星型网络拓扑上N量子比特稳定子态的蒸馏
Distillation of N-Qubit Stabilizer States on a Star Network Topology
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中文总结 AI 辅助
提出一种基于任意稳定子码的纠缠蒸馏协议，在星型网络拓扑上高效地将N量子比特GHZ态转换为高保真逻辑态，并通过数值实验和理论证明其普适性。
中文摘要 AI 辅助
我们提出了一种纠缠蒸馏协议，该协议利用任意的$[[n,k,d]]$稳定子码，在泡利噪声存在的情况下，将$N$量子比特格林伯格-霍恩-泽林格（GHZ）态的$n$个原始副本转换为$k$个逻辑副本。我们在星型网络拓扑上对该方案的显式表述可高效扩展到任意$N$，仅需局域操作，并最小化空闲物理量子比特上误差的影响，从而能够在任意数量的量子处理器之间分发高保真度的纠缠逻辑态。我们报告了使用5量子比特码、环面码和$[[144,12,12]]$二元双循环码进行数值实验的结果，以抵御所有量子比特上独立的单量子比特去极化噪声。对于所有测试的码，在去极化率高达或超过$6\%$时，我们的编码方案相对于通过相同噪声信道发送的单个裸GHZ态，提高了最终GHZ态的保真度。此外，我们利用稳定子形式主义证明，我们的协议可应用于任意$N$量子比特的卡尔德班克-肖尔-斯蒂恩（CSS）稳定子态，GHZ态是其中的一个特例。这一结果明确确立了先前基于稳定子的贝尔对和GHZ态蒸馏方案的工作原理，并将此类协议推广到传统上考虑的状态之外。我们还表明，某些稳定子码可以用我们的协议蒸馏任意稳定子态。
英文摘要
We introduce an entanglement distillation protocol that utilizes an arbitrary $[[n,k,d]]$ stabilizer code to convert $n$ raw copies of an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state into $k$ logical copies in the presence of Pauli noise. Our explicit formulation of the scheme on a star network topology is efficiently scalable to arbitrary $N$, requires only local operations, and minimizes the impact of errors on idle physical qubits, enabling the distribution of high-fidelity entangled logical states between any number of quantum processors. We report the results of numerical experiments using the 5-qubit code, toric code, and $[[144,12,12]]$ bivariate bicyle code to protect against independent single-qubit depolarizing noise on all qubits. Our encoding scheme improves the final GHZ state fidelity relative to a single bare GHZ state sent over the same noisy channel for depolarizing rates up to or above $6 \%$ for all codes tested. Additionally, we use the stabilizer formalism to prove that our protocol can be applied to any $N$-qubit Calderbank-Shor-Steane (CSS) stabilizer state, from which the GHZ state emerges as a special case. This result explicitly establishes the working principle of previous stabilizer-based Bell pair and GHZ state distillation schemes, and generalizes such protocols beyond the traditionally considered states. We also show that some stabilizer codes can distill any stabilizer state with our protocol.
发表机构
- University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
- University of Maryland, College Park（马里兰大学帕克分校）
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