In a recent work, Prof. Biao Huang from Kavli Institute for Theoretical Sciences (KITS) and the experimental team at Zhejiang University on superconducting qubits led by Prof. Haohua Wang and Prof. Qiujiang Guo demonstrated the protection of Greenberger-Horne-Zeilinger (GHZ) states using a peculiar discrete time crystal, which involves on-demand engineered quantum many-body scars of Schrödinger’s cat type. Globally entangled GHZ states shielded in this way survive for about three times longer than the unprotected ones, and also outlive the quantum states protected by usual spin echoes. The experiment was published on October 12th in [Nature Communications 15, 8233 (2024)], following an earlier theoretical blueprint [Biao Huang, Physical Review B 108, 104309 (2023)].
GHZ states are the qubit-analogues of the famous Schrödinger’s cat. They are made of two macroscopically distinct qubit excitation patterns, and feature entanglement between every pair of qubits. These states play essential roles in quantum computation and quantum information processing. However, they are extreme fragile, as their coherence, just like that for Schrödinger’s cats, can be easily destroyed by perturbations on any single constituent. Over the past decades, extraordinary efforts have been made across all quantum platforms to enlarge the size of the generated GHZ states, with the previous world-record in 2023 being that of 32-qubits in trapped ions. Further experiments on protecting large-scale GHZ states have remained scarce.
In the current experiment at ZJU, a record-breaking size of 60 qubits is consistently generated for the GHZ states, nearly doubling the previous record. Based on the improvement of quantum devices, the researchers march towards the more challenging objective of protecting the GHZ states over long-time drivings, a scenario closer to the ultimate applications of these states.
Schematic illustration of storing GHZ states using cat scar discrete time crystals
Their idea to protect the GHZ state is to embed it into an exotic nonequilibrium quantum matter dubbed discrete time crystals (DTC), which host pairwise cat eigenstates as “safety house”, to accommodate and shield the GHZ states from perturbations.
The concept of time crystals was originally introduced by the Nobel Laureate Frank Wilczek in 2012, who generalized the Landau’s scheme of spontaneous symmetry breaking from the usual spatial/internal degrees of freedoms to the dimension of time. A DTC is an interacting system, which is driven with period T, but shows robust subharmonic response, i.e. with rigid period 2T, regardless of perturbations, and therefore resembles a “temporal spin density wave”.
In a concrete model, a DTC in each period T is made of two driving steps. First, the system undergoes a single-qubit-flip pulse, which serves as echoes to cancel external dephasing noise. Then, on the second step, the system experiences two-qubit interaction of Ising type, which then suppresses internal delocalization effects. Together, the DTC hosts long-range-entangled cat eigenstates to protect the macroscopic coherence of GHZ states from both external and internal perturbations. Moreover, for the particular purpose here, a special upgrade of the DTC into a “cat scar DTC” is realized. It enables analytically prediction of the quality of rare cat eigenstates, dubbed cat scars, to effectively accommodate the GHZ states. Also, it realizes compatible inhomogeneous qubit patterns of cat scars requiring only homogeneous two-qubit gates. Such upgrades enhances the certainty and resource usage efficiency, which finally lead to a clear advantage of GHZ state protection scheme in the experiment. Moreover, it is demonstrated in the experiment that the protection of different GHZ states can even be switched seamlessly during evolution.
Implications of this experiments can be viewed from two perspectives. Technologically, the application of Ising interaction in a DTC suppresses generic internal perturbation to the GHZ states, constituting a promising alternative to the usual spin echo scheme that cannot affect interacting (two-qubit) perturbations. Physically, the detection of the periodic-doubled oscillation of macroscopic coherent phase for GHZ states constitutes a powerful sensing scheme, which allows for seeing individual cat eigenstates with pairwise quasienergy difference π. This is a central feature of DTCs dubbed “spectral pairing”, whose direct evidence has been long-sought-after since the original researches in 2016.
The experiment stems from the collaboration between Prof. Biao Huang’s (KITS) theory group and Prof. Haohua Wang (School of Physics, Zhejiang University) and Prof. Qiujiang Guo’s (ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University) experimental team. The project was completed with contributions from Zehang Bao (co-first author, PhD at ZJU), Shibo Xu (co-first author, PhD at ZJU), and others on the experimental front, and Yang-Ren Liu (PhD at KITS) on the theory side. Prof. Qiujiang Guo, Prof. Biao Huang, and Prof. Haohua Wang are co-corresponding authors. This work is supported by the National Natural Science Foundation of China, the Innovation Program for Quantum Science and Technology, the National Key Research and Development Program of China, the Zhejiang Provincial Natural Science Foundation of China, Zhejiang Pioneer (Jianbing) Project and New Cornerstone Science Foundation through the XPLORER PRIZE.
Article link: https://www.nature.com/articles/s41467-024-53140-5
