Abstracts
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Counterdiabaticity and the quantum approximate optimization algorithm
Presenting Author: Jonathan Wurtz, Tufts University
Contributing Author(s): Peter Love
The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut. QAOA can be made to mimic an adiabatic schedule, and in the $p\to\infty$ limit the final state is an exact maximal eigenstate in accordance with the adiabatic theorem. In this presentation I will make the connection between QAOA and adiabaticity explicit by inspecting the regime of $p$ large but finite. By connecting QAOA to counterdiabatic (CD) evolution, we construct CD-QAOA angles which mimic a counterdiabatic schedule by matching Trotter ``error" terms to approximate adiabatic gauge potentials which suppress diabatic excitations arising from finite ramp speed. In our construction, these ``error" terms are helpful, not detrimental, to QAOA, and QAOA is found to be always at least counterdiabatic, not just adiabatic. While applied specifically to QAOA, the talk will also discuss applications of counterdiabatic ideas to construct better ansatz for more general variational algorithms, such as the VQE for quantum chemistry.
Read this article online: https://arxiv.org/abs/2106.15645
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