Extended Data Table 1 Parameters used to prepare an approximate GKP eigenstate \(\left|{\psi }_{L}\right\rangle\) in equation (16) using the measurement free method from19. In the notation of the main text \(\left|-{Z}_{L}\right\rangle =\left|{1}_{L}\right\rangle\)
From: Error correction of a logical grid state qubit by dissipative pumping
Square code | Hexagonal code | |||||
|---|---|---|---|---|---|---|
Eigenstate | \(\left|-{X}_{L}\right\rangle\) | \(\left|-{Y}_{L}\right\rangle\) | \(\left|-{Z}_{L}\right\rangle\) | \(\left|-{X}_{L}\right\rangle\) | \(\left|-{Y}_{L}\right\rangle\) | \(\left|-{Z}_{L}\right\rangle\) |
θ | \(\frac{\pi }{2}\) | \(\frac{\pi }{4}\) | 0 | \(\frac{2\pi }{3}\) | \(\frac{\pi }{3}\) | 0 |
λ | 1 | \(\sqrt{2}\) | 1 | \(\sqrt{\frac{2}{\sqrt{3}}}\) | \(\sqrt{\frac{2}{\sqrt{3}}}\) | \(\sqrt{\frac{2}{\sqrt{3}}}\) |
