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Exact minimizer for the counterdiabatic gauge field in Q-CHOP

Determine the exact gauge field G that minimizes the Hilbert–Schmidt norm of O(G, H_obj^feas) for counterdiabatic driving within the feasible subspace of Q-CHOP’s single-body objective, rather than relying on a variational ansatz.

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Background

Appendix B develops a variational approach to approximate counterdiabatic driving for single-body objectives by proposing an ansatz for the gauge field. The authors explicitly state that an exact minimization is unclear, motivating the need for a precise solution.

Solving this would provide optimal counterdiabatic terms for Q-CHOP and potentially tighten performance guarantees.

References

It is unclear how to minimize the norm of O(G,H_objfeas) exactly, so we resort to minimizing it variationally with respect to the ansatz G_g = g_x S_xfeas + g_y S_yfeas + g_z S_zfeas, where S_αfeas = P_feas S_α P_feas, for which O(G_g, H_objfeas) = θ H_objfeas(θ) + i cos(θ) {G_g, H{obj,z}feas} + i sin(θ) {G_g, H_{obj,x}feas}.

— Q-CHOP: Quantum constrained Hamiltonian optimization (2403.05653 - Perlin et al., 8 Mar 2024) in Appendix B (Counterdiabatic driving for single-body objectives)