Table 1 Gate decomposition of each term in our Hamiltonian evolution operator
From: Digital quantum simulation of gravitational optomechanics with IBM quantum computers
\(H_{0}\) | U | |
|---|---|---|
\(U_{\varepsilon}^{ (1 )}=e^{-i\tilde{\varepsilon}\sigma _{x}^{0}\sigma_{x}^{1}\sigma_{x}^{2}\sigma_{x}^{3}}\) | \(-\sigma _{z}^{0}\) | \(e^{i\frac{\pi}{4}\sigma_{x}^{0}} e^{i\frac{\pi}{4}\sigma_{z}^{0}\sigma_{x}^{1}}e^{i\frac{\pi }{4}\sigma_{z}^{0}\sigma_{x}^{2}}e^{i\frac{\pi}{4}\sigma _{z}^{0}\sigma_{x}^{3}}\) |
\(U_{\varepsilon}^{ (2 )}=e^{-i\tilde{\varepsilon}\sigma _{x}^{0}\sigma_{x}^{1}\sigma_{y}^{2}\sigma_{y}^{3}}\) | \(-\sigma _{z}^{0}\) | \(e^{i\frac{\pi}{4}\sigma_{x}^{0}} e^{i\frac{\pi}{4}\sigma_{z}^{0}\sigma_{x}^{1}}e^{i\frac{\pi }{4}\sigma_{z}^{0}\sigma_{x}^{2}}e^{i\frac{\pi}{4}\sigma _{z}^{0}\sigma_{x}^{3}}e^{i\frac{\pi}{4}\sigma_{z}^{2}}e^{i\frac {\pi}{4}\sigma_{z}^{3}}\) |
\(U_{\varepsilon}^{ (3 )}=e^{-i\tilde{\varepsilon}\sigma _{y}^{0}\sigma_{y}^{1}\sigma_{x}^{2}\sigma_{x}^{3}}\) | \(-\sigma _{z}^{0}\) | \(e^{i\frac{\pi}{4}\sigma_{x}^{0}} e^{i\frac{\pi}{4}\sigma_{z}^{0}\sigma_{x}^{1}}e^{i\frac{\pi }{4}\sigma_{z}^{0}\sigma_{x}^{2}}e^{i\frac{\pi}{4}\sigma _{z}^{0}\sigma_{x}^{3}}e^{i\frac{\pi}{4}\sigma_{z}^{0}}e^{i\frac {\pi}{4}\sigma_{z}^{1}}\) |
\(U_{\varepsilon}^{ (4 )}=e^{-i\tilde{\varepsilon}\sigma _{y}^{0}\sigma_{y}^{1}\sigma_{y}^{2}\sigma_{y}^{3}}\) | \(-\sigma _{z}^{0}\) | \(e^{i\frac{\pi}{4}\sigma_{x}^{0}} e^{i\frac{\pi}{4}\sigma_{z}^{0}\sigma_{x}^{1}}e^{i\frac{\pi }{4}\sigma_{z}^{0}\sigma_{x}^{2}}e^{i\frac{\pi}{4}\sigma _{z}^{0}\sigma_{x}^{3}}e^{i\frac{\pi}{4}\sigma_{z}^{0}}e^{i\frac {\pi}{4}\sigma_{z}^{1}}e^{i\frac{\pi}{4}\sigma_{z}^{2}}e^{i\frac {\pi}{4}\sigma_{z}^{3}}\) |