Fault-tolerant quantum computing promises significant computational speedup over classical computing for a variety of important problems. One of the biggest challenges for realizing fault-tolerant quantum computing is preparing magic states with sufficiently low error rates. Magic state distillation is one of the most efficient schemes for preparing high-quality magic states. However, since magic state distillation circuits are not fault-tolerant, all the operations in the distillation circuits must be encoded in a large distance error-correcting code, resulting in a significant resource overhead. Here, we propose a fault-tolerant scheme for directly preparing high-quality magic states, which makes magic state distillation unnecessary. In particular, we introduce a concept that we call redundant ancilla encoding. The latter combined with flag qubits allows for circuits to both measure stabilizer generators of some code, while also being able to measure global operators to fault-tolerantly prepare magic states, all using nearest neighbor interactions. We apply such schemes to a planar architecture of the triangular color code family and demonstrate that our scheme requires at least an order of magnitude fewer qubits and space–time overhead compared to the most competitive magic state distillation schemes. Since our scheme requires only nearest-neighbor interactions in a planar architecture, it is suitable for various quantum computing platforms currently under development.

容错量子计算有望在各种重要问题上比传统计算显着提高计算速度。实现容错量子计算的最大挑战之一是准备具有足够低错误率的魔术状态。魔术状态蒸馏是制备高质量魔术状态的最有效方案之一。然而，由于魔术状态蒸馏电路不是容错的，所以蒸馏电路中的所有操作必须以大距离的纠错码进行编码，从而导致大量的资源开销。在这里，我们提出了一种直接准备高质量魔术状态的容错方案，这使得魔术状态蒸馏成为不必要。特别是，我们引入了一种称为冗余辅助编码的概念。后者与标志量子位相结合，使电路既可以测量某些代码的稳定器生成器，又可以测量全局算子以容错地准备魔术状态，所有这些操作都使用最近的邻居交互。我们将这种方案应用于三角色代码系列的平面体系结构，并证明与最有竞争力的魔术状态蒸馏方案相比，我们的方案至少需要少一个数量级的量子位和时空开销。由于我们的方案仅要求平面架构中的最近邻居交互，因此它适合当前正在开发的各种量子计算平台。全部使用最近邻居互动。我们将这种方案应用于三角色代码系列的平面体系结构，并证明与最有竞争力的魔术状态蒸馏方案相比，我们的方案至少需要少一个数量级的量子位和时空开销。由于我们的方案仅要求平面架构中的最近邻居交互，因此它适合当前正在开发的各种量子计算平台。全部使用最近邻居互动。我们将这种方案应用于三角色代码系列的平面体系结构，并证明与最有竞争力的魔术状态蒸馏方案相比，我们的方案至少需要少一个数量级的量子位和时空开销。由于我们的方案仅要求平面架构中的最近邻居交互，因此它适合当前正在开发的各种量子计算平台。