Qumode Tensor Networks for False Vacuum Decay in Quantum Field Theory

Abstract: False vacuum decay in scalar quantum field theory (QFT) plays a central role in cosmology and particle physics but has remained intractable for classical simulation due to its non-perturbative, highly entangled dynamics. We present a novel method for Hamiltonian simulation of false-vacuum decay in a self-interacting scalar QFT, based on a spatial discretisation into a lattice of bosonic modes. Each mode has a continuous or quasi-continuous local Hilbert space whose dimension is large enough to capture the self-interactions in the Hamiltonian. We refer to these local modes generically as ``qumodes'', echoing the ideal case in which the lattice would be realised on a continuous-variable quantum computer. Here we show that the same framework can be implemented on a tensor network, in which case the qumodes are quasi-continuous, corresponding to the local sites of the network having a very high dimensional Hilbert space. Using a time-evolving block decimation algorithm with Trotterised time evolution, we capture the real-time dynamics of the scalar field. In (1+1)-dimensions, we initialise a metastable vacuum and observe the coherent entanglement growth that seeds true-vacuum bubble nucleation. Our approach establishes the qumode network as a scalable framework for non-equilibrium scalar QFT phenomena and paves the way for higher-dimensional studies and continuous-variable quantum computing implementations.