论文标题
恒定深度耐故障的Clifford电路，用于多Qubit大型大块代码
Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes
论文作者
论文摘要
易于故障量子计算（FTQC）方案，使用大型块代码$ k> 1 $ QUBITS中的$ n $物理量子台上的物理Qubits可能会在很大程度上在很大程度上减少资源开销，因为它们的编码率很高。但是，很难找到和实现编码量子位的耐故障（FT）逻辑操作，这通常不仅要将很大的资源开销，还会带来长$ \ textit {intuti {In-Situ} $计算时间。在本文中，我们专注于calderbank-s-s-s-steane $ [\！[n，k，d] \！] $（CSS）代码及其逻辑FT Clifford电路。我们表明，可以通过Knill或Steane综合征测量电路在$ O（1）$ o（1）$ step \ emph {In-Situ}中实现任意逻辑Clifford电路的深度，并在合格的Ancilla状态下有效地准备了。特别是，对于满足$ k/n \simθ（1）$的这些代码，逻辑级别上克利福德电路的资源扩展可以与在物理级别上实现，直至常数，这与代码距离$ d $无关。使用适当的管道来生产Ancilla状态，我们的计划仅需要在非常大的FTQC的物理柜，物理门和计算时间中的资源成本适中。
Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode $k>1$ qubits in $n$ physical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the fault-tolerant (FT) logical operations for the encoded qubits are difficult to find and implement, which usually takes not only a very large resource overhead but also long $\textit{in-situ}$ computation time. In this paper, we focus on Calderbank-Shor-Steane $[\![ n,k,d ]\!]$ (CSS) codes and their logical FT Clifford circuits. We show that the depth of an arbitrary logical Clifford circuit can be implemented fault-tolerantly in $O(1)$ steps \emph{in-situ} via either Knill or Steane syndrome measurement circuit, with the qualified ancilla states efficiently prepared. Particularly, for those codes satisfying $k/n\sim Θ(1)$, the resource scaling for Clifford circuits implementation on the logical level can be the same as on the physical level up to a constant, which is independent of code distance $d$. With a suitable pipeline to produce ancilla states, our scheme requires only a modest resource cost in physical qubits, physical gates, and computation time for very large scale FTQC.
