Title:            A sparse model of quantum holography 

Abstract:     We use a probabilistic pruning procedure to define new sparse quantum  Hamiltonians  from  all-to-all  connected  Hamiltonians.   By  suitably adjusting the pruning probability, we obtain a model where the number of interaction terms scales like kN where N is the number of degrees of freedom and k is a parameter.  Applied to the Sachdev-Ye-Kitaev (SYK) model, we obtain a sparse SYK (s-SYK) model which in the large N limit admits a 1/k expansion  with  the  fully  connected  solution  as  the  leading term.  Applying the procedure to a supersymmetric version of SYK yields a model in which the fully connected saddle point is dominant down to the lowest temperatures.  Hence, we exhibit a sparse quantum Hamiltonian which has a sector dual to a supersymmetric gravity theory.  The sparsity gives  additional technical  benefits: classical and  quantum simulation of the model is easier, at least for certain physical properties. In particular, the best previous algorithm for quantum simulation of SYK had complexity cost per unit time proportional to N^7/2; the  analogous cost in the sparse model is of order N^2.