System-size scaling of the high-magic trajectory weight

Determine how the weight of near-Haar-magic trajectories in the optimized quantum-jump unraveling scales with the number of qubits, and thereby establish whether the associated reduction in stabilizer-simulation cost persists for larger systems.

Background

The optimized unraveling reduces the frequency of trajectories carrying near-Haar magic, but the average simulation cost remains controlled by these high-magic trajectories because stabilizer-expansion costs grow exponentially with magic.

The attainable computational gain is bounded by the inverse weight of the near-Haar portion of the trajectory distribution. The paper leaves unresolved whether this weight decreases, remains finite, or behaves otherwise as the system size increases.

References

Whether it persists for larger systems depends on how this weight scales with $n$, which we leave for future work.

— Magic in quantum trajectory unravelings of noisy random quantum circuits  (2610.22318 - Santos et al., 15 Oct 2026) in Section Distribution of magic over trajectories

Several questions remain open. First, it is unclear how the broad distribution of magic affects the estimation of physical observables.

— Magic in quantum trajectory unravelings of noisy random quantum circuits  (2610.22318 - Santos et al., 15 Oct 2026) in Section Discussion and Conclusions, first paragraph beginning “Several questions remain open”

Whether more general unravelings, such as nonminimal ones, can reduce the magic of its trajectories remains to be seen.

— Magic in quantum trajectory unravelings of noisy random quantum circuits  (2610.22318 - Santos et al., 15 Oct 2026) in Section Discussion and Conclusions, third paragraph beginning “Several questions remain open”

How the two resources depend jointly on the unraveling, and which unraveling is best for methods sensitive to both, remains to be understood.

— Magic in quantum trajectory unravelings of noisy random quantum circuits  (2610.22318 - Santos et al., 15 Oct 2026) in Section Discussion and Conclusions, final paragraph