Table 10 Phase parameters required to simulate the time evolution of the vertical hopping \(h_{1}\) and \(h_{6}\), see Eq. (108a)
From: Superconducting circuit architecture for digital-analog quantum computing
Vertical Hopping | ||
|---|---|---|
Operator | \(\tilde{\varphi }^{(j)}_{1}\) | \(\tilde{\varphi }^{(j)}_{2}\) |
\(U_{(7,9)}^{{y,y}^{\dagger }}U_{(2,4)}^{{y,y}^{\dagger }}\) | \(\tilde{\varphi }^{(1),(4),(6),(9)}_{1}= \pi \) | \(\tilde{\varphi }^{(1),(4),(6),(9)}_{2}=\pi \) |
\(U_{8}^{x}U_{3}^{x}\) | \(\tilde{\varphi }^{(3),(8)}_{1}= 2\pi \) | \(\tilde{\varphi }^{(3),(8)}_{2}=\pi \) |
\(\operatorname{exp} (-\frac{i\mathcal{A}}{2}(\sigma _{2}^{x}\sigma _{3}^{y}+\sigma _{7}^{x}\sigma _{8}^{y})\frac{t}{n} )\) | \(\tilde{\varphi }^{(2)}_{1}= 1/2\pi \) \(\tilde{\varphi }^{(7)}_{1}= 3/2\pi \) | \(\tilde{\varphi }^{(2)}_{2}=3/2\pi \) \(\tilde{\varphi }^{(7)}_{2}=3/2\pi \) |
\(U_{3}^{x^{\dagger }}U_{8}^{x^{\dagger }} \) | \(\tilde{\varphi }^{(3),(8)}_{1}= \pi \) | \(\tilde{\varphi }^{(3)}_{2}=2\pi \) |
\(U_{(2,4)}^{y,y}U_{(7,9)}^{y,y}\) | \(\tilde{\varphi }^{(1),(4),(6),(9)}_{1}={2} \pi \) | \(\tilde{\varphi }^{(1),(4),(6),(9)}_{2}={2}\pi \) |
\(U_{(7,9)}^{{x,x}^{\dagger }}U_{(2,4)}^{{x,x}^{\dagger }}\) | \(\tilde{\varphi }^{(1),(4),(6),(9)}_{1}=\pi \) | \(\tilde{\varphi }^{(1),(4),(6),(9)}_{2}=2\pi \) |
\(U_{8}^{y^{\dagger }}U_{3}^{y^{\dagger }}\) | \(\tilde{\varphi }^{(3),(8)}_{1}=\pi \) | \(\tilde{\varphi }^{(3),(8)}_{2}=\pi \) |
\(\operatorname{exp} (-\frac{i\mathcal{A}}{2}(\sigma _{2}^{y}\sigma _{3}^{x}+\sigma _{7}^{y}\sigma _{8}^{x})\frac{t}{n} )\) | \(\tilde{\varphi }^{(2)}_{1}=3/2\pi \) \(\tilde{\varphi }^{(7)}_{1}=1/2\pi \) | \(\tilde{\varphi }^{(2)}_{2}=3/2\pi \) \(\tilde{\varphi }^{(7)}_{2}=3/2\pi \) |
\(U_{3}^{y}U_{8}^{y}\) | \(\tilde{\varphi }^{(3),(8)}_{1}=2\pi \) | \(\tilde{\varphi }^{(3),(8)}_{2}=2\pi \) |
\(U_{(2,4)}^{x,x}U_{(7,9)}^{x,x} \) | \(\tilde{\varphi }^{(1),(4),(6),(9)}_{1}=2\pi \) | \(\tilde{\varphi }^{(1),(4),(6),(9)}_{2}=\pi \) |