We provide a bucket of noisy intermediate-scale quantum era algorithms for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithms do not require any classical-quantum feedback loop, bypass the barren plateau problem and do not necessitate any complicated measurements such as the Hadamard test. To simplify and bolster our algorithms, we introduce the notion of the hybrid density matrix. The aforementioned concept enables us to disentangle the different steps of our algorithm and facilitate delegation of the classically demanding tasks to the quantum computer. Our algorithms proceed in three disjoint steps. The first step entails the selection of the Ansatz. The second step corresponds to the measuring overlap matrices on a quantum computer. The final step involves classical post-processing based on the data from the second step. Due to the absence of the quantum-classical feedback loop, the quantum part of our algorithms can be parallelized easily. Our algorithms have potential applications in solving the Navier-Stokes equation, plasma hydrodynamics, quantum Boltzmann training, quantum signal processing and linear systems, among many. The entire framework is compatible with the current experimental faculty and hence can be implemented immediately.
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