Quantum Annealing: a journey through Digitalization, Control, and hybrid Quantum Variational schemes

Understand

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-$\mathrm{P}$ quantum circuit has to satisfy $\epsilon^\mathrm{res}_{\mathrm{P}}\ge (2\mathrm{P}+2)^{-1}$.