Optimality of T-gate for generating magic resource  

作　　者：Xiaohui Li Shunlong Luo 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Communications in Theoretical Physics》2023年第4期1-9,共9页理论物理通讯（英文版）

基　　金：supported by the National Key R&D Program of China,Grant No.2020YFA0712700;the National Natural Science Foundation of China,Grant No.11875317。

摘　　要：In the stabilizer formalism of fault-tolerant quantum computation,stabilizer states serve as classical objects,while magic states(non-stabilizer states)are a kind of quantum resource(called magic resource)for promoting stabilizer circuits to universal quantum computation.In this framework,the T-gate is widely used as a non-Clifford gate which generates magic resource from stabilizer states.A natural question arises as whether the T-gate is in some sense optimal for generating magic resource.We address this issue by employing an intuitive and computable quantifier of magic based on characteristic functions(Weyl transforms)of quantum states.We demonstrate that the qubit T-gate,as well as its qutrit extension,the qutrit T-gate,are indeed optimal for generating magic resource among the class of diagonal unitary operators.Moreover,up to Clifford equivalence,the T-gate is essentially the only gate having such an optimal property.This reveals some intrinsic optimal features of the T-gate.We further compare the T-gate with general unitary gates for generating magic resource.

关 键 词：stabilizer formalism Pauli group Clifford group quantifiers of magic T-GATE 

分 类 号：O413[理学—理论物理] TP38[理学—物理]