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Table 9 Phase parameters required to simulate the time evolution of the vertical hopping \(h_{2}\) and \(h_{7}\), see Eq. (108b)

From: Superconducting circuit architecture for digital-analog quantum computing

Vertical Hopping
Operator \(\tilde{\varphi }^{(j)}_{1}\) \(\tilde{\varphi }^{(j)}_{2}\)
\(U_{(8,10)}^{{y,y}^{\dagger }}U_{(3,5)}^{{y,y}^{\dagger }}\) \(\tilde{\varphi }^{(2),(5),(7),(10)}_{1}= \pi \) \(\tilde{\varphi }^{(2),(5),(7),(10)}_{2}=\pi \)
\(U_{9}^{x}U_{4}^{x}\) \(\tilde{\varphi }^{(4),(9)}_{1}=2 \pi \) \(\tilde{\varphi }^{(4),(9)}_{2}=\pi \)
\(\operatorname{exp} (-\frac{i\mathcal{A}}{2}(\sigma _{3}^{x}\sigma _{4}^{y}+\sigma _{8}^{x}\sigma _{9}^{y})\frac{t}{n} )\) \(\tilde{\varphi }^{(3)}_{1}= 3/2\pi \)
\(\tilde{\varphi }^{(8)}_{1}= 1/2\pi \)
\(\tilde{\varphi }^{(3)}_{2}=3/2\pi \)
\(\tilde{\varphi }^{(8)}_{2}=3/2\pi \)
\(U_{4}^{x ^{\dagger }}U_{9}^{x^{\dagger }} \) \(\tilde{\varphi }^{(4),(9)}_{1}= \pi \) \(\tilde{\varphi }^{(4),(9)}_{2}=2\pi \)
\(U_{(3,5)}^{y,y}U_{(8,10)}^{y,y}\) \(\tilde{\varphi }^{(2),(5),(7),(10)}_{1}={2} \pi \) \(\tilde{\varphi }^{(2),(5),(7),(10)}_{2}={2}\pi \)
\(U_{(8,10)}^{{x,x}^{\dagger }}U_{(3,5)}^{{x,x}^{\dagger }}\) \(\tilde{\varphi }^{(2),(5),(7),(10)}_{1}=\pi \) \(\tilde{\varphi }^{(2),(5),(7),(10)}_{2}=2\pi \)
\(U_{9}^{y^{\dagger }}U_{4}^{y^{\dagger }}\) \(\tilde{\varphi }^{(4),(9)}_{1}=\pi \) \(\tilde{\varphi }^{(4),(9)}_{2}=\pi \)
\(\operatorname{exp} (-\frac{i\mathcal{A}}{2}(\sigma _{3}^{y}\sigma _{4}^{x}+\sigma _{8}^{y}\sigma _{9}^{x})\frac{t}{n} )\) \(\tilde{\varphi }^{(3)}_{1}=1/2\pi \)
\(\tilde{\varphi }^{(8)}_{1}=3/2\pi \)
\(\tilde{\varphi }^{(3)}_{2}=3/2\pi \)
\(\tilde{\varphi }^{(8)}_{2}=3/2\pi \)
\(U_{4}^{y}U_{9}^{y} \) \(\tilde{\varphi }^{(4),(9)}_{1}=2\pi \) \(\tilde{\varphi }^{(4),(9)}_{2}=2\pi \)
\(U_{(3,5)}^{x,x}U_{(8,10)}^{x,x}\) \(\tilde{\varphi }^{(2),(5),(7),(10)}_{1}=2\pi \) \(\tilde{\varphi }^{(2),(5),(7),(10)}_{2}=\pi \)