标题： 魔术态很少是优化最重要的资源 显示英文标题

标题： Magic states are rarely the most important resource to optimize

摘要： 我们提出了一种缩放方法，用于评估嵌套容错量子计算所需的量子比特资源。 该方法给出了闭式表达式，即使在多层嵌套的情况下也保持简单，使其成为比较和最小化不同嵌套方案资源成本的理想工具。 我们随后用它来研究正常操作和魔术操作所需的资源。 在这里，魔术操作需要准备、验证和注入称为“魔术态”的复杂状态，而正常操作则不需要。 通常预期魔术操作将主导计算的物理资源需求（量子比特、门等），尽管这一预期对于表面码来说已被质疑。 我们的结果表明，对于典型的嵌套码，这一预期也是错误的，魔术操作很少是昂贵的。 我们给出了使用Steane纠错装置或旗量子比特方法的嵌套7量子比特方案的具体例子。 虽然影响所有操作的优化自然比仅影响魔术操作的优化更有效，但我们工作的惊人结论是，前者可以将成本降低几个数量级，而后者仅带来微小的减少。 考虑到有许多关于仅影响魔术操作的优化工作，这一点尤其令人惊讶。 显示英文摘要

摘要： We propose a scaling approach to evaluating the qubit resources required by concatenated fault-tolerant quantum computing. The approach gives closed-form expressions, which remain simple for multiple levels of concatenation, making it an ideal tool to compare and minimize the resource costs of different concatenation schemes. We then use it to study the resources required for normal and magic operations. Here, magic operations require the preparation, verification and injection of complicated states called "magic states", while normal operations do not. It is often expected that magic operations will dominate a computation's physical resource requirements (qubits, gates, etc.), although this expectation has been cast in doubt for surface codes. Our results show that this expectation is also wrong for typical concatenated codes, with magic operations rarely being costly. We give concrete examples for the concatenated 7-qubit scheme with Steane error-correction gadgets or a flag-qubits approach. While optimizations that affect all operations are naturally more effective than ones that affect only magic operations, the surprising conclusion of our work is that the former can reduce costs by several orders of magnitude whereas the latter contributes only marginal reductions. This is particularly surprising given the numerous works on optimizations that affect only magic operations.