Shadows of quantum machine learning

arXiv (Cornell University)

Abstract

An empirical test of whether the "flipped model" construction from Jerbi, Gyurik, Marshall, Molteni & Dunjko, "Shadows of quantum machine learning," Nat. Commun. 15, 5676 (2024) (arXiv:2306.00061) is viable as a quantum error correction (QEC) syndrome decoder. The source paper contains zero numerical experiments (its own Data Availability statement: "no datasets were generated or analyzed during the current study") and its only worked example is described by its own authors as "somewhat contrived." This release provides the first empirical test of the construction on a physically relevant task. Method: A flipped shadow model (f_θ(s) = Tr[ρ(θ)O(s)], k≤2 Pauli locality) was built as a distance-3 surface-code decoder, with shadowfiability verified by direct structural code inspection (per the paper's Lemma 4) rather than empirically. Result 1 (standalone): The flipped decoder's exact-analytic-readout logical error rate (12.3%) underperforms a trivial always-predict-zero baseline (10.9%) and is 6.8x worse than PyMatching (1.8%) on the tested patch. Result 2 (hybrid): Using the model's continuous soft output to reweight a PyMatching minimum-weight-perfect-matching graph, per-detector, found no operating point that both (a) moved enough predictions to test the hypothesis and (b) preserved the detector-error-model's calibrated weights — two failure regimes, no fair test in between, reported honestly as a valid but inconclusive negative rather than a claim that soft information does not help. Both results are pre-registered against three possible outcome branches declared before the experiment ran (see included mission specification README), reported as measured regardless of which branch occurred, and independently reproducible from the included code and seeded runs, with a V6 post-quantum signed attestation certificate (ECDSA-P256 + ML-DSA-65 + SLH-DSA-128s) covering the SHA-256 hashes of the three primary result files (see included README for exactly which). This is an independent, honest negative-results release — not a claim that classical shadow models are unsuitable for QEC in general, but a specific, narrow, measured finding about this construction on this task, at this scale.

Authors 5

1. Sofiène Jerbi

   Universität Innsbruck · Freie Universität Berlin

   Affiliation as printed

   Dahlem Center for Complex Quantum Systems , Freie Universität Berlin , Germany

   Institute for Theoretical Physics , University of Innsbruck , Austria

   Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Germany

   Institute for Theoretical Physics, University of Innsbruck, Austria

2. Casper Gyurik Aachen applied Quantum algorithms (aQa)

   Leiden University

   Affiliation as printed

   applied Quantum algorithms (aQa) , Leiden University , The Netherlands

   applied Quantum algorithms (aQa), Leiden University, The Netherlands

3. Simon C. Marshall Aachen applied Quantum algorithms (aQa)

   Leiden University

   Affiliation as printed

   applied Quantum algorithms (aQa) , Leiden University , The Netherlands

   applied Quantum algorithms (aQa), Leiden University, The Netherlands

4. Riccardo Molteni Aachen applied Quantum algorithms (aQa)

   Leiden University

   Affiliation as printed

   applied Quantum algorithms (aQa) , Leiden University , The Netherlands

   applied Quantum algorithms (aQa), Leiden University, The Netherlands

5. Vedran Dunjko Aachen applied Quantum algorithms (aQa)

   Leiden University

   Affiliation as printed

   applied Quantum algorithms (aQa) , Leiden University , The Netherlands

   applied Quantum algorithms (aQa), Leiden University, The Netherlands