Measurement of fluid moments on quantum computer

Simulating non-linearity with a quantum computer is a longstanding goal, with significant efforts from both the computational plasma physics and the quantum computing communities. Within the Koopman–von Neumann (KvN) framework, some non-linear dynamics can be recast into Liouvillian phase-space evolution suitable to quantum simulation.The main challenge then shifts to measurement. In this work, we review and adapt quantum-measurement schemes that efficiently recover physical observables, focusing on statistical and fluid moments. Moreover, measurement is where effective non-linearity enters quantum theory, identifying the right quantities to observe is crucial. Access to fluid moments further opens the door to modeling dissipative systems, including the heat and Burgers equations. Simulating both the system and its environment enables a phase-space representation of the system. Extracting fluid moments then isolates the degrees of freedom of interest, yielding the dissipative evolution of the system alone. Such an approach encodes these equations directly, avoiding block-encoding methods.