Fig. 3: Digitized circuit, correlation function \({C}_{x}^{(i,j)}\) and circuit fidelity. | Nature Communications

Fig. 3: Digitized circuit, correlation function \({C}_{x}^{(i,j)}\) and circuit fidelity.

From: Digital simulation of zero-temperature spontaneous symmetry breaking in a superconducting lattice processor

Fig. 3

a Gate sequence for each block of the digitized circuit, describing how to encode the arbitrary parameters \({\phi }_{z,n}^{0}\) and φJ,n in the circuit to implement digitized CSB. Here we use the notation \({(\alpha )}_{\eta }={\hat{R}}_{\eta }(\alpha )={e}^{-i\alpha {\hat{\sigma }}_{\eta }/2}\). In (b), we show the experimental data of \({C}_{x}^{(i,j)}\) immediately after the nth block of a 5-block digitized circuit. The graphs are ordered from the state initialization (n = 0) to the final state (n = M = 5), respectively, showing the digitized evolution for the system initialized in (top) the ground state and (bottom) the highest excited state. c The behavior of the similarity with respect to the ideal digital process, obtained for each corresponding \({C}_{x}^{(i,j)}\) shown in (b). In (d), we present the profile of the range of \({C}_{x}^{3,k}={C}_{x}({r}_{3k})\) as a function of the Manhattan distance from the kth spin to spin 3, and the block step, for the ground and excited states.

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