Abstract: Various systems and methods are presented regarding applying a non-Clifford logical CCZ gate in a 2D topological code, e.g., a 2D Abelian code. A Kirigami cut and fold process is applied to an initial 3D quantum error-correcting code composed of three copies of 3D surface codes to reduce (cut) a qubit lattice to a hollow cube such that the cube is formed of surfaces comprising qubits. The CCZ is applied to the hollow cube, with the cube subsequently flattened (folded) from the 3D arrangement to a 2D code arrangement. A lattice surgery process can be performed to map/transfer the 2D code arrangement to an ancilla Kirigami code(s), whereupon the 2D code arrangement can be returned to a 2D surface code for further application of a logical Clifford gate, if so desired.

Abstract: In this disclosure, example networks of coupled superconducting nanowires hosting MZMs are disclosed that can be used to realize a more powerful type of non-Abelian defect: a genon in an Ising×Ising topological state. The braiding of such genons provides the missing topological single-qubit ?/8 phase gate. Combined with joint fermion parity measurements of MZMs, these operations provide a way to realize universal TQC.

Abstract: In this disclosure, example networks of coupled superconducting nanowires hosting MZMs are disclosed that can be used to realize a more powerful type of non-Abelian defect: a genon in an Ising×Ising topological state. The braiding of such genons provides the missing topological single-qubit ?/8 phase gate. Combined with joint fermion parity measurements of MZMs, these operations provide a way to realize universal TQC.