Information-Theoretic Framework for Quantum State Purification and Error Correction via Symmetric Subspace Projection

The severe susceptibility of qubits to environmental noise remains the primary obstacle to practical quantum computing. To overcome this, we introduce a purification-assisted quantum error-correction (QEC) framework that embeds a symmetric subspace projection module between the encoding and physical layers. Acting as an information-theoretic noise-entropy filter, it compresses von Neumann entropy before encoding. Under depolarizing noise, a three-copy scheme elevates the surface-code threshold from 1.1% to a 2.0% noiseless bound (~1.6% at circuit level). Our iterative purification-assisted error-correction (IPEC) algorithm dynamically modulates purification depth via syndrome feedback, delivering a 46-fold logical error reduction for surface codes (d = 7) at a 1.0% physical error rate.