Kubica Aleksander, Demkowicz-Dobrzański Rafał
Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Phys Rev Lett. 2021 Apr 16;126(15):150503. doi: 10.1103/PhysRevLett.126.150503.
We present a simple proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code (QECC) with its ability to achieve a universal set of transversal logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols to characterize the QECC performance measured in terms of the worst-case entanglement fidelity. The theorem is applicable to a large class of decoherence models, including erasure and depolarizing noise. Our approach is unorthodox, as instead of following the established path of utilizing QECCs to mitigate noise in quantum metrological protocols, we apply methods of quantum metrology to explore the limitations of QECCs.
我们给出了近似伊斯特因 - 基尔定理的一个简单证明，该定理将量子纠错码（QECC）的质量与其实现通用横向逻辑门集的能力联系起来。我们的推导采用了通用量子计量协议中量子费希尔信息的强大界限，以根据最坏情况纠缠保真度来表征QECC的性能。该定理适用于一大类退相干模型，包括擦除噪声和去极化噪声。我们的方法是非传统的，因为我们不是遵循利用QECC来减轻量子计量协议中噪声的既定路径，而是应用量子计量方法来探索QECC的局限性。
