Physics Nature Is Weird

Quantum physics has a rule that works perfectly every time—as long as you have 26 particles or fewer. At 27, the whole thing falls apart.

March 27, 2026

Original Paper

The 27-qubit Counterexample to the LU-LC Conjecture is Minimal

Nathan Claudet

arXiv · 2603.25219

The Takeaway

Physicists long suspected that two different ways of mathematically describing quantum states were identical, until a strange exception was found at 27 qubits. This study proves that 27 is the exact 'tipping point' where quantum complexity breaks our standard models, showing that the rules of reality effectively change once you add that 27th particle.

From the abstract

It was once conjectured that two graph states are local unitary (LU) equivalent if and only if they are local Clifford (LC) equivalent. This so-called LU-LC conjecture was disproved in 2007, as a pair of 27-qubit graph states that are LU-equivalent, but not LC-equivalent, was discovered. We prove that this counterexample to the LU-LC conjecture is minimal. In other words, for graph states on up to 26 qubits, the notions of LU-equivalence and LC-equivalence coincide. This result is obtained by st