Description
Weak ergodicity breaking describes scenarios where a subpart of the Hilbert space does not thermalise under generic time evolution. In Hamiltonian systems, this corresponds to so-called quantum many-body scar states, which are eigenstates of the Hamiltonian but disobey the eigenstate thermalisation hypothesis. Here, we extend the concept to chaotic quantum circuits by implementing conditioned unitary gates and measurements with feedback. The unitary gates implement the projector-based Shiraishi-Mori construction that leaves the scarred-subspace invariant. Measurements and feedback are designed such that they preserve this subspace and, in addition, guide the dynamics towards the scarred subspace. We study the robustness of the scarred subspace by categorizing the evolution into the scars and their stability against external perturbations. To do so, we combine efficient numerical simulations of so-called conditioned Haar random gates and feedback with analytical arguments.
