Hamiltonian simulation of minimal holographic sparsified SYK model
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≪N3/24 (where k is the total number of interaction terms times 1/N) us...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325000252 |
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| Summary: | 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≪N3/24 (where k is the total number of interaction terms times 1/N) using the second-order Trotter method and Jordan-Wigner encoding is found to be O˜(kαN3/2logN(Jt)3/2ε−1/2) where t is the simulation time, ε is the desired error in the implementation of the unitary U=exp(−iHt) measured by the operator norm, J is the disorder strength, and constant α<1. This complexity implies that with less than a hundred logical qubits and about 106 gates, it might be possible to achieve an advantage in this model and simulate real-time dynamics. |
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| ISSN: | 0550-3213 |