Quantum Topological Error Correction Codes: The Classical‐to‐quantum Isomorphism Perspective

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In this chapter, we explore the family of quantum topological error correction codes (QTECCs) by developing their foundations from those of classical lattice-based error correction codes. The classical construction of topological codes using square and triangular lattices is first introduced, showing their relationship with respect to low-density parity-check (LDPC) codes. We then analyze the impact of their parameters, such as their coding rate and minimum distance. This chapter also establishes how these lattice-based codes can be “quantumized” for creating stabilizer codes, including surface, toric, rotated-surface, and color codes, while highlighting their inherent fault-tolerance. The chapter also characterizes the QTECC performance attained under depolarization impairments.

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