Quantum simulation and control of topologically-ordered quantum matter

• Applicant: Dr. Francesco Petiziol
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 555842149

Topologically-ordered quantum phases of matter are strongly-correlated phases of quantum many-body systems, in which long-range entanglement gives rise to unique properties. These include topology-dependent ground state degeneracy and the emergence of quasiparticle excitations possessing anyon quantum statistics. These intriguing features make topological order interesting both from the perspective of fundamental science and in view of technological applications, for instance as the potential backbone of fault-tolerant quantum computers. The goal of attaining controllable topological order represents an outstanding challenge, which recently spurred major efforts towards its synthetic realization across several experimental platforms. In this theory project, we aim at shedding light on the properties of topologically-ordered systems in out-of-equilbrium conditions, for the purpose of developing novel protocols for their quantum simulation, control and stabilization, as well as for applications, e.g., to the design of stable topological quantum memories. We will study topologically-ordered systems subject to time-dependent control or coupled to engineered environments. We will, for instance, investigate opportunities to control quantum localization of anyon quasiparticles and to induce their autonomous and dissipative re-annihilation. We will search for novel effects resulting from the interplay of periodic driving, topology and interactions. One example is the potential emergence of non-Abelian order in Abelian dimer liquids of blockaded Rydberg excitations subject to temporal modulations. We will design novel quantum simulation schemes of model Hamiltonians of topologically ordered systems, such as topological spin liquids, and to probe their competition with other quantum phases. These schemes will be conceived for implementations in state-of-the-art platforms such as superconducting circuits and ultracold atoms. We will further develop coherent-control protocols to efficiently prepare and manipulate topologically-ordered states. Our approach will build on the synergy of techniques from Floquet engineering, digital quantum simulation, shortcut-to-adiabatic and optimal control. Building on these results, we will study whether the interplay of controlled anyon localization and engineered dissipation can be harnessed to counteract the thermal breakdown of self-correcting quantum memories based on topological order. We will explore whether the anyon re-annihilation mechanisms developed can be exploited to enhance the memory lifetime, paving the way to functional self-correcting topological quantum memories.

• DFG Programme: Emmy Noether Independent Junior Research Groups