Towards quantum computing Feynman diagrams in hybrid qubit-oscillator devices

S. Varona; S. Saner; O. BÄzÄvan; G. Araneda; G. Aarts; A. Bermudez

doi:10.22331/q-2026-10-28-2252

Towards quantum computing Feynman diagrams in hybrid qubit-oscillator devices

S. Varona¹, S. Saner², O. BÄzÄvan², G. Araneda², G. Aarts³, and A. Bermudez¹

¹Instituto de Física Teorica, UAM-CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain.
²Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
³Department of Physics, Swansea University, Singleton Campus, SA2 8PP Swansea, United Kingdom

Published:	2026-10-28, volume 10, page 2252
Editor:	Yu Tong
Eprint:	arXiv:2411.05092v2
Doi:	https://doi.org/10.22331/q-2026-10-28-2252
Citation:	Quantum 10, 2252 (2026).

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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.

Popular summary

Feynman diagrams are one of the most iconic tools in modern physics: simple drawings that encode how quantum particles propagate and interact. But could we actually measure these diagrams in a quantum experiment, rather than only calculate them on paper?

In this work, we show how this could be done in a toy model that uses hybrid quantum systems, where a qubit acts as a probe of a quantum oscillator. Through a Ramsey-type experiment, information about the oscillator’s quantum dynamics is imprinted onto the qubit. From repeated measurements, individual contributions associated with Feynman diagrams can then be reconstructed using statistical inference.

Using realistic simulations of trapped-ion experiments, we study how accurately this can be achieved in the presence of experimental imperfections and finite temperature. The approach provides a first step towards using quantum computers not only to simulate quantum fields, but also to experimentally probe and benchmark their underlying dynamics through Feynman diagrams.

In a nutshell: it connects two of Feynman’s most influential ideas — Feynman diagrams and quantum computing — turning diagrams traditionally calculated with pen and paper into quantities that could be extracted from a quantum experiment

► BibTeX data

@article{Varona2026towardsquantum,
  doi = {10.22331/q-2026-10-28-2252},
  url = {https://doi.org/10.22331/q-2026-10-28-2252},
  title = {Towards quantum computing {F}eynman diagrams in hybrid qubit-oscillator devices},
  author = {Varona, S. and Saner, S. and B{\"{A}}z{\"{A}}van, O. and Araneda, G. and Aarts, G. and Bermudez, A.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2252},
  month = oct,
  year = {2026}
}

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[6] E. J. W. Koh, Rongjie Zhang, and Dzmitry Matsukevich, "Exponential-SWAP gate between bosonic motional modes of trapped ions", arXiv:2610.23208, (2026).

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