AOA digitizes an asymptotic curve: A path sum approach

Presenting Author: Lucas Brady, National Institute of Standards and Technology, Maryland
Contributing Author(s): Aniruddha Bapat, Alexey Gorshkov

We numerically and analytically explore the behavior of the Quantum Approximate Optimization Algorithm (QAOA) as the number of steps p is increased. QAOA alternates between two operators, keeping one on for a variable time and then switching to the other for a different length of time, repeating this procedure for p steps with varying optimized timings. We develop a path sum approach to analyzing QAOA that provides analytic insight into the state dynamics under QAOA, and allows us to derive several results analytically. One such is that we find that the optimal timings form a curve that approaches an asymptotic form as p increases, allowing researchers to predict the optimal times for p+1 steps given the optimal angles for p steps. We additionally use our methods to analyze low p cases, reproducing important existing results. We present numerics that confirm the analytically suggested results, even for relatively low p, focusing on the transverse field Ising model but with similar results in other models.

(Session 5 : Sunday from 5:00pm - 7:00pm)


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