Table 7 Phase parameters to simulate the time evolution of the vertical hopping \(h_{4}\), see Eq. (108d)
From: Superconducting circuit architecture for digital-analog quantum computing
Vertical Hopping | ||
|---|---|---|
Operator | \(\tilde{\varphi }^{(j)}_{1}\) | \(\tilde{\varphi }^{(j)}_{2}\) |
\(U_{(5,7)}^{{y,y}^{\dagger }}\) | \(\tilde{\varphi }^{(4),(7)}_{1}= \pi \) | \(\tilde{\varphi }^{(4),(7)}_{2}=\pi \) |
\(U_{6}^{x}\) | \(\tilde{\varphi }^{(6)}_{1}= 2\pi \) | \(\tilde{\varphi }^{(6)}_{2}=\pi \) |
\(\operatorname{exp} (-\frac{i\mathcal{A}}{2}\sigma _{5}^{x}\sigma _{6}^{y}\frac{t}{n} )\) | \(\tilde{\varphi }^{(5)}_{1}= 3/2\pi \) | \(\tilde{\varphi }^{(5)}_{2}=3/2\pi \) |
\(U_{6}^{x^{\dagger }}\) | \(\tilde{\varphi }^{(6)}_{1}= \pi \) | \(\tilde{\varphi }^{(6)}_{2}={2}\pi \) |
\(U_{(5,7)}^{y,y}\) | \(\tilde{\varphi }^{(4),(7)}_{1}={2} \pi \) | \(\tilde{\varphi }^{(4),(7)}_{2}={2}\pi \) |
\(U_{(5,7)}^{{x,x}^{\dagger }}\) | \(\tilde{\varphi }^{(4),(7)}_{1}=\pi \) | \(\tilde{\varphi }^{(4),(7)}_{2}=2\pi \) |
\(U_{6}^{y^{\dagger }}\) | \(\tilde{\varphi }^{(6)}_{1}=\pi \) | \(\tilde{\varphi }^{(6)}_{2}=\pi \) |
\(\operatorname{exp} (-\frac{i\mathcal{A}}{2}\sigma _{5}^{y}\sigma _{6}^{x}\frac{t}{n} )\) | \(\tilde{\varphi }^{(5)}_{1}=1/2\pi \) | \(\tilde{\varphi }^{(5)}_{2}=3/2\pi \) |
\(U_{6}^{y}\) | \(\tilde{\varphi }^{(6)}_{1}=2\pi \) | \(\tilde{\varphi }^{(6)}_{2}=2\pi \) |
\(U_{(5,7)}^{x,x}\) | \(\tilde{\varphi }^{(4),(7)}_{1}=2\pi \) | \(\tilde{\varphi }^{(4),(7)}_{2}=\pi \) |