论文标题
使用冗余的Ancilla编码和标志Qubits非常低的高架耐魔法魔术状态准备
Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
论文作者
论文摘要
大规模量子算法执行通用耐断层量子计算的间接费用非常高。尽管尝试了几次替代方案,但魔术状态蒸馏仍然是以耐断层的方式模拟非克利福德大门的最有效方案之一。但是,由于魔术状态蒸馏电路不容易耐断层,因此所有Clifford操作都必须以较大的距离代码进行编码,以便具有可比的故障率,而魔术状态被蒸馏出来。在这项工作中,我们介绍了一个新概念,我们称之为多余的Ancilla编码。后者与标志量子台结合使用,可以使电路都测量某些代码的稳定器发生器,同时也能够测量全局运算符,以便使用最近的邻居相互作用来准备魔术状态。特别是,我们将这些方案应用于三角形颜色代码家族的平面体系结构。除了适合实验实现的计划外,我们还表明,对于$ 10^{ - 4} $的物理错误率,在完整的电路级噪声模型下,我们的方案可以使用较小的量子量和时空高架来产生魔术状态,而与最竞争性的魔术状态蒸馏方案相比。此外,我们可以利用电路的断层耐受性来产生魔术状态,其逻辑失败率使用编码的克利福德门,其噪声速率与注射的魔术状态相当。因此,稳定器操作不需要用非常大的距离代码编码。因此,我们认为我们的计划适合使用目前正在开发的硬件实施易于故障的通用量子计算。
The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high. Despite several attempts at alternative schemes, magic state distillation remains one of the most efficient schemes for simulating non-Clifford gates in a fault-tolerant way. However, since magic state distillation circuits are not fault-tolerant, all Clifford operations must be encoded in a large distance code in order to have comparable failure rates with the magic states being distilled. In this work, we introduce a new concept which 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. In particular, we apply such schemes to a planar architecture of the triangular color code family. In addition to our scheme being suitable for experimental implementations, we show that for physical error rates near $10^{-4}$ and under a full circuit-level noise model, our scheme can produce magic states using an order of magnitude fewer qubits and space-time overhead compared to the most competitive magic state distillation schemes. Further, we can take advantage of the fault-tolerance of our circuits to produce magic states with very low logical failure rates using encoded Clifford gates with noise rates comparable to the magic states being injected. Thus, stabilizer operations are not required to be encoded in a very large distance code. Consequently, we believe our scheme to be suitable for implementing fault-tolerant universal quantum computation with hardware currently under development.