Calibration overhead for unknown noise in global orthogonal shadows

Determine whether an overhead comparable to the O( sqrt n) calibration cost established for related orthogonal-Haar-based fermionic protocols suffices to learn the relevant noise parameter for global orthogonal shadows on a Hilbert space of dimension 2^n.

Background

The paper assumes that the completely positive trace-preserving noise channel E is characterized in advance, so that the noisy shadow channel can be inverted deterministically. If E must instead be learned from experimental data, the residual estimation bias and the calibration sample complexity become additional issues.

The authors note that the directly relevant invariant for the real-basis global protocol is the scalar beta, while the order-three analysis is governed by the Brauer algebra. They compare this setting with a fermionic protocol whose noise-calibration overhead is O(sqrt n), and ask whether a comparable overhead can be achieved when the underlying orthogonal representation acts on a 2^n-dimensional Hilbert space.