论文标题
在Clifford+T中构建所有QUTRIT控制的Clifford+T Gates
Constructing all qutrit controlled Clifford+T gates in Clifford+T
论文作者
论文摘要
对于许多有用的量子电路，已经发现了QUDIT结构，这些构造降低了资源需求，而不是已知或最佳的量子构建。但是，这些结构中的许多必要的Qutrit大门从未以耐断层的方式明确有效地构建。我们展示了如何使用Clifford+T门且不使用Ancillae来确切和单位构建任何QUTRIT多控制的Clifford+T统一。这样做的T计数是在$ k $的$ k $中的多项式，将缩放为$ o（k^{3.585}）$。通过我们的结果，我们可以构建多控制T门的无acncilla clifford+t实现，以及Qutrit多控制的Toffoli的所有版本，而Qubits的类似结果是不可能的。作为结果的应用，我们提供了一个程序，以使用$ o（3^n n n^{3.585}）$ t gates来实现$ n $ trits上的任何三元经典可逆函数。
For a number of useful quantum circuits, qudit constructions have been found which reduce resource requirements compared to the best known or best possible qubit construction. However, many of the necessary qutrit gates in these constructions have never been explicitly and efficiently constructed in a fault-tolerant manner. We show how to exactly and unitarily construct any qutrit multiple-controlled Clifford+T unitary using just Clifford+T gates and without using ancillae. The T-count to do so is polynomial in the number of controls $k$, scaling as $O(k^{3.585})$. With our results we can construct ancilla-free Clifford+T implementations of multiple-controlled T gates as well as all versions of the qutrit multiple-controlled Toffoli, while the analogous results for qubits are impossible. As an application of our results, we provide a procedure to implement any ternary classical reversible function on $n$ trits as an ancilla-free qutrit unitary using $O(3^n n^{3.585})$ T gates.
