Oral: Simulating Collective Neutrino Oscillations on a Quantum Computer

Neutrinos are fascinating, elusive particles that play crucial roles in astrophysical environments such as dense stars, and the early universe, where they dominate energy transport and entropy. As neutral fermions in the Standard Model, neutrinos interact only weakly and exist in three flavors: electron, muon, and tau neutrinos. The discovery of neutrino flavor oscillation—a quantum phenomenon—reveals that neutrinos possess tiny mass, likely less than 0.2 eV.

In dense environments, collective neutrino oscillations involving self-interactions emerge, complicating the numerics. However, these oscillations can be naturally simulated using quantum computers, by taking only two flavors as an isospin doublet leading to a spin model.

In this review, we discuss the hybrid quantum-classical Lanczos (QLanczos) algorithm, which is used to find the eigenvalues of the collective neutrino Hamiltonian. This method uses the quantum imaginary-time evolution (QITE) to simulate the non-unitary imaginary-time evolution (ITE) of a quantum system using only unitary operations. Unlike variational algorithms that rely on a fixed ansatz, ITE always converges to the ground state.

We also explore, as an altenative ITE, the probability ITE (PITE), in which an ancillary qubit is added to apply the ITE operator within an extended unitary. Once the ancilla is measured, the acted state collapses to the desired state. we also address the case with no mid-circuit measurements by employing quantum signal processing techniques.