Simulations of the Neutrino Many-Body Problem Using Hybrid Algorithms

The evolution of collective neutrino flavor oscillations at high densities is a genuinely time-dependent quantum many-body problem. Solving this problem is computationally challenging because the dimension of the Hilbert space grows exponentially with the number of neutrinos. A common simplification is to work within the mean-field approximation, but this approach fails to capture the neutrino–neutrino correlations that arise from two-body interactions. This motivates the development of numerical methods that incorporate controlled approximations while still accessing beyond-mean-field effects. Tensor-network techniques offer a powerful framework in this direction. However, current tensor-network simulations can typically handle only a few tens of neutrinos. Quantum computers, in principle, provide an ideal platform for simulating such many-body dynamics, but today's devices remain error-prone. To bridge this gap, we must design hybrid quantum–classical algorithms that exploit the strengths of both platforms. In this talk, I will present how stabilizers, combined with tensor-network methods, can be used to compress the state space and extend simulations to larger neutrino numbers. Finally, I will discuss how these stabilizer-based tensor-network ideas naturally interface with quantum computing, offering a promising pathway toward scalable hybrid simulations of collective neutrino oscillations.