Logical qubit encoding surface

A method for use with a quantum computing device, the method comprising:

• at a measurement device:
• performing a measurement of a logical qubit encoded by a logical qubit encoding surface including a plurality of plaquettes, wherein:
• each plaquette of the plurality of plaquettes includes a plurality of measurement-based qubits;
• the plurality of measurement-based qubits includes four data qubits and a first ancilla qubit;
• and
• the first ancilla qubit is electrically connected, via separate corresponding electrical connections, to the four data qubits and a second ancilla qubit included in the logical qubit encoding surface;
• and
• measuring a respective stabilizer operator of each plaquette included in the logical qubit encoding surface;
• and
• at a classical computing device, identifying an error in the measurement of the logical qubit based on respective measurement results of the stabilizer operators.

A method for use with a quantum computing device, the method comprising:

• performing a surface code error correction at a logical qubit encoding surface including a plurality of measurement-based physical qubits, wherein:
• the plurality of measurement-based physical qubits includes four data qubits, a first ancilla qubit, and a second ancilla qubit;
• the first ancilla qubit is electrically connected, via separate corresponding electrical connections, to the four data qubits and the second ancilla qubit;
• performing the surface code error correction includes implementing one or more two-qubit logic gates;
• and
• implementing each two-qubit logic gate includes performing a plurality of measurements, wherein each measurement is a one-qubit measurement or a two-qubit measurement.