Decoding Quantum Field Theory with Machine Learning - Local Measurements with Neural Networks

Aug 3, 2026

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Machine learning techniques are proposed to extract information from local measurements in quantum field theory. The work shows how neural networks can efficiently process outcomes from local probes to infer both local and non-local features of the field. Using toy examples, it demonstrates that particle detectors can distinguish boundary conditions without signals propagating from them and can estimate the field’s temperature before thermalization. The method is framed as a general data-processing translation tool for broad local measurement scenarios.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages9

Reading Time23 min

AccessFree to download

Introduction

Local probes and the measurement information problem

Learning global features from local outcomes

A simple model

1+1 dimensional scalar field with a harmonic oscillator probe

Interaction Hamiltonian and coupling protocol

arXiv : 19 10 .03637v1 [ quant-ph] 8 Oct 2019 Machine learning quantum 􀀌eld theory with local probes Daniel Grimmer, 1, 2, 􀀃 Irene Melgarejo-Lermas, 1, 3, y and Eduardo Mart􀀓􀀐n-Mart􀀓􀀐nez 1, 3, 4, z 1 Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1, Canada 2 Dept. Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada 3 Dept. Applied Math. , University of Waterloo, Waterloo, ON, N2L 3G1, Canada 4 Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada We propose the use of machine learning techniques to address the problem of local measurements in quantum 􀀌eld theory. In particular we discuss how neural networks can e􀀎ciently process measurement outcomes from local probes to determine both local and non-local features of the quantum 􀀌eld. As toy examples we show: a) how a particle detector distinguishes boundary conditions imposed on the 􀀌eld without the need of signals propagating from them, and b) how detectors can determine the temperature of the quantum 􀀌eld without thermalizing with it. We discuss how the formalism proposed can be used for any kind of local measurement on a quantum 􀀌eld and, by extension, to local measurements of non-local features in many-body quantum systems. Introduction. -Our current understanding of the fundamental nature of matter comes from quantum 􀀌eld theory (QFT) . However, the process of obtaining experimental information from QFTs is arguably a di􀀎cult task to formalize. For example, projective measurements in QFT are incompatible with its relativistic nature: they cannot be localized [1], they can introduce ill-de􀀌ned operations [2] and enable superluminal signaling even in simple setups [3] . For these reasons, it has been strongly argued that projective measurements should be rejected in any relativistic 􀀌eld theory [3{5] . Nevertheless, from experiments at the LHC to the role of the retina in human sight, quantum 􀀌elds are subject to measurements where data is extracted through their interaction with localized probes. Such probes (e.g., atoms for the electromagnetic 􀀌eld) can be generally modeled by particle detectors [6] . Particle detectors allow us to perform indirect measurements on the 􀀌eld that are well-de􀀌ned [7] and physically meaningful [8] . Given the result of local measurements, how much information can one recover about the 􀀌eld? It is thinkable that with a su􀀎cient number of carefully chosen measurements on an array of probes coupling to the 􀀌eld long enough, one should be able to determine everything about the 􀀌eld, at least in principle. We say `in principle'because there is usually no direct translation between 1) the theoretical predictions of particle detectors in two different scenarios (usually transition probabilities [9{14]), and 2) the actual experimental data obtained when measuring a 􀀌eld locally in those scenarios. The probes we use to measure quantum 􀀌elds are usually simple in nature, and certainly much simpler and with smaller Hilbert spaces than the QFT itself. Because of this, translating measurement data (e.g., a large set of zeros and ones generated by measuring a two-dimensional particle detector) into concrete claims about the 􀀌eld seems, a priori, a very complicated task. 􀀃 y z [dgrimmer@uwaterloo.ca](dgrimmer@uwaterloo.ca)[i2melgar@uwaterloo.ca](i2melgar@uwaterloo.ca)[emartinmartinez@uwaterloo.ca](emartinmartinez@uwaterloo.ca) However we will see that one does not need complicated protocols to learn about global features of the 􀀌eld. As we will show, a simple measurement protocol on a single probe coupling for short times is enough. This is because a thermalized quantum 􀀌eld stores information about its global structure locally, albeit in a very scrambled way [15{20] . To extract and unscramble this information we propose the use of machine learning. In recent years, machine learning has proven e􀀋ective at processing data from quantum systems [21{29] . By

FAQs

Why are projective measurements in quantum field theory considered problematic?

Projective measurements conflict with relativistic requirements: they cannot be localized, can introduce ill-defined operations, and may enable superluminal signaling in simple setups.

How does the proposed approach recover global information from local probes?

A neural network learns a translation from probe measurement outcomes into features of the quantum field, enabling local probes to reveal global structure without needing complex experimental protocols.

What do the toy examples illustrate about detector capabilities?

One example shows detectors distinguishing boundary conditions without signals traveling between them, and another shows accurate inference of the quantum field’s KMS temperature before the probe thermalizes with the field.

Aug 3, 2026

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