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.

Simultaneous excitation of two noninteracting atoms with time-frequency correlated photon pairs in a superconducting circuit

  1. Wenhui Ren,
  2. Wuxin Liu,
  3. Chao Song,
  4. Hekang Li,
  5. Qiujiang Guo,
  6. Zhen Wang,
  7. Dongning Zheng,
  8. Girish S. Agarwal,
  9. Marlan O. Scully,
  10. Shi-Yao Zhu,
  11. H. Wang,
  12. and Da-Wei Wang
Here we report the first observation of simultaneous excitation of two noninteracting atoms by a pair of time-frequency correlated photons in a superconducting circuit. The strong coupling
regime of this process enables the synthesis of a three-body interaction Hamiltonian, which allows the generation of the tripartite Greenberger-Horne-Zeilinger state in a single step with a fidelity as high as 0.95. We further demonstrate the quantum Zeno effect of inhibiting the simultaneous two-atom excitation by continuously measuring whether the first photon is emitted. This work provides a new route in synthesizing many-body interaction Hamiltonian and coherent control of entanglement.

Generation and controllable switching of superradiant and subradiant states in a 10-qubit superconducting circuit

  1. Zhen Wang,
  2. Hekang Li,
  3. Wei Feng,
  4. Xiaohui Song,
  5. Chao Song,
  6. Wuxin Liu,
  7. Qiujiang Guo,
  8. Xu Zhang,
  9. Hang Dong,
  10. Dongning Zheng,
  11. H. Wang,
  12. and Da-Wei Wang
Superradiance and subradiance concerning enhanced and inhibited collective radiation of an ensemble of atoms have been a central topic in quantum optics. However, precise generation
and control of these states remain challenging. Here we deterministically generate up to 10-qubit superradiant and 8-qubit subradiant states, each containing a single excitation, in a superconducting quantum circuit with multiple qubits interconnected by a cavity resonator. The N−−√-scaling enhancement of the coupling strength between the superradiant states and the cavity is validated. By applying appropriate phase gate on each qubit, we are able to switch the single collective excitation between superradiant and subradiant states. While the subradiant states containing a single excitation are forbidden from emitting photons, we demonstrate that they can still absorb photons from the resonator. However, for even number of qubits, a singlet state with half of the qubits being excited can neither emit nor absorb photons, which is verified with 4 qubits. This study is a step forward in coherent control of collective radiation and has promising applications in quantum information processing.

Observation of multi-component atomic Schrödinger cat states of up to 20 qubits

  1. Chao Song,
  2. Kai Xu,
  3. Hekang Li,
  4. Yuran Zhang,
  5. Xu Zhang,
  6. Wuxin Liu,
  7. Qiujiang Guo,
  8. Zhen Wang,
  9. Wenhui Ren,
  10. Jie Hao,
  11. Hui Feng,
  12. Heng Fan,
  13. Dongning Zheng,
  14. Dawei Wang,
  15. H. Wang,
  16. and Shiyao Zhu
We report on deterministic generation of 18-qubit genuinely entangled Greenberger-Horne-Zeilinger (GHZ) state and multi-component atomic Schrödinger cat states of up to 20 qubits on
a quantum processor, which features 20 superconducting qubits interconnected by a bus resonator. By engineering a one-axis twisting Hamiltonian enabled by the resonator-mediated interactions, the system of qubits initialized coherently evolves to an over-squeezed, non-Gaussian regime, where atomic Schrödinger cat states, i.e., superpositions of atomic coherent states including GHZ state, appear at specific time intervals in excellent agreement with theory. With high controllability, we are able to take snapshots of the dynamics by plotting quasidistribution Q-functions of the 20-qubit atomic cat states, and globally characterize the 18-qubit GHZ state which yields a fidelity of 0.525±0.005 confirming genuine eighteen-partite entanglement. Our results demonstrate the largest entanglement controllably created so far in solid state architectures, and the process of generating and detecting multipartite entanglement may promise applications in practical quantum metrology, quantum information processing and quantum computation.

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.

Parallel quantum operations with chiral spin states in a superconducting circuit

  1. Da-Wei Wang,
  2. Chao Song,
  3. Wei Feng,
  4. Han Cai,
  5. Da Xu,
  6. Hui Deng,
  7. Dongning Zheng,
  8. Xiaobo Zhu,
  9. H. Wang,
  10. Shiyao Zhu,
  11. and Marlan O. Scully
Recently it was shown that mesoscopic superpositions of photonic states can be prepared based on a spin-gated chiral photon rotation in a Fock-state lattice of three cavities coupled
to a spin (two-level atom). By exchanging the roles of the cavities and the spin, we have performed parallel operations on chiral spin states based on an antisymmetric spin exchange interaction (ASI) in a superconducting circuit. The ASI, which is also called Dzyaloshinskii-Moriya interaction, plays an important role in the formation of topological spin textures such as skyrmions. By periodically modulating the transition frequencies of three superconducting qubits interacting with a bus resonator, we synthesize a chiral ASI Hamiltonian with spin-gated chiral dynamics, which allow us to demonstrate a three-spin chiral logic gate and entangle up to five qubits in Greenberger-Horne-Zeilinger states. Our results pave the way for quantum simulation of magnetism with ASI and quantum computation with chiral spin states.

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.