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 γk=2νk2. 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.