Digital quantum simulation of Floquet topological phases with a solid-state quantum simulator

Understanding matter—a collection of many interacting constituents, such as atoms and electrons, which is a major endeavor in physics. Discoveries of topological insulator and quantum Hall effect have boosted the exploration of novel topological phases of matters. It provides both fascinating physics and exciting opportunities for devices.

Although topological quantum states were first discovered in solid-state materials, quantum simulators provide opportunities to go beyond what is possible in real materials, taking advantage of the high controllability and flexibility of these platforms. And such high tunability could greatly enhance the prospects for probing exotic topological phases. In many of the recent achievements, topological phases were mainly probed on the analog quantum simulators (AQS). As a counterpart of AQS, the circuit-based simulator, so-called digital quantum simulator can, in principle, efficiently simulate any finite-dimensional local Hamiltonian, hence owning the advantage of universality. However, digital quantum simulation and detection of topological phases are still less explored.

Prof. Chen and Prof. Xu from Hefei University of Technology reports the realization of the digital quantum simulation periodically-driven Floquet systems with a solid-state quantum simulator at room temperature, together with Pro. Jia, Prof. Mei and Prof. Shen from Shanxi University. The research results are published in Photonics Research, Vol. 9, No. 1, 2021 (Bing Chen, Shuo Li, Xianfei Hou, Feifei Ge, Feifei Zhou, Peng Qian, Feng Mei, Suotang Jia, Nanyang Xu, Heng Shen. Digital quantum simulation of Floquet topological phases with a solid-state quantum simulator[J]. Photonics Research, 2021, 9(1): 01000081).

(a)Schematic of digital quantum simulation in solid-state platform; (b) opological winding number in different phase

Floquet systems are generally defined by periodically driven with a time-dependent Hamiltonian for a fixed period, leading to the translation- invariance of eigenvalues in frequency domain. Classical Floquet engineering provides the general mechanism to realize the non-reciprocal transportation devices such as optical isolator and circulator. Periodically driven Floquet quantum systems could provide a promising platform to investigate novel physics out of equilibrium, for instance, Floquet time crystal.

Building upon the well-controlled quantum simulator with Nitrogen-Vacancy center in diamond, Floquet topological phases is naturally simulated, which is inaccessible in static equilibrium systems, and hereby providing a way to better understand the associated Floquet topological features. Moreover, in order to distinguish the distinct topological phases, topological invariants are unambiguously detected by means of quantum quench.

Building upon the well-controlled solid state quantum simulator with high fidelity gate operation, the quantum simulator presented here can be widely utilized to emulate the complex systems in quantum many-body and condense matter physics. Moreover, due to the feasibility of implementing the quantum quench in this platform, it opens a new front for understanding the dynamics of non-equilibrium topological phases. Prof. Xu believes that further applications of this protocol will certainly encourage the studies of digital quantum simulation of topological phases with programmable quantum simulators, such as Floquet Hopf insulators that are hard to be engineered in other topological systems. Prof. Mei from Shanxi University additionally points out that this approach may offer the opportunities for using quantum computers to investigate non-equilibrium topological phases and design topological materials.