Comparison of QAOA with Quantum and Simulated Annealing

Abstract

We present a comparison between the Quantum Approximate Optimization Algorithm (QAOA) and two widely studied competing methods, Quantum Annealing (QA) and Simulated Annealing (SA). To achieve this, we define a class of optimization problems with respect to their spectral properties which are exactly solvable with QAOA. In this class, we identify instances for which QA and SA have an exponentially small probability to find the solution. Consequently, our results define a first demarcation line between QAOA, Simulated Annealing and Quantum Annealing, and highlight the fundamental differences between an interference-based search heuristic such as QAOA and heuristics that are based on thermal and quantum fluctuations like SA and QA respectively.

Parameter Concentration in Quantum Approximate Optimization

“…Although adiabatic approaches can prepare an arbitrary state [36,37], the same can be addressed with a variational approach, e.g. variational quantum eigensolver (VQE) or QAOA, by tuning short quantum circuits [15,20,[38][39][40][41][42][43].…”

Quantum Optimization for Training Quantum Neural Networks

“…In Ref. [41] it is shown that QAOA is able to deterministically find the solution of specially constructed optimization problems in cases where quantum annealing fail. We emphasise that QAOA is an interference-based algorithm such that non-target states interfere destructively while the target states interfere constructively.…”

Training Saturation in Layerwise Quantum Approximate Optimisation

“…The optimization task is evidently challenging for deep circuits. Several approaches have been suggested to simplify optimization including leveraging parameter concentrations [18,23] and exploiting problem symmetries [22].…”

“…Optimization becomes increasingly challenging by considering more parameters, which increase linearly with depth. Various techniques have been developed to aid in optimization-leveraging problem symmetries [22], and parameter concentrations [18,23], which these same authors previously studied. Several heuristic strategies have been explored to speed-up this challenging outer loop optimization step.…”