Long-lived topological time-crystalline order on a quantum processor

  1. Liang Xiang,
  2. Wenjie Jiang,
  3. Zehang Bao,
  4. Zixuan Song,
  5. Shibo Xu,
  6. Ke Wang,
  7. Jiachen Chen,
  8. Feitong Jin,
  9. Xuhao Zhu,
  10. Zitian Zhu,
  11. Fanhao Shen,
  12. Ning Wang,
  13. Chuanyu Zhang,
  14. Yaozu Wu,
  15. Yiren Zou,
  16. Jiarun Zhong,
  17. Zhengyi Cui,
  18. Aosai Zhang,
  19. Ziqi Tan,
  20. Tingting Li,
  21. Yu Gao,
  22. Jinfeng Deng,
  23. Xu Zhang,
  24. Hang Dong,
  25. Pengfei Zhang,
  26. Si Jiang,
  27. Weikang Li,
  28. Zhide Lu,
  29. Zheng-Zhi Sun,
  30. Hekang Li,
  31. Zhen Wang,
  32. Chao Song,
  33. Qiujiang Guo,
  34. Fangli Liu,
  35. Zhe-Xuan Gong,
  36. Alexey V. Gorshkov,
  37. Norman Y. Yao,
  38. Thomas Iadecola,
  39. Francisco Machado,
  40. H. Wang,
  41. and Dong-Ling Deng
Topologically ordered phases of matter elude Landau’s symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness
against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon — a prethermal topologically ordered time crystal — with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface-code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors.

Observation of a symmetry-protected topological time crystal with superconducting qubits

  1. Xu Zhang,
  2. Wenjie Jiang,
  3. Jinfeng Deng,
  4. Ke Wang,
  5. Jiachen Chen,
  6. Pengfei Zhang,
  7. Wenhui Ren,
  8. Hang Dong,
  9. Shibo Xu,
  10. Yu Gao,
  11. Feitong Jin,
  12. Xuhao Zhu,
  13. Qiujiang Guo,
  14. Hekang Li,
  15. Chao Song,
  16. Zhen Wang,
  17. Dong-Ling Deng,
  18. and H. Wang
We report the observation of a symmetry-protected topological time crystal, which is implemented with an array of programmable superconducting qubits. Unlike the time crystals reported
in previous experiments, where spontaneous breaking of the discrete time translational symmetry occurs for local observables throughout the whole system, the topological time crystal observed in our experiment breaks the time translational symmetry only at the boundaries and has trivial dynamics in the bulk. More concretely, we observe robust long-lived temporal correlations and sub-harmonic temporal response for the edge spins up to 40 driving cycles. We demonstrate that the sub-harmonic response is independent of whether the initial states are random product states or symmetry-protected topological states, and experimentally map out the phase boundary between the time crystalline and thermal phases. Our work paves the way to exploring peculiar non-equilibrium phases of matter emerged from the interplay between topology and localization as well as periodic driving, with current noisy intermediate-scale quantum processors.

Synthesizing five-body interaction in a superconducting quantum circuit

  1. Ke Zhang,
  2. Hekang Li,
  3. Pengfei Zhang,
  4. Jiale Yuan,
  5. Jinyan Chen,
  6. Wenhui Ren,
  7. Zhen Wang,
  8. Chao Song,
  9. Da-Wei Wang,
  10. H. Wang,
  11. Shiyao Zhu,
  12. Girish S. Agarwal,
  13. and Marlan O. Scully
Synthesizing many-body interaction Hamiltonian is a central task in quantum simulation. However, it is challenging to synthesize interactions including more than two spins. Borrowing
tools from quantum optics, we synthesize five-body spin-exchange interaction in a superconducting quantum circuit by simultaneously exciting four independent qubits with time-energy correlated photon quadruples generated from a qudit. During the dynamic evolution of the five-body interaction, a Greenberger-Horne-Zeilinger state is generated in a single step with fidelity estimated to be 0.685. We compare the influence of noise on the three-, four- and five-body interaction as a step toward answering the question on the quantum origin of chiral molecules. We also demonstrate a many-body Mach-Zehnder interferometer which potentially has a Heisenberg-limit sensitivity. This study paves a way for quantum simulation involving many-body interactions and high excited states of quantum circuits.

Stark many-body localization on a superconducting quantum processor

  1. Qiujiang Guo,
  2. Chen Cheng,
  3. Hekang Li,
  4. Shibo Xu,
  5. Pengfei Zhang,
  6. Zhen Wang,
  7. Chao Song,
  8. Wuxin Liu,
  9. Wenhui Ren,
  10. Hang Dong,
  11. Rubem Mondaini,
  12. and H. Wang
Quantum emulators, owing to their large degree of tunability and control, allow the observation of fine aspects of closed quantum many-body systems, as either the regime where thermalization
takes place or when it is halted by the presence of disorder. The latter, dubbed many-body localization (MBL) phenomenon, describes the non-ergodic behavior that is dynamically identified by the preservation of local information and slow entanglement growth. Here, we provide a precise observation of this same phenomenology in the case the onsite energy landscape is not disordered, but rather linearly varied, emulating the Stark MBL. To this end, we construct a quantum device composed of thirty-two superconducting qubits, faithfully reproducing the relaxation dynamics of a non-integrable spin model. Our results describe the real-time evolution at sizes that surpass what is currently attainable by exact simulations in classical computers, signaling the onset of quantum advantage, thus bridging the way for quantum computation as a resource for solving out-of-equilibrium many-body problems.

Probing the dynamical phase transition with a superconducting quantum simulator

  1. Kai Xu,
  2. Zheng-Hang Sun,
  3. Wuxin Liu,
  4. Yu-Ran Zhang,
  5. Hekang Li,
  6. Hang Dong,
  7. Wenhui Ren,
  8. Pengfei Zhang,
  9. Franco Nori,
  10. Dongning Zheng,
  11. Heng Fan,
  12. and H. Wang
Non-equilibrium quantum many-body systems, which are difficult to study via classical computation, have attracted wide interest. Quantum simulation can provide insights into these problems.
Here, using a programmable quantum simulator with 16 all-to-all connected superconducting qubits, we investigate the dynamical phase transition in the Lipkin-Meshkov-Glick model with a quenched transverse field. Clear signatures of the dynamical phase transition, merging different concepts of dynamical criticality, are observed by measuring the non-equilibrium order parameter, nonlocal correlations, and the Loschmidt echo. Moreover, near the dynamical critical point, we obtain the optimal spin squeezing of −7.0±0.8 decibels, showing multipartite entanglement useful for measurements with precision five-fold beyond the standard quantum limit. Based on the capability of entangling qubits simultaneously and the accurate single-shot readout of multi-qubit states, this superconducting quantum simulator can be used to study other problems in non-equilibrium quantum many-body systems.

Dephasing-insensitive quantum information storage and processing with superconducting qubits

  1. Qiujiang Guo,
  2. Shi-Biao Zheng,
  3. Jianwen Wang,
  4. Chao Song,
  5. Pengfei Zhang,
  6. Kemin Li,
  7. Wuxin Liu,
  8. Hui Deng,
  9. Keqiang Huang,
  10. Dongning Zheng,
  11. Xiaobo Zhu,
  12. H. Wang,
  13. C.-Y. Lu,
  14. and Jian-Wei Pan
A central task towards building a practical quantum computer is to protect individual qubits from decoherence while retaining the ability to perform high-fidelity entangling gates involving
arbitrary two qubits. Here we propose and demonstrate a dephasing-insensitive procedure for storing and processing quantum information in an all-to-all connected superconducting circuit involving multiple frequency-tunable qubits, each of which can be controllably coupled to any other through a central bus resonator. Although it is generally believed that the extra frequency tunability enhances the control freedom but induces more dephasing impact for superconducting qubits, our results show that any individual qubit can be dynamically decoupled from dephasing noise by applying a weak continuous and resonant driving field whose phase is reversed in the middle of the pulse. More importantly, we demonstrate a new method for realizing two-qubit phase gate with inherent dynamical decoupling via the combination of continuous driving and qubit-qubit swapping coupling. We find that the weak continuous driving fields not only enable the conditional dynamics essential for quantum information processing, but also protect both qubits from dephasing during the gate operation.

Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit

  1. Chao Song,
  2. Shi-Biao Zheng,
  3. Pengfei Zhang,
  4. Kai Xu,
  5. Libo Zhang,
  6. Qiujiang Guo,
  7. Wuxin Liu,
  8. Da Xu,
  9. Hui Deng,
  10. Keqiang Huang,
  11. Dongning Zheng,
  12. Xiaobo Zhu,
  13. and H. Wang
Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications,
among which geometric quantum computation is a paradigm, where quantum logic operations are realized through geometric phase manipulation that has some intrinsic noise-resilient advantages and may enable simplified implementation of multiqubit gates compared to the dynamical approach. Here we report observation of a continuous-variable geometric phase and demonstrate a quantum gate protocol based on this phase in a superconducting circuit, where five qubits are controllably coupled to a resonator. Our geometric approach allows for one-step implementation of n-qubit controlled-phase gates, which represents a remarkable advantage compared to gate decomposition methods, where the number of required steps dramatically increases with n. Following this approach, we realize these gates with n up to 4, verifying the high efficiency of this geometric manipulation for quantum computation.

Emulating many-body localization with a superconducting quantum processor

  1. Kai Xu,
  2. Jin-Jun Chen,
  3. Yu Zeng,
  4. Yuran Zhang,
  5. Chao Song,
  6. Wuxin Liu,
  7. Qiujiang Guo,
  8. Pengfei Zhang,
  9. Da Xu,
  10. Hui Deng,
  11. Keqiang Huang,
  12. H. Wang,
  13. Xiaobo Zhu,
  14. Dongning Zheng,
  15. and Heng Fan
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence
of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization that only addresses noninteracting particles in the presence of disorder, greatly challenges this concept because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment of fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.

10-qubit entanglement and parallel logic operations with a superconducting circuit

  1. Chao Song,
  2. Kai Xu,
  3. Wuxin Liu,
  4. Chuiping Yang,
  5. Shi-Biao Zheng,
  6. Hui Deng,
  7. Qiwei Xie,
  8. Keqiang Huang,
  9. Qiujiang Guo,
  10. Libo Zhang,
  11. Pengfei Zhang,
  12. Da Xu,
  13. Dongning Zheng,
  14. Xiaobo Zhu,
  15. H. Wang,
  16. Y.-A. Chen,
  17. C.-Y. Lu,
  18. Siyuan Han,
  19. and J.-W. Pan
Here we report on the production and tomography of genuinely entangled Greenberger-Horne-Zeilinger states with up to 10 qubits connecting to a bus resonator in a superconducting circuit,
where the resonator-mediated qubit-qubit interactions are used to controllably entangle multiple qubits and to operate on different pairs of qubits in parallel. The resulting 10-qubit density matrix is unambiguously probed, with a fidelity of 0.668±0.025. Our results demonstrate the largest entanglement created so far in solid-state architectures, and pave the way to large-scale quantum computation.