发表机构
Department of Applied Physics, University of Geneva（日内瓦大学应用物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一族利用码加倍和量子比特回收的蒸馏协议，可在Clifford层次各级以固定逻辑量子比特数实现任意高距离，并发现如111到1的紧凑协议。
AI 中文摘要
为了规避在给定量子纠错码上无法实现通用门集的问题，可以通过魔法态注入来执行额外的门。然而，这需要获得高保真度的魔法态，而高保真度魔法态可以通过将低质量态蒸馏为少量更高质量态来获得。在本文中，我们提供了一族蒸馏协议，能够在Clifford层次的每一级产生对角态。该族通过使用码加倍技术并利用量子比特回收（即协议中一些空闲量子比特可以被测量并重新使用）递归地获得。在Clifford层次的给定级别上，我们证明了所推导的协议可以在固定数量的逻辑量子比特上以任意高的距离执行。该族恢复了许多已知的高效协议，并发现了新的协议，例如距离为7的|T>态蒸馏的111到1协议，这些协议在体积方面最为紧凑。最后，我们讨论了该框架在产生多个输出态的蒸馏协议中的可能扩展。
英文摘要
In order to circumvent that no universal set of gates can be achieved on a given quantum error-correcting codes, additional gates can be performed through magic state injection. This however requires to have access to high fidelity magic state, which can be obtained by the distillation of low quality states to fewer higher quality ones. In this paper, we provide a family of distillation protocols able to produce diagonal states at every level of the Clifford hierarchy. This family is obtained recursively using code doubling techniques and leveraging qubit recycling, the fact that some idle qubits of the protocols can be measured and re-used. At a given level of the Clifford hierarchy, we show that the protocols we derive can be performed at arbitrary high distance on a fix number of logical qubits. This family recovers many known efficient protocols, and uncovers new ones, such as a $111 \to 1$ protocol for $|T\rangle$ state distillation at distance $7$, which are the most compact in term of volume. Finally, we discuss possible extension of this framework for distillation protocols producing more than one output state.
Comments8+5 pages, 2 tables
