From Bell products to Greenberger-Horne-Zeilinger states: Quantum memories via emergent Hamiltonians

With the advent of exquisite quantum emulators, storing highly entangled many-body states becomes essential. While entanglement typically builds over time when evolving a quantum system initialized in a product state, freezing that information at any given instant requires quenching to a Hamiltonian with the time-evolved state as an eigenstate, a concept we realize via an emergent Hamiltonian framework. While the emergent Hamiltonian is generically nonlocal and may lack a closed form, we show examples where it is exact and local, thereby enabling, in principle, indefinite state storage limited only by experimental imperfections. Unlike other phenomena, such as many-body localization, our method preserves both local and global properties of the quantum state. In some of our examples, we demonstrate that this protocol can be used to store maximally entangled multiqubit states, such as tensor products of Bell states, or fragile, globally distributed entangled states, in the form of Greenberger-Horne-Zeilinger states, which are often challenging to initialize in actual devices.