# Quantum simulations of one dimensional quantum systems

@article{Somma2016QuantumSO, title={Quantum simulations of one dimensional quantum systems}, author={Rolando D. Somma}, journal={Quantum Inf. Comput.}, year={2016}, volume={16}, pages={1125-1168} }

We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the quantum harmonic oscillator (QHO) based on a refined analysis of the Trotter-Suzuki formula that exploits the Lie algebra structure. For total evolution time $t$ and precision $\epsilon>0$, the complexity of our method is $ O(\exp(\gamma \sqrt{\log(N/\epsilon…

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