2026-10-23 · arXiv Quantum Physics
arXiv:2610.31007v1 Announce Type: new
Abstract: We present an organizing framework for concatenated quantum error correction based on the observation that the syndrome projection of a stabilizer code reshapes the noise channel in a code-determined manner. For any stabilizer code, one level of QEC maps the physical noise to a block-diagonal logical channel whose diagonal Pauli weights are fixed by the code geometry. Coherences between different syndrome classes vanish, and no physical Pauli twirl is required to reach this block-diagonal form. Concatenation can then be viewed as the iteration of the same redistribution step: the dominant logical error after one level selects the code used at the next. We instantiate the framework with the two smallest stabilizer codes, the bit-flip and phase-flip codes, and apply it to amplitude damping. The redistribution rules give the concatenation protocol $C_2(\hat\sigma_y) C_1(\hat\sigma_x)$, whose ideal-recovery fidelity scales as $f_l=1-\mathcal O(\gamma^2)$. Solving the crossover condition $F_lF_{l-1}$ in the ideal-gate limit yields a critical damping parameter $\gamma_c\approx0.30$; in terms of the initial channel fidelity, $f=1-1.72755\gamma^2$. Under the same ideal-recovery assumption, we compare the overall gate accuracy rate with that of the five-qubit code. The scope of the framework, in particular for coherent and correlated noise, is stated explicitly.
原文链接：https://arxiv.org/abs/2610.31007
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