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

arXiv:2610.11071v1 Announce Type: new 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 $\phi^4$ 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 $\phi^4$ 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 $\phi^4$ theory. This regime enables scattering experiments between counter-propagating particle wave packets. The second parameter set yields a double-well potential that emulates $\phi^4$ 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.

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 $\phi^4$ 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 $\phi^4$ 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 $\phi^4$ theory. This regime enables scattering experiments between counter-propagating particle wave packets. The second parameter set yields a double-well potential that emulates $\phi^4$ 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.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); High Energy Physics - Lattice (hep-lat)

arXiv:2610.11071 [quant-ph]

(or arXiv:2610.11071v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.11071 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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

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