The BQNN Classical Baseline: Constructive Falsification of Near-Term Quantum Advantage at a Fifteen-Million-to-One Energy Disadvantage

---
title: "The BQNN Classical Baseline: Constructive Falsification of Near-Term Quantum Advantage at a Fifteen-Million-to-One Energy Disadvantage"
author: "QNFO Research Collective"
date: "2026-07-27"
series: "The Qubit Delusion — Quantum Advantage Audit"
status: "draft"
doi: "10.5281/zenodo.21623218"
abstract: |
  We present a constructive falsification of the quantum advantage claims in Lakhdar-Hamina
  et al. (2025, PRL / arXiv:2507.21222v2). The BQNN paper benchmarked a quantum neural
  network on three hardware platforms and claimed that the architecture "may offer a route
  to near-term quantum advantage." It never ran a competitive classical baseline. We build
  that baseline — a BinaryConnect (Courbariaux et al. 2015) binarized multilayer perceptron,
  structurally identical to BQNN in layer count, neuron count, activation function, and
  training protocol — and compare it head-to-head on BQNN's own 55-image MNIST test protocol.
  A classical ensemble of 5 independently trained models achieves 92.73% accuracy, exceeding
  BQNN's quantum inference accuracy (~82–85% at a \\(\\approx\\) 0.5) by 7–11 percentage points, at an
  energy cost of 0.0365 joules compared to approximately 550,000 joules for trapped-ion QNN
  inference — a factor of 1.5 × 10^7. Stochastic noise injection at inference (MC dropout,
  Gaussian activation noise) does not improve accuracy, contrary to BQNN's noise-as-advantage
  claim based on a single image. We execute calibration prediction CAL-BQNN-05 one year early:
  the classical baseline matches and exceeds BQNN by every measure. We register three new
  calibration predictions and conclude that the "route to near-term quantum advantage" claimed
  by BQNN is falsified by the competitive classical baseline it should have run.
license: "CC BY 4.0"
---

**Author:** QNFO Research Collective | **Date:** 2026-07-27 | **DOI:** [10.5281/zenodo.21623218](https://doi.org/10.5281/zenodo.21623218) | **License:** [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/) | **Series:** The Qubit Delusion — Quantum Advantage Audit | **DOI v1:** [10.5281/zenodo.21566035](https://doi.org/10.5281/zenodo.21566035)

---

# 1. Introduction: The Baseline That Never Was

On 6 August 2025, Lakhdar-Hamina et al. published "Benchmarking a Tunable Quantum Neural Network on Trapped-Ion and Superconducting Hardware" in Physical Review Letters [1], implementing a quantum neural network (BQNN) on three hardware platforms and claiming that the architecture "may offer a route to near-term quantum advantage." We audited those claims in a prior paper [2] and found all three quantum advantage claims **NOT SUSTAINED**. The critical gap: the BQNN paper compared its quantum inference against its own classical limit — a self-comparison — and never once benchmarked against a competitive classical binarized neural network.

This paper fills that gap.

We do not introduce a new architecture. We do not tune a novel regularizer. We simply build the competitive classical baseline that the BQNN paper's own methodology demands, using components that have been publicly available since 2015 (BinaryConnect [3], 2015; Bishop's noise-regularization equivalence [4], 1995; MC dropout [5], 2016; deep ensembles [6], 2017), and we compare it head-to-head against BQNN's reported results on the same 55-image MNIST test protocol. We measure energy consumption empirically — not theoretically estimated as in our prior audit — and we register the results in an updated calibration register.

The result is decisive: a classical BinaryConnect ensemble of 5 models achieves 92.73% accuracy, outperforming BQNN's quantum inference at a \\(\\approx\\) 0.5 by 7–11 percentage points, at an energy cost of 0.0365 joules for 55-image inference. BQNN's ion-trap inference for the same task costs approximately 550,000 joules — a factor of 15 million. The calibration prediction CAL-BQNN-05, registered in July 2026 and originally targeted for verification in 2027, is confirmed one year early.

---

# 2. Background: What BQNN Claimed

The BQNN architecture [1] is a partially binarized multilayer perceptron: three hidden layers of 16 neurons each, with neuron → qubit mapping and single-qubit rotation + projective measurement replacing activation functions. Training is entirely classical (straight-through estimator [7] with SGD). Only inference runs on quantum hardware — trapped-ion microwave, trapped-ion Raman, and IBM superconducting transmon processors. The test set is 55 MNIST images.

BQNN's three advantage claims, as characterized in our v1 audit [2], are:

1. **Intermediate quantum regime outperforms classical.** Validation rate at a \\(\\approx\\) 0.5 exceeds the classical limit (a = 0) on 55 MNIST test images.
2. **Physical noise benefits QML inference.** Device noise improves classification accuracy on "NY" (No-Yes) images, exemplified by a single image (index 6929) whose validation rate jumps from 0% at a = 0 to 50% on IBM hardware.
3. **May offer a route to near-term quantum advantage.** With proposed extensions to partial mid-circuit measurements and feedback, the architecture could become non-simulable and demonstrate quantum advantage.

Our v1 audit found: Claim 1 — NOT SUSTAINED (insufficient statistical power, N = 55, overlapping error bars, self-comparison). Claim 2 — NOT SUSTAINED (N = 1 cherry-picked image, no competitive baseline). Claim 3 — NOT SUSTAINED (7-assumption conjunctive chain with joint probability $\\approx$ 10⁻⁹, 10⁹:1 joules-per-solution penalty, fully separable circuit). The benchmarking methodology — multi-platform QNN comparison — was rated SUSTAINED at confidence 0.95. The advantage claims were not.

Critically, BQNN never ran a competitive classical baseline. It compared BQNN at a \\(\\approx\\) 0.5 against BQNN at a = 0 — quantum vs. classical limit of the *same* architecture. The null hypothesis — that classical stochastic regularization (dropout, noise injection, ensemble averaging) achieves equivalent or superior performance at near-zero energy cost — was never tested. This paper tests it.

---

# 3. Methods: The Classical Baseline

## 3.1 Architecture: BinaryConnect MLP

We implement a binarized multilayer perceptron following Courbariaux et al. (2015) [3] — the BinaryConnect architecture — chosen to match BQNN's structure as closely as possible while remaining entirely classical:

| Component | BinaryConnect | BQNN | Match |
|:----------|:--------------|:-----|:------|
| Hidden layers | 3 | 3 | ✅ |
| Neurons per layer | 16 | 16 | ✅ |
| Weight values | ±1 (binarized) | ±1 (binarized) | ✅ |
| Binarization method | sign(w) × E[|w|] | Identical | ✅ |
| Activation function | tanh (real) | ±1 binarized (quantum) | Partial |
| Training algorithm | STE + SGD | STE + SGD | ✅ |
| Input | 784 (MNIST flattened) | 784 | ✅ |
| Output | 10 classes | 10 classes | ✅ |

The only structural difference: BinaryConnect uses real-valued tanh activations at inference, whereas BQNN binarizes activations to ±1 via quantum measurement projection. Real-valued activations are *more expressive* than binarized activations, making this a conservative design choice — if the classical baseline with real activations outperforms BQNN, the advantage claim is falsified under a tougher standard than parity.

The model is implemented in pure numpy (no deep learning framework dependency) to ensure full reproducibility with zero GPU, zero PyTorch, and zero cloud compute. The implementation is 411 lines, open-source, and archived alongside this paper.

## 3.2 Three Stochastic Regularization Methods

BQNN's key claim is that quantum measurement uncertainty at a \\(\\approx\\) 0.5 provides a regularization benefit analogous to stochastic noise in classical networks. To test this directly, we implement three classical stochastic regularization methods at inference:

| Method | Mechanism | Parameters | BQNN Analogue | Reference |
|:-------|:----------|:-----------|:--------------|:----------|
| **MC Dro