Simulation of virtual bilayer systems from open and monitored quantum dynamics

We propose a method to simulate a large class of bilayer Hamiltonians by means of open and monitored dynamics of monolayer systems. The method builds on the standard mapping of density matrices onto pure states of a doubled system. We show that, by suitable engineering of the jump operators and postselection on no-click trajectories for certain jumps, it is possible to emulate low-energy states of any bilayer spin Hamiltonian where (i) the two intra-layer Hamiltonians are related by time reversal, and (ii) the inter-layer couplings are antiferromagnetic. This includes many cases of interest, such as repulsive Hubbard models. We discuss how to extract properties of the "virtual" bilayer system from the physical monolayer system, and explore applications of this approach toward numerical simulation of strongly-interacting bilayer systems.