Exponential stabilizer-rank lower bound for T-state tensor powers

Prove the conjectured exponential lower bound for the stabilizer rank of tensor powers of the qubit T state, both for exact decompositions and at fixed approximation error, thereby closing the gap between the currently known nearly quadratic bounds and the conjectured exponential behavior.

Background

The introduction describes the longstanding stabilizer-rank problem for tensor powers of the qubit T state. It states that the best known lower bounds remain only nearly quadratic for both exact rank and fixed approximation error, while an exponential lower bound is conjectured. This unresolved stabilizer-rank problem is presented as a contrasting open challenge that is not solved by the Gaussian-rank results of the paper.

References

However, despite its evident importance and sustained efforts over the past decade, proving good lower bounds has remained notoriously difficult, with the best bounds for $T$-state tensor powers remaining only nearly quadratic both for exact rank and at fixed approximation error, leaving a substantial gap to the conjectured exponential lower bound.

— Robust exponential lower bounds for fermionic and bosonic Gaussian ranks  (2610.02172 - Wei et al., 1 Oct 2026) in Section Introduction