State-adaptive quantum error correction and fault-tolerant quantum computing

Abstract: We present a theoretical framework for state-adaptive quantum error correction (SAQEC) that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we establish a new capacity regime governed by quantum mutual information rather than coherent information. This approach reveals a fundamental connection to entanglement-assisted protocols. We demonstrate practical applications in fault-tolerant quantum computation, showing how state-adaptivity enables enhanced error correction without additional measurement overhead. The framework provides new insights into quantum channel capacities while offering implementation advantages for current quantum computing platforms.