论文标题
计数T-Depth One的单位
Counting unitaries of T-depth one
论文作者
论文摘要
我们表明，$ n $ Qubits上的t-depth一个单位数为$ \ sum_ {m = 1}^{n} \ tfrac {1} {1} {m！} {m！} \ prod_ {k = 0}^{m-1} {m-1}（4^n/2^k-2^k） $ \＃\ MATHCAL {C} _n $是$ n $ Qubit Clifford组的大小，即T-Depth Zero的单位数量。 $ n $ Qubits上的T-Depth一个单位数的数量增长为$ 2^{ω（n^2）} \ cdot \＃\ Mathcal {C} _n $。
We show that the number of T-depth one unitaries on $n$ qubits is $ \sum_{m=1}^{n}\tfrac{1}{m!}\prod_{k=0}^{m-1}(4^n/2^k - 2^k) \times \# \mathcal{C}_n, $ where $\#\mathcal{C}_n$ is the size of the $n$-qubit Clifford group, that is the number of unitaries of T-depth zero. The number of T-depth one unitaries on $n$ qubits grows as $2^{Ω(n^2)} \cdot \# \mathcal{C}_n$.
