Hamiltonian simulation of minimal holographic sparsified SYK model

• URL: http://arxiv.org/abs/2404.14784v2
• Date: Thu, 9 May 2024 10:29:33 GMT
• Title: Hamiltonian simulation of minimal holographic sparsified SYK model
• Authors: Raghav G. Jha,
• Abstract summary: Hamiltonian simulation of the sparsified SYK model with $N$ Majorana fermions and $q=4$ (quartic interactions) This complexity implies that with less than a hundred logical qubits and about $106$ gates, it will be possible to achieve an advantage in this model and simulate real-time dynamics up to scrambling time.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The circuit complexity for Hamiltonian simulation of the sparsified SYK model with $N$ Majorana fermions and $q=4$ (quartic interactions) which retains holographic features (referred to as `minimal holographic sparsified SYK') with $k\ll N^{3}/24$ (where $k$ is the total number of interaction terms times 1/$N$) using second-order Trotter method and Jordan-Wigner encoding is found to be $\widetilde{\mathcal{O}}(k^{p}N^{3/2} \log N (\mathcal{J}t)^{3/2}\varepsilon^{-1/2})$ where $t$ is the simulation time, $\varepsilon$ is the desired error in the implementation of the unitary $U = \exp(-iHt)$, $\mathcal{J}$ is the disorder strength, and $p < 1$. This complexity implies that with less than a hundred logical qubits and about $10^{6}$ gates, it will be possible to achieve an advantage in this model and simulate real-time dynamics up to scrambling time.

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