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![Arrangements of discs S, S(D), B and S ′ as described in Proposition 1.](publication/364518510/figure/fig1/AS:11431281091155478@1666325682531/Arrangements-of-discs-S-SD-B-and-S-as-described-in-Proposition-1.png)
Arrangements of discs S, S(D), B and S ′ as described in Proposition 1.
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We prove a nontrivial circuit-depth lower bound for preparing a low-energy state of a locally interacting quantum many-body system in two dimensions, assuming the circuit is geometrically local. For preparing any state which has an energy density of at most $\epsilon$ with respect to Kitaev's toric code Hamiltonian on a two dimensional lattice $\La...
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... 4. Let (P, Π, ρ Λ ) be a (δ,r,t)-triple. Let S be any disc of radius at most r − D and let B := S(t ′ ) for t ′ ≥ t + D (see Figure 3). Then for any σ Λ , such that σ B = ρ B , we have ...
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