Towards quantum computing Feynman diagrams in hybrid qubit-oscillator devices

TL;DR

This paper develops a novel framework connecting hybrid qubit-oscillator experiments with quantum field theory Feynman diagrams, enabling new methods for quantum state reconstruction and simulation.

Contribution

It introduces a Feynman diagram expansion for the characteristic function in hybrid qubit-oscillator systems, linking experimental measurements with quantum field theory techniques.

Findings

Feynman diagram expansion models the oscillator's characteristic function.

Maximum-likelihood estimation enables diagram measurement from Ramsey data.

Numerical simulations identify optimal regimes for diagram reconstruction.

Abstract

We show that recent experiments in hybrid qubit-oscillator devices that measure the phase-space characteristic function of the oscillator via the qubit can be seen through the lens of functional calculus and path integrals, drawing a clear analogy with the generating functional of a quantum field theory. This connection suggests an expansion of the characteristic function in terms of Feynman diagrams, exposing the role of the real-time bosonic propagator, and identifying the external source functions with certain time-dependent couplings that can be controlled experimentally. By applying maximum-likelihood techniques, we show that the ``measurement'' of these Feynman diagrams can be reformulated as a problem of multi-parameter point estimation that takes as input a set of Ramsey-type measurements of the qubit. By numerical simulations that consider leading imperfections in trapped-ion devices, we identify the optimal regimes in which Feynman diagrams could be reconstructed from measured data with low systematic and stochastic errors. We discuss how these ideas can be generalized to finite temperatures via the Schwinger-Keldysh formalism, contributing to a bottom-up approach to probe quantum simulators of lattice field theories by systematically increasing the qubit-oscillator number.