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Table 2 Interactions between jth qubit and \((j+1)\)th qubit produced by different choice of the phases \(\tilde{\varphi }^{(j)}_{1}\) and \(\tilde{\varphi }^{(j)}_{1}\), where we take odd j and even j both into account

From: Superconducting circuit architecture for digital-analog quantum computing

Operator \(\tilde{\varphi }^{(j)}_{1}\) \(\tilde{\varphi }^{(j)}_{2}\)
\(\sigma ^{y}_{j} \sigma ^{y}_{j+1}\) 2π 2π
\(-\sigma ^{y}_{j} \sigma ^{y}_{j+1}\) π π
\(\sigma ^{x}_{j} \sigma ^{x}_{j+1}\) 2π π
\(-\sigma ^{x}_{j} \sigma ^{x}_{j+1}\) π 2π
\(\sigma ^{y}_{j} \sigma ^{x}_{j+1}\) \((1+(-1)^{j}/2)\pi \) 3/2π
\(-\sigma ^{y}_{j} \sigma ^{x}_{j+1}\) \((1+(-1)^{j+1}/2)\pi \) 1/2π
\(\sigma ^{x}_{j} \sigma ^{y}_{j+1}\) \((1+(-1)^{j+1}/2)\pi \) 3/2π
\(-\sigma ^{x}_{j} \sigma ^{y}_{j+1}\) \((1+(-1)^{j}/2)\pi \) 1/2π