Qumode Tensor Networks for False Vacuum Decay in Quantum Field Theory

Abstract

False vacuum decay in scalar quantum field theory (QFT) is a cornerstone of early Universe cosmology and high energy physics, yet its real-time dynamics is essentially inaccessible to classical computation due to its non-perturbative, highly entangled dynamics. We introduce a general Hamiltonian framework for simulating full interacting QFTs, using a spatial lattice of continuos-variable ``qumodes''-- bosonic local oscillators whose high-dimensional local Hilbert space faithfully captures interacting field dynamics. This construction is rooted in continuous-variable quantum computing (CVQC), and provides a unified platform spanning efficient classical tensor-network methods and emerging photonic quantum hardware. The first key advance of this work is a robust and scaleable method for preparing the QFT in its correct initial vacuum state. We develop an imaginary-time preparation algorithm tailored to qumode lattices, that efficiently projects onto the vacuum even in strongly coupled regimes. This provides a controllable starting point for studying nonperturbative dynamics such as tunnelling and real-time decay. Building on this, we use a time-evolving block decimation algorithm to capture the real-time dynamics of the scalar field. Our second key advance is the identification and excitation of the negative fluctuation mode of the bounce configuration on the qumode lattice. A small displacement along this mode produces the expected tachyonic growth, driving fully coherent bubble nucleation without requiring classically supercritical seeds. This demonstrates that the qumode lattice captures non-perturbative quantum dynamics that lie beyond the classical treatments. Our results establish the qumode network as a scalable framework for non-equilibrium scalar QFT phenomena and pave the way for higher-dimensional studies and continuous-variable quantum computing implementations.