Interferometric Quantum Polynomial Chaos Expansion as a Generative Model for Calorimeter Shower Simulation

arXiv (Cornell University)

Abstract

We present the quantum polynomial chaos expansion, a generative algorithm in which a single circuit is the entire model, and we use it to learn calorimeter images. In a classical chaos expansion the randomness is the input and the coefficients are fitted. Here the randomness is still the only input, entering the circuit as rotation angles and re-uploaded at every block, so that each measured observable is a chaos expansion of the latent variables whose order equals the circuit depth, and what is fitted are the gate angles themselves. Expressivity therefore grows with depth rather than with classical coefficients, correlations between outputs arise only from entangling gates, and a single latent wire read by all qubits carries the collective mode of the data. Nothing fitted stands between the circuit and the sample, so switching the entanglers off is a setting of the model itself and provably yields independent outputs, and attribution of the learned correlations to individual gates becomes a measurement. Choosing between two measurement bases shot by shot sharpens attribution into certification, and the trained model violates the Bell bound obeyed by every classical generative model with local response, whatever its size. We train the model on Geant4 shower data, execute the identical circuit on a superconducting processor with its accuracy loss predicted in advance, prove a no-go theorem for the tail dependence of every smooth generator read out through expectation values, and identify the circuit primitive that removes this limit.

Authors 6

1. J. Slim

   Deutsches Elektronen-Synchrotron DESY

   Affiliation as printed

   Deutsches Elektronen-Synchrotron DESY , 22603 Hamburg , Germany

2. Saverio Monaco Aachen

   Deutsches Elektronen-Synchrotron DESY · RWTH Aachen University

   Affiliation as printed

   Deutsches Elektronen-Synchrotron DESY , 22603 Hamburg , Germany

   RWTH Aachen University , 52062 Aachen , Germany

3. Florian Rehm

   European Organization for Nuclear Research

   Affiliation as printed

   European Organization for Nuclear Research (CERN) , 1211 Geneva , Switzerland

4. D. Kruecker
5. Frank Gaede

   Deutsches Elektronen-Synchrotron DESY

   Affiliation as printed

   Deutsches Elektronen-Synchrotron DESY , 22603 Hamburg , Germany

6. Kerstin Borras Aachen

   Deutsches Elektronen-Synchrotron DESY · RWTH Aachen University

   Affiliation as printed

   Deutsches Elektronen-Synchrotron DESY , 22603 Hamburg , Germany

   RWTH Aachen University , 52062 Aachen , Germany