the topological charge to implement the full set of Clifford gates in a quantum computer,
• wherein the non-Abelian quasiparticles are Majorana zero modes, and
• wherein the measuring comprises measuring a joint parity P of the Majorana zero modes using the quantum dots, the joint parity being the product of the topological charge of the plurality of the Majorana zero modes.

A method for operating a quantum system, comprising:

• altering gate voltages at a set of gates to create tunnel couplings between one or more quantum dots and two or more Majorana zero modes, the tunnel couplings altering energy levels of the one or more quantum dots, resulting in a hybridization of quantum states in the quantum system;
• measuring a hybridization energy of the quantum system;
• and
• determining a joint parity of the two or more Majorana zero modes based on the measured hybridization.

A quantum computer phase gate comprising a quantum-dot-supported quantum device that is quasiparticle-poisoning-protected, wherein the quantum device comprises one of:

• (a)
• a first superconducting island on which one or more first-island nanowires are located, the one or more first-island nanowires including a first first-island nanowire having a first end and a second end distal to the first end;
• a second superconducting island on which one or more second-island nanowires are located, the one or more second-island nanowires including a first second-island nanowire having a first end and a second end distal to the first end;
• a first quantum dot having a first tunable quantum-tunneling coupling to the first end of the first first-island nanowire and a second tunable quantum-tunneling coupling to the first end of the first second-island nanowire;
• and
• a second quantum dot having a third tunable quantum-tunneling coupling to the second end of the first first-island nanowire and a fourth tunable quantum-tunneling coupling to the second end of the first second-island nanowire;
• (b)
• a first superconducting island on which two or more first-island nanowires are located, the two or more first-island nanowires including a first first-island nanowire having a first end and a second end distal to the first end, and a second first-island nanowire having a first end and a second end distal to the first end;
• a second superconducting island on which two or more second-island nanowires are located, including a first second-island nanowire having a first end and a second end distal to the first end, and a second second-island nanowire having a first end and a second end distal to the first end;
• a first quantum dot having a first tunable quantum-tunneling coupling to the second end of the first first-island nanowire and a second tunable quantum-tunneling coupling to the first end of the first second-island nanowire;
• and
• a second quantum dot having a third tunable quantum-tunneling coupling to the second end of the second first-island nanowire and a fourth tunable quantum tunneling coupling to the first end of the second second-island nanowire;
• or
• (c)
• a first superconducting island on which one or more first-island nanowires are located, the one or more first-island nanowires including a first first-island nanowire having a first end and a second end distal to the first end;
• a second superconducting island on which two or more second-island nanowires are located, including a first second-island nanowire having a first end and a second end distal to the first end, and a second second-island nanowire having a first end and a second end distal to the first end;
• a first quantum dot having a first tunable quantum-tunneling coupling to the first end of the first first-island nanowire and a second tunable quantum-tunneling coupling to the first end of the second second-island nanowire;
• and
• a second quantum dot having a third tunable quantum-tunneling coupling to the second end of the first first-island nanowire and a fourth tunable quantum tunneling coupling to the second end of the first second-island nanowire.