Exploring Emergent Hamiltonians as a Framework for Open-System Quantum Memory

Advances in quantum simulation and computation now place renewed emphasis on how entangled many-body states can be preserved once created. Building on our recent work (arXiv:2510.01117), where the Emergent Hamiltonian framework was shown to render a time-evolved state stationary and preserve entanglement in isolated systems, we study how this behavior changes in the presence of noise. Using quantum trajectory simulations, we examine the effects of dephasing and particle loss on the stability of states governed by emergent Hamiltonians and investigate how the parent-Hamiltonian gap influences decoherence and memory lifetime. To characterize open-system dynamics, we analyze the complex spectra of the effective non-Hermitian generators that govern the no-jump evolution and decay modes that control correlation loss. We also explore whether designed dissipative generators can yield steady states reproducing the target states of the unitary case, suggesting a path toward gap-engineered and noise-resilient quantum memories.