Closed-form analytic expressions for shadow estimation with brickwork circuits

Understand

Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries.

• Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits.
• Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications.
• In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries.