Over the first half of the project, substantial progress on the central objectives was achieved, producing a coherent set of advances on the stabilization of exotic quantum states through engineered dissipation in weakly driven integrable systems, the importance of conserved quantities in such systems, and the controlled manipulation of strongly correlated non-equilibrium phases in Mott insulators.
Larger part of the work considered the role of approximately conserved quantities due to approximate symmetries in weakly open quantum systems, most prominent in weakly dissipative nearly integrable setups. In our work we addressed two aspects: how to efficiently describe such systems with macroscopically many approximately conserved quantitites and whether driving such systems can allow for stabilization of exotic states:
In SciPost Physics 19, 068 (2025), we demonstrated that optimized driving and engineered weak dissipation can be used to counteract integrability breaking and stabilize exotic generalized Gibbs ensembles. An important insight is the realization that digital quantum-computing architectures can naturally implement these controlled weak couplings through reset-based protocols. These protocols can stabilize non-thermal stationary states characteristic of nearly integrable models, even in the presence of native noise, thereby offering a practical pathway for realizing exotic states on near-term quantum devices.
In Phys. Rev. Lett. 132, 230402 (2024), we developed a general iterative framework for identifying the essential conserved quantities that govern such stationary states of weakly dissipative, nearly integrable systems. The key insight is that weak integrability-breaking processes naturally select a small subset of dominant integrals of motion, enabling a principled construction of reduced statistical descriptions. This framework replaces previous heuristic truncation approaches.
In Phys. Rev. Research 6, 023160 (2024), we made complementary methodological developments that allow one to learn relevant dynamical features directly from observables. We extracted emergent effective Hamiltonians or generators of long-time behavior from thermal, prethermal, or generally driven steady states. These tools provide a unified strategy for identifying the key structures that control relaxation in a broad class of non-equilibrium settings. In SciPost Physics 19, 149 (2025) we used machine learning tools in combination with a tensor network approach to learn effective dissipative description of subsystem dynamics, relevant for reconstruction of physical observables.
Within the second major direction, we search for driving protocols that can stabilize exotic transient phases that emerge in driven or photodoped strongly correlated electronic systems:
One outcome was the discovery of a non-equilibrium pairing regime characterized by robust spatial correlations that do not appear in equilibrium (Phys. Rev. B 113, L161109 (2026)). Another result showed that periodic driving can significantly enhance the formation and stability of correlated bound states in both doped and photodoped regimes (Phys. Rev. Res. 6, 033331 (2024)). These findings provide a framework for using driving to manipulate effective interactions and coherence in systems with strong electronic correlations.
Across all objectives, the project introduced several methodological innovations, ranging from iterative conserved-quantity construction and machine-learning–assisted extraction of effective generators, to digital implementations of engineered dissipation and combined analytical–numerical approaches to driven correlated systems. These developments connect ideas from integrability, open quantum systems, tensor-network simulation, machine learning, and quantum computing, significantly broadening the conceptual and technical foundations for future progress.
