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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, Julian Bender

quant-phcond-mat.mes-hallhep-latSubmitted Oct 8, 2026• Announced Oct 9, 2026• 0 citations
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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.

Comments
16 pages, 13 figures

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Analog quantum simulation of φ4φ^4φ4 field theory with a superconducting transmission line
Understanding the dynamics of interacting quantum fields remains a fundamental challenge. We propose a superconducting transmission line for analog quantum simulation of (1+1)(1+1)(1+1)-dimensional φ4φ^4φ4 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 φ4φ^4φ4 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 φ4φ^4φ4 theory. This regime enables scattering experiments between counter-propagating particle wave packets. The second parameter set yields a double-well potential that emulates φ4φ^4φ4 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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Recently, quantum simulation of low-dimensional lattice gauge theories (LGTs) has attracted many interests, which may improve our understanding of strongly correlated quantum many-body systems. Here, we propose an implementation to approximate ℤ2 LGT on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. By using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gauss law of the ℤ2 LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the emergent Gauss law under the strong transverse field, the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.