Classical shadows with Pauli-invariant unitary ensembles

Understand

The classical shadow estimation protocol is a noise-resilient and sample-efficient quantum algorithm for learning the properties of quantum systems.

• Its performance depends on the choice of a unitary ensemble, which must be chosen by a user in advance.
• What is the weakest assumption that can be made on the chosen unitary ensemble that would still yield meaningful and interesting results? To address this question, we consider the class of Pauli-invariant unitary ensembles, i.e.
• unitary ensembles that are invariant under multiplication by a Pauli operator.