The recent successful computation beyond the capability of classical computers has brought considerable attention to the Noisy Intermediate Scale Quantum (NISQ) processors. The only way to evaluate the promise of NISQ devices is to implement algorithms on them that are of interest to the scientific community. In this talk, I will present two of such examples based on our recent works on time crystals and the Kitaev toric code [1,2]. The first work is on study phase transitions, which is challenge due to limited programmability, finite coherence time, and finite size of NISQ hardware. With addressing these issues, we provide a set of experimental benchmarks and establish a scalable approach to study phases of matter on current quantum processors. The theme of the second work is in studying topological states. The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit. Our results demonstrate the potential of NISQ processors to provide key insights into topological quantum matter and quantum error correction.
[1] https://arxiv.org/abs/2107.13571
[2] https://arxiv.org/abs/2104.01180