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arXiv · 2610.11071

Analog quantum simulation of $ϕ^4$ field theory with a superconducting transmission line

Ilan T. Rosen·Neill C. Warrington·Max Hays·Christopher McNally·Joshua Lin·Stephen Sorokanich III·Julian Bender
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Abstract

Understanding the dynamics of interacting quantum fields remains a fundamental challenge. We propose a superconducting transmission line for analog quantum simulation of $(1+1)$-dimensional $ϕ^4$ field theory. The transmission line comprises fluxonium-like circuit elements whose continuous and unbounded phase variables encode a scalar field without Hilbert-space truncation. Their anharmonic potentials provide strong interactions. Tuning the circuit parameters provides access to two distinct regimes. In the first, the transmission line emulates $ϕ^4$ field theory with a single-well potential. We confirm this correspondence through lattice Monte Carlo calculations of the low-energy spectra of both the circuit and lattice $ϕ^4$ theory. This regime enables scattering experiments between counter-propagating particle wave packets. The second parameter set yields a double-well potential that emulates $ϕ^4$ theory in the symmetry-broken phase and hosts degenerate vacua. Interfaces between the two vacua form topological kinks, and the transmission line can simulate kink-antikink collisions. We present state preparation and measurement protocols for both collision experiments, enabling spatially resolved, real-time studies of particle and soliton scattering in an interacting quantum field theory.

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Ilan T. Rosen, Neill C. Warrington, Max Hays, Christopher McNally, Joshua Lin, Stephen Sorokanich III, Julian Bender. 2026-10-08. Analog quantum simulation of $ϕ^4$ field theory with a superconducting transmission line. https://arxiv.org/abs/2610.11071

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