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The ability to prepare desired quantum states with high precision is essential in developing contemporary quantum science and technology. To this end, various approximations based on the quantum adiabatic theorem are widely used. However, determining the optimal rate of adiabatic evolution for approaching desired target states is generally a challenging task, particularly in quantum many-body systems. In this talk, I will first explain how one can estimate the quantum fidelity of adiabatic evolution in quantum many-body systems using two more handily calculated quantities: generalized orthogonality catastrophe and quantum speed limit [1, 2]. The proposed approach allows us to establish stronger bounds on adiabatic fidelity than those previously obtained in the literature. I will then demonstrate how these new bounds can be applied to adiabatic quantum computing [3]. Notably, our method can provide lower bounds for the runtime of an example of adiabatic quantum algorithms with undetermined quantum speedups (where the traditional approach based on calculating spectral gaps is ineffective).

References:

[1] J.-H. Chen and V. Cheianov, Phys. Rev. Research 4, 043055 (2022).

[2] J.-H. Chen and V. Cheianov, arXiv: 2208.02620 [quant-ph].

[3] J.-H. Chen, Phys. Rev. Research 5, 033175 (2023)