A feed-Forward Method for Encoding a Stabilizer Code Using Measurement-Based Quantum Computing

We present an approach for encoding an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$[[n,\ k]]$</tex> stabilizer code within the measurement-based quantum computing (MBQC) framework. Our proposed method leverages projective measurements of stabilizer generators, inspired by a stabilizer encoding methodology within gate-based quantum computation [1]. To achieve the encoding of a general stabilizer code, we introduce a suite of gadgets tailored for stabilizer projective measurements utilizing a three-dimensional regular cluster state. The sequential nature of the proposed method offers a new perspective and ensures simplicity, flexibility, and intuitive visualization for stabilizer code encoding using MBQC.