We demonstrate that the non-Hermitian quantum geometric tensor (QGT) governs nonlinear electrical responses in systems with a spectral line gap. The quantum metric, which is the symmetric component of the QGT and takes complex values in non-Hermitian systems, generates an intrinsic nonlinear conductivity independent of the scattering time. In contrast, the full complex-valued QGT induces a distinct conductivity that depends explicitly on the wave-packet width. Using one- and two-dimensional non-Hermitian models, we establish a direct link between nonlinear dynamics and the QGT, thereby connecting quantum state geometry to observable transport phenomena. Crucially, we reveal that the finite wave-packet width fundamentally alters non-Hermitian transport, a mechanism strictly absent in Hermitian systems. This framework elucidates non-Hermitian response theory by revealing how the complex geometry of quantum states, captured by the QGT, and the wave-packet width jointly encode transport in open and synthetic quantum matter.

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