Qumode Tensor Networks for False Vacuum Decay in Quantum Field Theory

TL;DR

This work develops a qumode-lattice Hamiltonian framework to simulate real-time, non-perturbative dynamics in scalar quantum field theories, enabling false-vacuum decay studies that are inaccessible to classical Euclidean methods. It combines imaginary-time TEBD initial-state preparation with a TEBD-driven qumode lattice for real-time evolution, and demonstrates the emergence of coherent bubble nucleation and phase transitions in (1+1)D, including seeding via the negative fluctuation mode. A central finding is that substantial entanglement (bond dimension) is required to capture bubble formation and growth, linking the decay rate to entanglement entropy scaling as expected from instanton physics. The approach unifies classical tensor-network techniques with continuous-variable quantum computing concepts, offering a scalable path to higher-dimensional QFT dynamics and non-renormalisable potentials on CV hardware or its classical emulation.

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.

Figures (18)

• Figure 1: Schematic overview of simulating quantum field theories with the qumode lattice. A (1+1)-dimensional quantum field theory, with field dynamics governed by a local potential $V(\phi)$, is discretised in space to form a lattice of qumodes, where each site encodes the field and its conjugate momentum as continuous quadratures $\hat{q}$ and $\hat{p}$, respectively. This qumode lattice can be simulated in two ways: directly on a continuous-variable quantum computer, as outlined in Ref. Abel:2025zxb; or emulated classically using a qumode TEBD tensor network, where time evolution is approximated by alternating layers of single- and two-mode gates.
• Figure 2: The polynomial potential of Eq. \ref{['eq:pot_poly']} with $\varphi_0=2$, $\lambda=0.5$, $\varepsilon=0.1$ and ${\mathscr{V}}_0=0.2$.
• Figure 3: Exact evolution of a single qumode under the potential in Fig. \ref{['fig:pot_poly']} (first panel) versus a Trotterised evolution (second panel) in which the local Hilbert space is discretised as 50-dimensional, while the Trotter time-step is $\delta t=0.05$. Thus, the evolution represents up to $1200$ Trotter steps, respectively, for the five plots.
• Figure 4: Initialising the false vacuum state with $\lambda =1$ and $\varepsilon = 0.1$: the solid line is the full potential, the dotted line is the SHO approximation around the false vacuum where we begin the qumode in the corresponding SHO groundstate, and the dashed line is the full potential plus lift potential, where here we have taken $\delta=4$. During the adiabatic preparation of the vacuum, the potential is gradually changed from the dotted SHO potential to the dashed potential. For imaginary-time TEBD preparation of the false vacuum, the potential is set as the dashed potential.
• Figure 5: The SHO groundstate versus the true ground state for the full potential, and the "false vacuum ground state". Both of these states were found by adiabatically evolving from the SHO ground state. As might have been anticipated from the shape of the full potential compared to the SHO potential, the "false vacuum ground state" is shifted to the right and broadened compared to the SHO ground state. The simulation has been run for $t=300$ with a $\delta t=0.01$.