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Abstract
The quantum approximate optimization algorithm (QAOA) is widely seen as a possible usage of noisy intermediate-scale quantum (NISQ) devices. We analyze the algorithm as a bang-bang protocol with fixed total time and a randomized greedy optimization scheme. We investigate the performance of bang-bang QAOA on MAX-2-SAT, finding the appearance of phase transitions with respect to the total time. As the total time increases, the optimal bang-bang protocol experiences a number of jumps and plateaus in performance, which match up with an increasing number of switches in the standard QAOA formulation. At large times, it becomes more difficult to find a globally optimal bang-bang protocol and performances suffer. We also investigate the effects of changing the initial conditions of the randomized optimization algorithm and see that better local optima can be found by using an adiabatic initialization.
Highlights
The use of quantum computation to solve problems deemed hard for classical computation is an area of massive interest in both the physics and computer science communities
We attribute this to be the minimal total time needed for protocols to start enacting nontrivial behavior, corresponding to SD1 converging on a p ≈ 2 and ≈ 3 protocol, respectively, when viewed as a standard quantum approximate optimization algorithm (QAOA) protocol
It is not clear the bang-bang QAOA should be used in practice with noisy intermediate-scale quantum (NISQ) devices
Summary
The use of quantum computation to solve problems deemed hard for classical computation is an area of massive interest in both the physics and computer science communities. Farhi et al [1] were able to show that as p → ∞, QAOA is able to achieve a perfect approximation ratio, since in that limit QAOA is as powerful as adiabatic quantum computation [3,4]. While we know that as p → ∞ that one can choose the QAOA parameters to correspond to a Trotterized adiabatic quantum computation and achieve a perfect approximation ratio [1], in the finite p regime it is not fully understood whether or not the optimal parameters for QAOA should appear adiabatic [7,8,9,10].
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