2019/06/21 by Mbeng, Glen Bigan, Fazio, Rosario, Santoro, Giuseppe · 5 citations
#FOS: Physical sciences #J.2 #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1906.08948
We establish and discuss a number of connections between a digitized version of Quantum Annealing (QA) with the Quantum Approximate Optimization Algorithm (QAOA) introduced by Farhi et al. (arXiv:1411.4028) as an alternative hybrid quantum-classical variational scheme for quantum-state preparation and optimization. We introduce a technique that allows to prove, for instance, a rigorous bound concerning the performance of QAOA for MaxCut on a 2-regular graph, equivalent to an unfrustrated antiferromagnetic Ising chain. The bound shows that the optimal variational error of a depth-P quantum circuit has to satisfy εresP≥ (2P+2)-1. In a separate work (Mbeng et al., arXiv:1911.12259) we have explicitly shown, exploiting a Jordan-Wigner transformation, that among the 2P degenerate variational minima which can be found for this problem, all strictly satisfying the equality εresP=(2P+2)-1, one can construct a special \em regular optimal solution, which is computationally optimal and does not require any prior knowledge about the spectral gap. We explicitly demonstrate here that such a schedule is adiabatic, in a digitized sense, and can therefore be interpreted as an optimized digitized-QA protocol. We also discuss and compare our bound on the residual energy to well-known results on the Kibble-Zurek mechanism behind a continuous-time QA. These findings help elucidating the intimate relation between digitized-QA, QAOA, and optimal Quantum Control.