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Table 6 Phase parameters required to simulate the time evolution of the vertical hopping \(h_{5}\), see Eq. (108e)

From: Superconducting circuit architecture for digital-analog quantum computing

Vertical Hopping
Operator \(\tilde{\varphi }_{1}\) \(\tilde{\varphi }_{2}\)
\(U_{(6,8)}^{{y,y}^{\dagger }}\) \(\tilde{\varphi }^{5,8}_{1}= \pi \) \(\tilde{\varphi }^{5,8}_{2}=\pi \)
\(U_{7}^{x}\) \(\tilde{\varphi }^{7}_{1}= 2\pi \) \(\tilde{\varphi }^{7}_{2}=\pi \)
\(\operatorname{exp} (-\frac{i\mathcal{A}}{2}\sigma _{6}^{x}\sigma _{7}^{y}\frac{t}{n} )\) \(\tilde{\varphi }^{6}_{1}= 1/2\pi \) \(\tilde{\varphi }^{6}_{2}=3/2\pi \)
\(U_{7}^{x^{\dagger }}\) \(\tilde{\varphi }^{7}_{1}= \pi \) \(\tilde{\varphi }^{7}_{2}={2}\pi \)
\(U_{(6,8)}^{y,y}\) \(\tilde{\varphi }^{5,8}_{1}={2} \pi \) \(\tilde{\varphi }^{5,8}_{2}={2}\pi \)
\(U_{(6,8)}^{{x,x}^{\dagger }}\) \(\tilde{\varphi }^{5,8}_{1}=\pi \) \(\tilde{\varphi }^{5,8}_{2}=2\pi \)
\(U_{7}^{y^{\dagger }}\) \(\tilde{\varphi }^{7}_{1}=\pi \) \(\tilde{\varphi }^{7}_{2}=\pi \)
\(\operatorname{exp} (-\frac{i\mathcal{A}}{2}\sigma _{6}^{y}\sigma _{7}^{x}\frac{t}{n} )\) \(\tilde{\varphi }^{6}_{1}=3/2\pi \) \(\tilde{\varphi }^{6}_{2}=3/2\pi \)
\(U_{7}^{y}\) \(\tilde{\varphi }^{7}_{1}=2\pi \) \(\tilde{\varphi }^{7}_{2}=2\pi \)
\(U_{(6,8)}^{x,x}\) \(\tilde{\varphi }^{5,8}_{1}=2\pi \) \(\tilde{\varphi }^{5,8}_{2}=\pi \)