Physical layouts of Majorana-based qubits for implementations of pentagonal tilings
Physical layouts of Majorana -based qubits for implementations of pentagonal tilings are described. An example quantum device comprises a set of tetrons for enabling Majorana -based qubits. The set of tetrons is arranged in a lattice to allow pentagonal tilings associated with the set of tetrons. The vertices of the pentagonal tilings relate to the qubits and single qubit operations, and the edges of the pentagonal tilings (connecting different vertices) relate to 2-qubit operations acting on a pair of qubits connected by a given edge. As an example, the 1-qubit Pauli measurements relate to the operations performed on the vertices associated with the pentagonal tilings and the 2-qubit measurements relate to the operations performed along the edges of the pentagonal tilings.
1 . A quantum device comprising:
a set of tetrons for enabling Majorana -based qubits, wherein the set of tetrons is arranged in a lattice of only tetron qubits to allow pentagonal tilings associated with the set of tetrons, wherein the lattice is configurable to allow performance of a sequence of measurements for implementing an error correcting code, wherein the error correcting code comprises a surface code, wherein the surface code is implemented by repeatedly performing a sequence of qubit measurements having a time period of six, wherein the quantum device comprises semiconductor regions, and wherein at least a subset of the qubit measurements includes use of a measurement loop comprising at least a portion of at least one of the semiconductor regions.
2 . The quantum device of claim 1 , wherein the lattice comprises a brick-walled pentagonal lattice.
3 . The quantum device of claim 1 , wherein the qubit measurements comprise 1-qubit and 2-qubit Pauli measurements.
4 . The quantum device of claim 3 , wherein the quantum device comprises coherent links, and wherein at least a subset of the qubit measurements includes use of a measurement loop including at least one of the coherent links.
5 . The quantum device of claim 1 , wherein the lattice is configurable to allow performance of a first step of the sequence of qubit measurements comprising two qubit measurements applied across the lattice.
6 . The quantum device of claim 5 , wherein the lattice is configurable to allow performance of a second step of the qubit measurements comprising a single qubit measurement applied across the lattice.
7 . The quantum device of claim 6 , wherein the lattice is configurable to allow performance of a third step of the sequence of qubit measurements comprising two qubit measurements applied across the lattice.
8 . The quantum device of claim 7 , wherein the lattice is configurable to allow performance of a fourth step of the sequence of qubit measurements comprising two qubit measurements applied across the lattice.
9 . The quantum device of claim 8 , wherein the lattice is configurable to allow performance of a fifth step of the qubit measurements comprising a single qubit measurement applied across the lattice.
10 . The quantum device of claim 9 , wherein the lattice is configurable to allow performance of a sixth step of the sequence of qubit measurements comprising two qubit measurements applied across the lattice.
11 . The quantum device of claim 1 , wherein each of the set of tetrons comprises a Majorana -based qubit built out of two topological wires connected by a superconducting backbone.
12 . A quantum device comprising:
a set of tetrons for enabling Majorana -based qubits, wherein the set of tetrons is arranged in a brick-walled pentagonal lattice to allow pentagonal tilings associated with the set of tetrons, wherein the quantum device is configurable to allow performance of a sequence of measurements for implementing an error correcting code, wherein the error correcting code comprises a surface code wherein the surface code is implemented by repeatedly performing a sequence of qubit measurements having a time period of six, wherein the quantum device comprises semiconductor regions, and wherein at least a subset of the qubit measurements includes use of a measurement loop comprising at least a portion of at least one of the semiconductor regions.
13 . The quantum device of claim 12 , wherein the qubit measurements comprise 1-qubit and 2-qubit Pauli measurements.
14 . The quantum device of claim 12 , wherein the quantum device comprises coherent links, and wherein at least a subset of the qubit measurements includes use of a measurement loop including at least one of the coherent links.
15 . The quantum device of claim 12 , wherein each of the set of tetrons comprises a Majorana -based qubit built out of two topological wires connected by a superconducting backbone.
16 . A method for operating a quantum device comprising a set of tetrons arranged in a lattice of only tetron qubits to allow pentagonal tilings associated with the set of tetrons, wherein the lattice is configurable to allow performance of a sequence of qubit measurements for implementing an error correcting code, wherein the error correcting code comprises a surface code, wherein the quantum device comprises semiconductor regions, the method comprising:
assigning code steps corresponding to the surface code to the pentagonal tilings associated with the set of tetrons; and
performing the assigned code steps for implementing the surface code by repeatedly performing a sequence of qubit measurements having a time period of six, wherein at least a subset of the qubit measurements includes use of a measurement loop comprising at least a portion of at least one of the semiconductor regions.
17 . The method of claim 16 , wherein the lattice comprises a brick-walled pentagonal lattice.
18 . The method of claim 16 , wherein the qubit measurements comprise 1-qubit and 2-qubit Pauli measurements.
19 . The method of claim 16 , wherein the quantum device comprises coherent links, and wherein at least a subset of the qubit measurements includes use of a measurement loop comprising at least one of the coherent links.
20 . The method of claim 16 , wherein each of the set of tetrons comprises a Majorana -based qubit built out of two topological wires connected by a superconducting backbone.