论文标题
CZ，CNOT和Clifford电路的深度优化
Depth optimization of CZ, CNOT, and Clifford circuits
论文作者
论文摘要
我们寻求在量子CZ门，CNOT门和Clifford电路的深度上开发更好的上限保证。我们专注于Qubits $ n \，{\ leq} \，$ 1,345,000 [1]的数量，这代表了最实用的用例。我们对CZ电路深度的上限为$ \ lfloor n/2 + 0.4993 {\ cdot} \ log^2（n） + 3.0191 {\ cdot} \ log（n）-10.9139 \ rfloor $，通过大约构建的限制来改进最佳的interions interions intery intery intery interions intery interions intery tepen upper lught ofer of ground of ground of ground of the Inder lude lught of ground of the Inder lude lught ofer 2。 $ \ lfloor n + 1.9496 {\ cdot} \ log^2（n） + 3.5075 {\ cdot} \ log（n） - 23.4269 \ rfloor $ for cnot Gate Circuits，可改善大约4/3 $ bift the Art和depn + $ 4/3 $ $ $ $ $ $ $ $ y的$ 4/3 $。 2.9487 {\ cdot} \ log^2（n） + 8.4909 {\ cdot} \ log（n）-44.4798 \ rfloor $ for Clifford Circitits，提供了大约$ 5/3 $的一倍的改进。
We seek to develop better upper bound guarantees on the depth of quantum CZ gate, CNOT gate, and Clifford circuits than those reported previously. We focus on the number of qubits $n\,{\leq}\,$1,345,000 [1], which represents the most practical use case. Our upper bound on the depth of CZ circuits is $\lfloor n/2 + 0.4993{\cdot}\log^2(n) + 3.0191{\cdot}\log(n) - 10.9139\rfloor$, improving best known depth by a factor of roughly 2. We extend the constructions used to prove this upper bound to obtain depth upper bound of $\lfloor n + 1.9496{\cdot}\log^2(n) + 3.5075{\cdot}\log(n) - 23.4269 \rfloor$ for CNOT gate circuits, offering an improvement by a factor of roughly $4/3$ over state of the art, and depth upper bound of $\lfloor 2n + 2.9487{\cdot}\log^2(n) + 8.4909{\cdot}\log(n) - 44.4798\rfloor$ for Clifford circuits, offering an improvement by a factor of roughly $5/3$.
