论文标题
CNOT电路几乎不需要帮助来实施他们生成的无任意Hadamard Clifford转换
CNOT circuits need little help to implement arbitrary Hadamard-free Clifford transformations they generate
论文作者
论文摘要
无hadamard的克利福德转换是由量子相（P），CZ和CNOT大门组成的电路。众所周知，这样的电路可以写入三阶段计算-p-cz-cnot-，每个阶段仅由指定类型的门组成。 在本文中，我们通过纠缠大门来关注电路深度的最小化，对应于重要的时间到解决方案度量以及由于腐烂而导致的噪声降低。我们考虑了两个流行的连接图：线性最近的邻居（LNN）和全能。首先，我们表明，可以在LNN上以5n $（即与-not-阶段相同的深度）进行LNN实施一个无哈达玛的Clifford操作。这使我们能够在LNN上实施任意的Clifford转换，深度不超过$ 7n { - } 4 $，从而提高了$ 9N $的最佳上一个上限。其次，我们报告启发式证据表明，平均而言，在$ n {>}上平均无限分布的无hadamard的无hadamard clifford转换6 $ Qubits可以在全面连接的体系结构上仅一个微小的添加剂开销，而与最著名的 - 单独使用-cnot阶段的实现相比，只有一个微小的添加剂开销。这表明Clifford电路的深度从$ 2n \，{+} \，O（\ log^2（n））$（\ log^2（n））$ 1.5n \，{+} \，o（\ log^2（n））$（\ log^2（n））$在无限制的体系结构上。
A Hadamard-free Clifford transformation is a circuit composed of quantum Phase (P), CZ, and CNOT gates. It is known that such a circuit can be written as a three-stage computation, -P-CZ-CNOT-, where each stage consists only of gates of the specified type. In this paper, we focus on the minimization of circuit depth by entangling gates, corresponding to the important time-to-solution metric and the reduction of noise due to decoherence. We consider two popular connectivity maps: Linear Nearest Neighbor (LNN) and all-to-all. First, we show that a Hadamard-free Clifford operation can be implemented over LNN in depth $5n$, i.e., in the same depth as the -CNOT- stage alone. This allows us to implement arbitrary Clifford transformation over LNN in depth no more than $7n{-}4$, improving the best previous upper bound of $9n$. Second, we report heuristic evidence that on average a random uniformly distributed Hadamard-free Clifford transformation over $n{>}6$ qubits can be implemented with only a tiny additive overhead over all-to-all connected architecture compared to the best-known depth-optimized implementation of the -CNOT- stage alone. This suggests the reduction of the depth of Clifford circuits from $2n\,{+}\,O(\log^2(n))$ to $1.5n\,{+}\,O(\log^2(n))$ over unrestricted architectures.
