Patenting Quantum Computing Innovations – Part 3: Implementing a Logical Qubit in a Surface Code

By Sinan Utku

Example 2: Implementing a Logical Qubit in a Surface Code

Surface codes are a promising class of quantum error correction codes that will likely be used in fault-tolerant quantum computing. In a surface code, many physical data qubits collectively encode a logical qubit in a nonlocal, topologically protected manner, making it robust against physical errors. The qubits are arranged on a surface lattice, such as a plane, in which data qubits are interleaved with ancilla (measurement) qubits. These measurement qubits interact with neighboring data qubits to perform stabilizer measurements, extracting error syndromes without collapsing the encoded logical state. The syndromes reveal the presence and locations of errors, which can then be inferred and corrected using classical decoding algorithms. 

In particular, a quantum computer might carry out the following functionality to construct a logical qubit and maintain it without errors: 

• configure a plurality of data qubits on a two-dimensional lattice structure;
• interleave ancilla qubits with the data qubits, an configure the ancilla qubits to measure stabilizers of neighboring data qubits;
• periodically perform stabilizer measurements on the ancilla qubits to detect errors in the data qubits;
• determine error syndromes based on the stabilizer measurement results; and
• apply corrective operations to the data qubits based on the error syndromes.