Hamiltonian simulation of minimal holographic sparsified SYK model

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 $\tilde{\mathcal{O}}(k^p{N}^{3/2}\log N(\mathcal{J}t{)}^{3/2}{\epsilon }^{-1/2})$ where $t$ is the simulation time, $\epsilon$ 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.

v3: Matches the one accepted for publication in Nuclear Physics B. v2: Gate costs for up to 125 qubit-Hamiltonian i.e., N=250. Added few references, refined text. v1: Comments welcome

References in corpus (1)

• Sachdev-Ye-Kitaev model on a noisy quantum computer

Cited by in corpus (4)

• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Sparsity dependence of Krylov state complexity in the SYK model
• Two-local modifications of SYK model with quantum chaos
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors