Quantum simulation of scattering in the quantum Ising model

Abstract

We discuss real time evolution for the quantum Ising model in one spatial dimension with $N_s$ sites. In the limit where the nearest neighbor interactions $J$ in the spatial directions are small, there is a simple physical picture where qubit states can be interpreted as approximate particle occupations. Using exact diagonalization, for initial states with one or two particles, we show that for small $J$, discrete Bessel functions provide very accurate expressions for the evolution of the occupancies corresponding to initial states with one and two particles. Boundary conditions play an important role when the evolution time is long enough. We discuss a Trotter procedure to implement the evolution on existing quantum computers and discuss the error associated with the Trotter step size. We discuss the effects of gate and measurement errors on the evolution of one and two particle states using 4 and 8 qubits circuits approximately corresponding to existing or near term quantum computers.

13 pages, 12 figures

References in corpus (4)

• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State
• Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code