# Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization

@article{Babbush2019QuantumSO, title={Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization}, author={Ryan Babbush and Dominic W. Berry and Hartmut Neven}, journal={Physical Review A}, year={2019} }

We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with $N$ Majorana modes for time $t$ to precision $\epsilon$ with gate complexity $O(N^{7/2} t + N^{5/2} t \,{\rm polylog}(N/ \epsilon))$. In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in $1/\epsilon$ and large polynomial improvement in $N$ and $t$ over prior state-of-the-art algorithms which scale as $O(N^{10} t^2 / \epsilon)$. Our…

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