Unitary circuits for strongly correlated fermions

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Its spin representation s j , k = J O t + 1 ​ ( S j , k ) s_{j,k}=J_{O^{t+1}}(S_{j,k}) is given by s j , k = | 0 , 0 ⟩ ⟨ 0 , 0 | + | 0 , 1 ⟩ ⟨ 1 , 0 | + | 1 , 0 ⟩ ⟨ 0 , 1 | − | 1 , 1 ⟩ ⟨ 1 , 1 | s_{j,k}=|0,0\rangle\langle 0,0|+|0,1\rangle\langle 1,0|+|1,0\rangle\langle 0,1|-|1,1\rangle\langle 1,1|

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