论文标题
单Qudit Clifford+$ t $运算符的正常形式
A Normal Form for Single-Qudit Clifford+$T$ Operators
论文作者
论文摘要
我们为单Qudit大门提出了一种正常形式，该盖茨由Clifford和$ t $ gates组成，用于Odd Prime Dimension $ p \ geq 5 $。我们证明，在多项式时间内，任何单一的Clifford+$ t $运算符都可以以这种正常形式重新表达。我们还提供了有力的数值证据，表明这种正常形式是独特的。假设唯一性，我们能够使用此正常形式来提供算法，以确切合成任何具有最小$ t $ count的单Qudit Clifford+$ t $运算符。
We propose a normal form for single-qudit gates composed of Clifford and $T$-gates for qudits of odd prime dimension $p\geq 5$. We prove that any single-qudit Clifford+$T$ operator can be re-expressed in this normal form in polynomial time. We also provide strong numerical evidence that this normal form is unique. Assuming uniqueness, we are able to use this normal form to provide an algorithm for exact synthesis of any single-qudit Clifford+$T$ operator with minimal $T$-count.
