Quantum Monte Carlo Simulations of Tunneling in Quantum Adiabatic Optimization

Understand

We explore to what extent path-integral quantum Monte Carlo methods can efficiently simulate the tunneling behavior of quantum adiabatic optimization algorithms.

• Specifically we look at symmetric cost functions defined over n bits with a single potential barrier that a successful optimization algorithm will have to tunnel through.
• The height and width of this barrier depend on n, and by tuning these dependencies, we can make the optimization algorithm succeed or fail in polynomial time.
• In this article we compare the strength of quantum adiabatic tunneling with that of path-integral quantum Monte Carlo methods.