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A Flawed Falsification: Re-examining the Real-Number Quantum Theory Experiment

2025-09-17

Renou et al.'s 2021 Nature paper claimed that quantum theory based on real numbers can be experimentally falsified. This post argues otherwise. The paper proposed a test to distinguish between a full quantum gateset using complex numbers and a real-only subset. However, the author demonstrates that a real-only quantum computer, leveraging entanglement, can pass the test. The crucial, hidden assumption is that participating quantum computers begin without entanglement—a detail buried in the supplementary materials, severely undermining the experiment's validity.

Why Quantum Computers Haven't Factored 21 Yet (Despite Factoring 15 in 2001)

2025-08-31

In 2001, quantum computers factored 15. Now, in 2025, factoring 21 remains a challenge. This isn't due to a lack of progress, but rather a surprising complexity difference. Factoring 15 required 21 entangling gates, while factoring 21 needs a staggering 2405 – a 115x increase! This is because factoring 15 benefits from: 1. Most multiplications resulting in 1; 2. The first multiplication being cheap; 3. Modular multiplication simplifying to circular shifts. Factoring 21 lacks these advantages. Therefore, using number size alone to track quantum computing progress is misleading; focus should be on error correction and architectural advancements.