Quantum dynamics on complex quantum networks and its simulation using periodically driven systems

Man Luo, J. I. Cirac, Technische Universität München

Raditya Weda Bomantara, Sen Mu, Jiangbin Gong

Studies of periodically driven one-dimensional many-body systems have advanced our understanding of complex systems and stimulated promising developments in quantum simulation. It is hence of interest to go one step further, by investigating the topological and dynamical aspects of periodically driven spin ladders as clean quasi-one-dimensional systems with spin-spin interaction in the rung direction. Specifically, we find that such systems display subharmonic magnetization dynamics reminiscent to that of discrete time crystals (DTCs) at finite system sizes. Through the use of generalized Jordan-Wigner transformation, this feature can be attributed to the presence of corner Majorana $\ensuremath{\pi}$ modes (MPMs), which are of topological origin, in the systems' equivalent Majorana lattice. Special emphasis is placed on how the coupling in the rung direction of the ladder prevents degeneracy from occurring between states differing by a single spin excitation, thus preserving the MPM-induced $\ensuremath{\pi}/T$ quasienergy spacing of the Floquet eigenstates in the presence of parameter imperfection. This feature, which is absent in their strict one-dimensional counterparts, may yield fascinating consequences in future studies of higher dimensional Floquet many-body systems.

V. M. Akulin

Abhishek Kumar, Karunya Shirali, Nicholas J. Mayhall +2 more

Periodically driven quantum systems exhibit many fascinating phenomena absent in equilibrium systems, but their simulation is more challenging than that of static systems. Consequently, quantum simulation of these systems offers greater opportunity for achieving quantum advantage. To build the foundation for simulating time-periodic Hamiltonians, we utilize the Floquet-Hilbert space formalism to transform the Hamiltonian into a time-independent form and provide its Pauli decomposition. Within this formalism, we develop a hybrid quantum-classical algorithm, Floquet-ADAPT-VQE, that produces three key quantities that govern periodically driven quantum dynamics: the quasienergy, the associated Floquet eigenstates, and expectation values of observables with respect to these eigenstates. The latter is achieved by applying a fixed-depth quantum circuit to an initial Floquet eigenstate—an efficient construction made possible by the Floquet-Hilbert space formalism. We also identify a suitable auxiliary initial state whose squared Floquet energy is independent of the number of auxiliary qubits as well as the driving frequency, which leads to better convergence with fewer ADAPT iterations. We demonstrate our algorithm by performing numerical simulations on a periodically driven XYZ model with a magnetic field. We also explore potential applications of our algorithm for studying various non-equilibrium phenomena in periodically driven systems.

Zijun Shu, Yu Liu, Qingyun Cao +5 more

We experimentally observe Floquet Raman transitions in the weakly driven solid-state spin system of a nitrogen-vacancy center in diamond. The periodically driven spin system simulates a two-band Wannier-Stark ladder model and allows us to observe coherent spin state transfer arising from a Raman transition mediated by Floquet synthetic levels. It also leads to the prediction of an analog photon-assisted Floquet Raman transition and dynamical localization in a driven two-level quantum system. The demonstrated rich Floquet dynamics offers new capabilities to achieve effective Floquet coherent control of a quantum system with potential applications in various types of quantum technologies based on driven quantum dynamics. In particular, the Floquet Raman system may be used as a quantum simulator for the physics of periodically driven systems.

Xiang Ying Sun