Hamiltonian simulation of minimal holographic sparsified SYK model
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915140606099456 |
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| author | Jha, Raghav G. |
| author_facet | Jha, Raghav G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian simulation of minimal holographic sparsified SYK model Jha, Raghav G. Quantum Physics High Energy Physics - Lattice High Energy Physics - Theory 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. |
| title | Hamiltonian simulation of minimal holographic sparsified SYK model |
| topic | Quantum Physics High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.14784 |