Efficient Simulation of Multimode Bosonic Systems: A Tensor Network and Monte Carlo based method

Bosonic quantum error correction offers a promising route to hardware-efficient, fault-tolerant quantum computing by leveraging the extensive Hilbert spaces of harmonic oscillators for high redundancy. Predicting the performance of these codes under various conditions is crucial, yet the exponential scaling of Hilbert spaces with the number of modes makes full numerical simulations challenging or even infeasible. We study a simulation method combining tensor networks and Monte Carlo techniques to enable fast simulation of realistic multimode bosonic systems. We examine the validity of low entanglement approximations (reducing the bond dimension) across different quantum circuits and highlight the advantages of selecting an optimal computational basis for individual modes. Preliminary results demonstrating the efficacy of this approach are also presented.