We consider a model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet (total spin $0$) or triplet (total spin $1$) state. The physical motivation is that we can do these measurements in a way that is protected against revealing other information so long as all terms in the Hamiltonian are $SU(2)$-invariant. We conjecture that this model is equivalent to BQP. Towards this goal, we show: (1) this model is capable of universal quantum computation with polylogarithmic overhead if it is supplemented by single qubit $X$ and $Z$ gates. (2) Without any additional gates, it is at least as powerful as the weak model of "permutational quantum computation" of Jordan [14, 18]. (3) With postselection, the model is equivalent to PostBQP.

中文翻译：

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对称保护量子计算

我们考虑使用量子位的量子计算模型，其中可以测量给定对是处于单重态（总自旋 $0$）还是三重态（总自旋 $1$）状态。物理动机是，只要哈密顿量中的所有项都是 $SU(2)$ 不变的，我们就可以以一种不会泄露其他信息的方式进行这些测量。我们推测这个模型等价于 BQP。为了实现这一目标，我们展示了：（1）如果该模型由单个量子位 $X$ 和 $Z$ 门补充，则该模型能够进行具有多对数开销的通用量子计算。(2) 没有任何额外的门，它至少和 Jordan [14, 18] 的“置换量子计算”弱模型一样强大。(3) 使用postselection，模型等价于PostBQP。