Fig. 6: Transformation from \({b}_{1}^{{{{\dagger}}} }\left\vert {{{{{{{{\rm{M}}}}}}}}}_{1}\right\rangle\) to \({b}_{n}^{{{{\dagger}}} }\left\vert {{{{{{{{\rm{M}}}}}}}}}_{1}\right\rangle\) (a). | Nature Communications

Fig. 6: Transformation from \({b}_{1}^{{{{\dagger}}} }\left\vert {{{{{{{{\rm{M}}}}}}}}}_{1}\right\rangle\) to \({b}_{n}^{{{{\dagger}}} }\left\vert {{{{{{{{\rm{M}}}}}}}}}_{1}\right\rangle\) (a).

From: Effective light cone and digital quantum simulation of interacting bosons

Fig. 6

This process is equivalent to one hopping from left to right of all bosons (b), where the left-end two sites and the right-end two sites are merged into one site, respectively. Then, this process takes time of \({{{{{{{\mathcal{O}}}}}}}}(1)\) for arbitrarily long 1D chains.

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