2025/02/25 by Chen, Yiyuan, Helsen, Jonas, Ozols, Maris · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2502.18420
The Sachdev-Ye-Kitaev (SYK) model is a prominent model of strongly interacting fermions that serves as a toy model of quantum gravity and black hole physics. In this work, we study the Trotter error and gate complexity of the quantum simulation of the SYK model using Lie-Trotter-Suzuki formulas. Building on recent results by Chen and Brandao (arXiv:2111.05324), we derive bounds on the first- and higher-order Trotter error of the SYK model, and subsequently find near-optimal gate complexities for simulating these models using Lie-Trotter-Suzuki formulas. For the k-local SYK model on n Majorana fermions, our gate complexity estimates for the first-order Lie-Trotter-Suzuki formula scales with O(nk+(5)/(2)t2) for even k and O(nk+3t2) for odd k, and the gate complexity of simulations using higher-order formulas scales with O(nk+(1)/(2)t) for even k and O(nk+1t) for odd k. Given that the SYK model has Θ(nk) terms, these estimates are close to optimal. These gate complexities can be further improved when simulating the time-evolution of an arbitrary fixed input state |ψ⟩, leading to a O(n2)-reduction in gate complexity for first-order formulas and O(√(n))-reduction for higher-order formulas. We also apply our techniques to the sparse SYK model, a simplified variant of the SYK model obtained by deleting all but a Θ(n) fraction of the terms in a uniformly i.i.d. manner. We compute the average (over the random term removal) gate complexity for simulating this model using higher-order formulas to be O(n2 t), a bound that also holds for a general class of sparse Gaussian random Hamiltonians. Similar to the full SYK model, we obtain a O(√(n))-reduction simulating the time-evolution of an arbitrary fixed input state |ψ⟩.