面向容错量子计算的极低成本魔法态制备
Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing
- School of Physics, Peking University（北京大学物理学院）
- Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学前沿交叉学科研究院计算机学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出一种极低成本魔法态制备协议，通过协同设计稳定子生成元与标志小工具，在15量子比特码上制备逻辑态并规范固定为7量子比特码，以19个量子比特和82个CNOT门实现高保真度，显著降低容错量子计算开销。
AI中文摘要：
非克利福德资源态的容错制备是量子计算开销的主要来源，这促使人们设计以最少量子比特和电路成本实现高输出保真度的协议。我们提出了一种低成本魔法态制备协议，其中稳定子生成元的选择与标志小工具协同设计，使得综合征提取电路本身能够过滤非克利福德层中的相关故障。该协议在15量子比特量子里德-穆勒码中制备逻辑正号态，应用横向T门，并将同一寄存器规范固定为七量子比特斯坦恩码。通过将等价的Z型稳定子生成元重组为联合标记的测量组，该协议在破坏性错误检测下消除了所有由一或两个电路故障引起的可接受逻辑错误贡献。在均匀的电路级去极化噪声模型下，后选择不保真度为$210.2p^3+O(p^4)$。在$p=10^{-3}$时，精确的低阶枚举结合分层采样以99.9%的联合置信度将不保真度限制在$2.2\ imes10^{-7}$，同时保持86.9%的接受概率。完整电路仅需19个量子比特和82个CNOT门。这些结果表明，稳定子生成元设计可以大幅降低后选择魔法态制备的成本，尽管校正操作和未测量输出块的保真度需要单独分析。
英文摘要：
Fault-tolerant preparation of non-Clifford resource states is a major contributor to the overhead of quantum computation, motivating protocols that achieve high output fidelity with minimal qubit and circuit costs. We introduce a low-cost magic-state preparation protocol in which the choice of stabilizer generators is co-designed with the flag gadgets, allowing the syndrome-extraction circuit itself to filter correlated faults across a non-Clifford layer. The protocol prepares a logical plus state in the 15-qubit quantum Reed-Muller code, applies a transversal T gate, and gauge-fixes the same register into the seven-qubit Steane code. By reorganizing equivalent Z-type stabilizer generators into jointly flagged measurement groups, the protocol eliminates all accepted logical-error contributions arising from one or two circuit faults under destructive error detection. Under a uniform circuit-level depolarizing noise model, the postselected infidelity is $210.2p^3+O(p^4)$. At $p=10^{-3}$, exact low-order enumeration combined with stratified sampling bounds the infidelity by $2.2\times10^{-7}$ at 99.9% joint confidence, while retaining an acceptance probability of 86.9%. The complete circuit requires only 19 qubits and 82 CNOT gates. These results demonstrate that stabilizer-generator design can substantially reduce the cost of postselected magic-state preparation, although corrected operation and the fidelity of an unmeasured output block require separate analysis.
