Quantum simulations of one dimensional quantum systems

  title={Quantum simulations of one dimensional quantum systems},
  author={Rolando D. Somma},
  journal={Quantum Inf. Comput.},
  • R. Somma
  • Published 21 March 2015
  • Computer Science
  • Quantum Inf. Comput.
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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