  Recent investigations have demonstrated that multi-phonon scattering
processes substantially influence the thermal conductivity of materials, posing
significant computational challenges for classical simulations as the
complexity of phonon modes escalates. This study examines the potential of
quantum simulations to address these challenges, utilizing Noisy Intermediate
Scale Quantum era (NISQ) quantum computational capabilities and quantum error
mitigation techniques to optimize thermal conductivity calculations. Employing
the Variational Quantum Eigensolver (VQE) algorithm, we simulate phonon-phonon
contributions based on the Boltzmann Transport Equation (BTE). Our methodology
involves mapping multi-phonon scattering systems to fermionic spin operators,
necessitating the creation of a customized ansatz to balance circuit accuracy
and depth. We construct the system within Fock space using bosonic operators
and transform the Hamiltonian into the sum of Pauli operators suitable for
quantum computation. By addressing the impact of depolarization and non-unitary
noise effects, we benchmark the noise influence and implement error mitigation
strategies to develop a more efficient model for quantum simulations in the
NISQ era.
