Adiabatic preparation of excited states

Determine whether an adiabatic protocol with low noise sensitivity comparable to that of the ground-state preparation protocol can be devised for preparing arbitrary excited states of the tight-binding fermionic system.

Background

The paper demonstrates that adiabatic evolution can outperform the Fermionic Fourier Transform (FFT) for preparing low-energy ground states on noisy quantum hardware because local adiabatic circuits propagate errors less extensively. In contrast, the FFT can prepare arbitrary excited states directly by selecting different momentum modes. The authors explicitly leave unresolved whether a similarly noise-robust adiabatic construction exists for such excited-state targets.

References

This work leaves open a number of questions. For example, in this work we only discussed the use of the adiabatic evolution for preparing ground states. However, the FFT can also prepare arbitrary excited states, and it would be relevant to ask whether an adiabatic protocol with similar low noise sensitivity can be devised for these excited states.

— Less precise but less noisy: local circuits for momentum-space state preparation and measurement  (2610.01704 - Granet et al., 1 Oct 2026) in Section Discussion and outlook