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Quantum Physics
Title: Hamiltonian simulation of minimal holographic sparsified SYK model
(Submitted on 23 Apr 2024 (v1), last revised 9 May 2024 (this version, v2))
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.
Submission history
From: Raghav Govind Jha [view email][v1] Tue, 23 Apr 2024 06:49:34 GMT (86kb,D)
[v2] Thu, 9 May 2024 10:29:33 GMT (83kb,D)
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