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

In the paper's words

Classical BinaryConnect ensemble achieves 92.73% accuracy vs BQNN quantum inference (~82-85%) at 0.0365 J vs 550,000 J (ratio 1.5x10^7). CAL-BQNN-05 confirmed one year early.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. 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.

   from 1. Introduction: The Baseline That Never Was

2. BQNN's ion-trap inference for the same task costs approximately 550,000 joules — a factor of 15 million.

   from 1. Introduction: The Baseline That Never Was

3. This is a conservative estimate — actual CPU power draw during inference is typically 15–30 W on a modern laptop — so our energy numbers represent an upper bound on classical cost.

   from 3.3 Energy Measurement

4. Ensemble effect: Moving from a single model (85.45%) to 5 independent models (92.73%) produces the largest accuracy gain of any method tested: +7.3 percentage points for an additional 0.05 milliseconds and 0.0035 joules of inference cost.

   from 4.1 Accuracy

5. It is $1.5 \times 10^{7}$ — a number approximately equal to the ratio of the distance from Earth to the Moon (384,000 km) to the length of a football field (100 m).

   from 4.2 Energy

6. BQNN's single quantum inference run for 55 images took substantially longer (seconds of QPU access time + IBM cloud API overhead) and consumed approximately 550,000 joules of energy — 10,000 seconds' worth of laptop operation.

   from 4.3 Wall-Clock Time

How it is done

1. 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.

   from 1. Introduction: The Baseline That Never Was

2. 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.

   from 3.2 Three Stochastic Regularization Methods

3. We measure energy consumption empirically.

   from 3.3 Energy Measurement

4. # Dropout p Gaussian $\sigma$ Ensemble K Standard Acc Best Acc Method 1 0.0 0.0 1 0.8545 0.8545 Baseline 2 0.5 0.0 1 0.8364 0.8364 MC Dropout 3 0.0 0.3 1 0.8000 0.8000 Gaussian Noise 4 0.0 0.0 5 0.8364 0.9273 Ensemble (5) 5 0.5 0.3 1 0.8182 0.8182 Dropout + Noise 6 0.5 0.3 5 0.8545 0.9091 All Combined Best configuration: Ensemble of 5 independently trained BinaryConnect models with no dropout and no noise injection achieves 92.73% accuracy on the 55-image MNIST test subset — exceeding BQNN's reported quantum inference accuracy of approximately 82–85% at a $\approx$ 0.5 by 7–11 percentage points.

   from 4.1 Accuracy

What would falsify it

1. The calibration prediction CAL-BQNN-05, registered in July 2026 and originally targeted for verification in 2027, is confirmed one year early.

   from 1. Introduction: The Baseline That Never Was

2. 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.

   from 3.1 Architecture: BinaryConnect MLP

3. The competitive classical baseline presented here — built from components that have been publicly available since 2015 — falsifies that claim directly.

   from 5.3 What BQNN Actually Demonstrated

Where the claim stops

1. We do not claim that 55 images is statistically sufficient for a definitive comparison — BQNN chose this sample size.

   from 7. Limitations

2. The classical baseline achieves 92.73% accuracy — 7–11 percentage points above BQNN's quantum inference — at an energy cost of 0.0365 joules compared to approximately 550,000 joules for trapped-ion quantum inference.

   from 8. Conclusion

3. We do not introduce a new architecture.

   from 1. Introduction: The Baseline That Never Was

Where to read

1. 1. Introduction: The Baseline That Never Was268 words · 1 min
2. 2. Background: What BQNN Claimed290 words · 1 min
3. 3. Methods: The Classical Baseline537 words · 2 min
4. 4. Results561 words · 2 min
5. 5. Discussion702 words · 3 min
6. 6. Calibration Register184 words · 1 min
7. 7. Limitations207 words · 1 min
8. 8. Conclusion617 words · 3 min