  Quantum annealing is an emerging metaheuristic used for solving combinatorial
optimisation problems. However, hardware based physical quantum annealers are
primarily limited to a single vendor. As an alternative, we can discretise the
quantum annealing process (discretised quantum annealing or DiQA) and use it on
gate-model quantum computers. In this work, we first benchmark DiQA against
simulated annealing for a similar number of steps. We then propose and evaluate
a hybrid quantum classical heuristic: Quantum Accelerated Simulated Annealing
(QASA), where the traditional classical annealing procedure can be sped up with
the use of (relatively) low depth DiQA circuits. This is done by (i) running a
partial annealing scheme with a fraction of the depth of the complete circuit
(ii) sampling the results from the circuit and fitting a Gibbs distribution on
it and (iii) Using the inverse temperature of the Gibbs distribution and the
best sample to initialise simulated annealing (SA). Our simulation results show
QASA performing comparably to SA but for a reduced amount of steps. With the
promising results of our work, we hope to generate interest for potential
future work in the area of fixed-parameter quantum optimisation.
