一句话：首次给出量子电路的极小且完备的等式理论，并证明任何完备等式理论都需作用于无界数量量子比特的规则。
本文引入首个针对量子电路的极小且完备的等式理论。作者证明量子电路上的任何真等式都可由简单规则推出，这些规则除一条新颖但直观的规则外均为标准规则：多控制 2π 旋转等价于恒等。相比近期完备等式理论，该工作去掉了若干规则，包括一条很不实用的规则。主要贡献之一是证明该等式理论的极小性，即任何规则都不能由其余规则推出。更一般地，作者表明：当所有门均为酉门时，任何量子电路完备等式理论都要求规则作用于无界数量的量子比特。最后，该工作还简化了带辅助量子比特和/或量子比特丢弃的完备等式理论。
We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one which states that a multi-control 2π rotation is nothing but the identity. Our work improves on the recent complete equational theories for quantum circuits, by getting rid of several rules including a fairly impractical one. One of our main contributions is to prove the minimality of the equational theory, i.e. none of the rules can be derived from the other ones. More generally, we demonstrate that any complete equational theory on quantum circuits (when all gates are unitary) requires rules acting on an unbounded number of qubits. Finally, we also simplify the complete equational theories for quantum circuits with ancillary qubits and/or qubit discarding.