Collective Neutrino Oscillations using the Stabilizer Tensor Network Formalism

Quantum computers provide a natural pathway for real-time simulations of a wide range of quantum systems, but are limited in the NISQ era by qubit decoherence and system noise. Thus, it is still important to develop classical and hybrid quantum-classical algorithms in the near-term. For 1D quantum systems, real-time evolution using Matrix Product States (MPS) has been very successful in simulating minimally entangled systems. To extend into more highly entangled systems, methods like Clifford dressing that perform transformations into less entangled bases are used. A recent method developed by Masot-Llima and Garcia-Saez, known as the Stabilizer Tensor Network (STN), parallelizes the simulation by using stabilizer tableaus for Clifford udpates and an MPS state for non-Clifford updates, allowing for majority of the entanglement to be stored in the basis, rather than the MPS. Thus, decreasing the required bond dimension. We use the STN to simulate highly entangled neutrino systems in the mass basis measuring mixng and oscillations for up to tens of neutrinos, comparing with traditional MPS methods like TEBD, TDVP, and Clifford dressing.