Title: Engineering quantum Hatano Nelson model by periodic modulation of a dissipative circuit.

We investigate the generation of effective Lindblad structures arising from two-step Floquet modulation of dissipative qubit dynamics. Starting from a sequence of fully non-unital dissipators D[L_σ-] and D[L_σ+ ], each responsible for incoherent population transfer, we show that their periodic alternation produces an effective Lindbladian generator L_eff that acquires non-reciprocal components absent in either step. We present the exceptional contours of L_eff (γ, Ω) and characterize the strength of the emergent non-reciprocal dissipator. Combined with post-selection, this framework provides a unified approach for creating non-commuting anti-Hermitian Hamiltonians that correspond to standard gain-loss piece iγσ_z and Hatano–Nelson piece i∆Jσ_y in a single dissipative quantum circuit.