Methods and devices for obtaining quantum cluster states with high fault tolerance

A method, comprising:

• obtaining a first set of multiple entangled qubits;
• obtaining a second set of multiple entangled qubits, the second set of multiple entangled qubits being mutually exclusive from the first set of multiple entangled qubits;
• and
• fusing (i) at least one qubit of the first set of multiple entangled qubits and (ii) at least one qubit of the second set of multiple entangled qubits, thereby obtaining a plurality of entangled qubits represented by a lattice structure, the lattice structure including a plurality of contiguous lattice cells, a respective edge of a respective lattice cell corresponding to one or more qubits of the plurality of entangled qubits, a respective face of the respective lattice cell corresponding to one or more qubits of the plurality of entangled qubits, each qubit of the one or more qubits that correspond to the respective face of the respective lattice cell being entangled with respective qubits that correspond to respective edges of the respective lattice cell that are adjacent to the respective face of the respective lattice cell, wherein:
• at least one of the following is satisfied:
• at least a first face of the respective lattice cell corresponds to two or more qubits of the plurality of entangled qubits, each qubit of the two or more qubits that correspond to the first face of the respective lattice cell being entangled with respective qubits that correspond to respective edges of the respective lattice cell that are adjacent to the first face of the respective lattice cell, and
• at least a first edge of the respective lattice cell corresponds to two or more qubits of the plurality of entangled qubits, each qubit of the two or more qubits that correspond to the first edge of the respective lattice cell being entangled with respective qubits that correspond to respective faces of the respective lattice cell that are adjacent to the first edge of the respective lattice cell.