Random superpositions of stabilizer states saturate SRE to Haar maximum in thermodynamic limit
The paper proves random superpositions saturate non-stabilizerness to its theoretical maximum, governed by a universal witness decomposition. This supplies a precise metric for when classical simulation becomes intractable. The work is theoretical with numerical validation but lacks experimental data from quantum hardware.
The authors apply Schur's lemma to derive a closed-form expression for the average witness <W(m)> that splits into a universal Haar floor plus an ensemble-specific excess. Numerical checks on random stabilizer states and Gaussian states confirm that as m grows the excess vanishes, producing logarithmic SRE growth before plateauing at the maximum. This directly quantifies when classical simulation hardness emerges from superpositions of classically tractable states.
The result reframes magic as a generic property of typical states rather than an engineered feature, tightening bounds on classical simulability for near-term devices. It also highlights a methodological gap: existing quantum processors have not yet been used to measure SRE scaling in controlled superpositions, leaving experimental verification open. Connecting to ongoing work on magic-state distillation suggests hardware demonstrations could test the predicted plateau within five years.
Limitations include the thermodynamic-limit assumption and restriction to ensembles obeying Schur's lemma; finite-size corrections and non-Schur ensembles remain uncharted. Strengthening evidence would require an experiment on a 20-plus qubit processor that prepares random m-superpositions and extracts SRE via randomized measurements.
IBM Quantum: Within 36 months a 50-qubit processor will measure SRE values within 5% of the predicted Haar plateau for m=8 stabilizer superpositions.
Sources (2)
- [1]Primary Source(https://arxiv.org/abs/2610.22476)
- [2]Supporting Source(https://arxiv.org/abs/2209.14316)