论文标题
功能控制的量子电路不是门
Quantum Circuits for Functionally Controlled NOT Gates
论文作者
论文摘要
我们概括了Selinger和Jones提供的Toffoli Gate的量子电路，即功能控制的不是门，即由任意$ n $ n $可变的布尔函数控制的$ x $门。我们的构造目标是由Clifford门和单个量子旋转组成的门集。我们的构造使用布尔功能的Walsh-Hadamard频谱，并建立在Schuch和Siewert和Welch等人的作品的基础上。我们介绍目标量子置量位于任意状态以及目标处于已知状态的特殊情况的情况。此外，我们提出的结构不需要旋转深度为1的辅助矩形和构造。
We generalize quantum circuits for the Toffoli gate presented by Selinger and Jones for functionally controlled NOT gates, i.e., $X$ gates controlled by arbitrary $n$-variable Boolean functions. Our constructions target the gate set consisting of Clifford gates and single qubit rotations by arbitrary angles. Our constructions use the Walsh-Hadamard spectrum of Boolean functions and build on the work by Schuch and Siewert and Welch et al. We present quantum circuits for the case where the target qubit is in an arbitrary state as well as the special case where the target is in a known state. Additionally, we present constructions that require no auxiliary qubits and constructions that have a rotation depth of 1.
