Lindblad-Engineered Spectral Viscosity for Quantum Simulation of Dissipative Fluid Dynamics

Abstract Molecular viscosity in a classical fluid imposes the mode-selective energy-decay law γ_k = 2νk^2. Independent damping of physical qubits follows the binary occupation pattern of a mode register and generally produces a different spectrum. We construct a trace-preserving open-system primitive that transfers resolved Fourier-mode population to an auxiliary heat/sink state through mode-selective Lindblad jumps. Its finite-time Kraus map and Stinespring dilation realize the resolved-to-sink channel. A reduced ancilla-controlled circuit measures the associated mode conditioned retention probabilities for prepared basis modes. Analytical derivation establishes the channel and its balance law. Ideal simulations verify the numerical implementations of the derived map and the retention-probability estimator. Heat-equation and viscous-Burgers calculations place the substep inside classical spectral time integration. IBM-processor experiments assess small-circuit feasibility. Two Nk = 2 hardware runs preserve modal ordering, with relative decay-rate errors of 13.0–19.9% for k = 1 and 7.3–7.4% for k = 2. The Nk = 4 hardware circuit fails quantitative reproduction. Its mean k = 1 relative error is 145.5%, and mode-register flips are approximately 15%. This case is retained to characterize the onset and nature of the implementation failure. The results establish the calibrated channel while identifying the depth of the reduced controlled-rotation implementation as the present hardware bottleneck. Complete quantum computational fluid dynamics integration and quantum-advantage assessment remain future work.