Collective Neutrino Oscillations on a Quantum Computer

In this study, we use the quantum Lanczos (QLanczos) algorithm to calculate the eigenvalues and eigenstates of a collective neutrino system as a function of the radial dependence of the coupling strength of neutrino interactions on IBM Q quantum hardware. To this end, we use neutrino interactions Hamiltonian expressed in terms of many-body Hamiltonian in [1] with limitation to two-flavor/mass states of neutrinos, exclusion of the anti-neutrino interactions, and neutrino background matter interactions. We demonstrate that the system Hamiltonian in mass basis can be separated into smaller blocks which can be represented using less number of qubits in a quantum circuit. This is an important result as this shows that a larger number of collective neutrino systems can be represented with less quantum resources. We also demonstrate the collective neutrino oscillations in flavor basis using a single-step Trotterization method on quantum hardware.
[1] A. V. Patwardhan, M. J. Cervia, and A. B. Balantekin, ``Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem", Phys. Rev. D 99, 123013 (2019).