Two-level approximation of transmons in quantum quench experiments

  1. H. S. Yan,
  2. Yong-Yi Wang,
  3. S. K. Zhao,
  4. Z. H. Yang,
  5. Z. T. Wang,
  6. Kai Xu,
  7. Ye Tian,
  8. H. F. Yu,
  9. Heng Fan,
  10. and S. P. Zhao
Quantum quench is a typical protocol in the study of nonequilibrium dynamics of quantum many-body systems. Recently a number of experiments with superconducting transmon qubits are
reported, in which the celebrated spin and hard-core Bose-Hubbard models with two energy levels on individual sites are used. The transmons have nonequidistant energy levels, among which the two lowest levels form the computational subspace. In this work, we numerically simulate realistic experiments of quantum quench dynamics and discuss the applicability of the two-level approximation for the multilevel transmons. We calculate the fidelity decay (i.e., the time-dependent overlap of evolving wave functions) due to the state leakage to transmon high energy levels for two kinds of quantum quench experiments with time reversal and time evolution in one direction, respectively. We present the results of the fidelity decay for different system Hamiltonians with various initial state, qubit coupling strength, and external driving. The extent to which the spin and hard-core Bose-Hubbard models can be applied under various circumstances is discussed and compared with experimental observations. Our work provides a precise way to assess the two-level approximation of transmons in quantum quench experiments and shows that good approximation is reachable using the present-day superconducting circuit architecture.

Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers

  1. Hao Li,
  2. Yong-Yi Wang,
  3. Yun-Hao Shi,
  4. Kaixuan Huang,
  5. Xiaohui Song,
  6. Gui-Han Liang,
  7. Zheng-Yang Mei,
  8. Bozhen Zhou,
  9. He Zhang,
  10. Jia-Chi Zhang,
  11. Shu Chen,
  12. Shiping Zhao,
  13. Ye Tian,
  14. Zhan-Ying Yang,
  15. Zhongcheng Xiang,
  16. Kai Xu,
  17. Dongning Zheng,
  18. and Heng Fan
Quantum simulation enables study of many-body systems in non-equilibrium by mapping to a controllable quantum system, providing a new tool for computational intractable problems. Here,
using a programmable quantum processor with a chain of 10 superconducting qubits interacted through tunable couplers, we simulate the one-dimensional generalized Aubry-André-Harper model for three different phases, i.e., extended, localized and critical phases. The properties of phase transitions and many-body dynamics are studied in the presence of quasi-periodic modulations for both off-diagonal hopping coefficients and on-site potentials of the model controlled respectively by adjusting strength of couplings and qubit frequencies. We observe the spin transport for initial single- and multi-excitation states in different phases, and characterize phase transitions by experimentally measuring dynamics of participation entropies. Our experimental results demonstrate that the newly developed tunable coupling architecture of superconducting processor extends greatly the simulation realms for a wide variety of Hamiltonians, and may trigger further investigations on various quantum and topological phenomena.

Entanglement-interference complementarity and experimental demonstration in a superconducting circuit

  1. Xin-Jie Huang,
  2. Pei-Rong Han,
  3. Wen Ning,
  4. Shou-Ban Yang,
  5. Xin Zhu,
  6. Jia-Hao Lü,
  7. Ri-Hua Zheng,
  8. Hekang Li,
  9. Zhen-Biao Yang,
  10. Qi-Cheng Wu,
  11. Kai Xu,
  12. Chui-Ping Yang,
  13. Dongning Zheng,
  14. Heng Fan,
  15. and Shi-Biao Zheng
Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays a central role for enforcing Bohr’s complementary principle,
but the quantitative relation between this entanglement and the fringe visibility remains untouched upon. Here we find an equality for quantifying this relation. Our equality characterizes how well the interference pattern can be preserved when an interfering particle, initially carrying a definite amount of coherence, is entangled with a which-path detector to a certain degree. This equality provides a connection between entanglement and interference in the unified framework of coherence, revealing the quantitative entanglement-interference complementarity for the first time. We experimentally demonstrate this relation with a superconducting circuit, where a resonator serves as a which-path detector for an interfering qubit. The results demonstrate quantum entanglement is the mechanism for prohibiting any detector from acquiring which-path information without deteriorating the interference pattern, which was not confirmed previously.

Observation of Emergent ℤ2 Gauge Invariance in a Superconducting Circuit

  1. Zhan Wang,
  2. Zi-Yong Ge,
  3. Zhongcheng Xiang,
  4. Xiaohui Song,
  5. Rui-Zhen Huang,
  6. Pengtao Song,
  7. Xue-Yi Guo,
  8. Luhong Su,
  9. Kai Xu,
  10. Dongning Zheng,
  11. and Heng Fan
Lattice gauge theory (LGT) is one of the most fundamental subjects in modern quantum many-body physics, and has recently attracted many research interests in quantum simulations. Here
we experimentally investigate the emergent ℤ2 gauge invariance in a 1D superconducting circuit with 10 transmon qubits. By precisely adjusting the staggered longitude and transverse fields to each qubit, we construct an effective Hamiltonian containing a LGT and gauge-broken terms. The corresponding matter sector can exhibit localization, and there also exist a 3-qubit operator, of which the expectation value can retain nonzero for long time in a low-energy regime. The above localization can be regarded as confinement of the matter field, and the 3-body operator is the ℤ2 gauge generator. Thus, these experimental results demonstrate that, despite the absent of gauge structure in the effective Hamiltonian, ℤ2 gauge invariance can still emerge in the low-energy regime. Our work paves the way for both theoretically and experimentally studying the rich physics in quantum many-body system with an emergent gauge invariance.

Probing Operator Spreading via Floquet Engineering in a Superconducting Circuit

  1. S. K. Zhao,
  2. Zi-Yong Ge,
  3. Zhongcheng Xiang,
  4. G. M. Xue,
  5. H. S. Yan,
  6. Z. T. Wang,
  7. Zhan Wang,
  8. H. K. Xu,
  9. F. F. Su,
  10. Z. H. Yang,
  11. He Zhang,
  12. Yu-Ran Zhang,
  13. Xue-Yi Guo,
  14. Kai Xu,
  15. Ye Tian,
  16. H. F. Yu,
  17. D. N. Zheng,
  18. Heng Fan,
  19. and S. P. Zhao
Operator spreading, often characterized by out-of-time-order correlators (OTOCs), is one of the central concepts in quantum many-body physics. However, measuring OTOCs is experimentally
challenging due to the requirement of reversing the time evolution of the system. Here we apply Floquet engineering to investigate operator spreading in a superconducting 10-qubit chain. Floquet engineering provides an effective way to tune the coupling strength between nearby qubits, which is used to demonstrate quantum walks with tunable coupling, dynamic localization, reversed time evolution, and the measurement of OTOCs. A clear light-cone-like operator propagation is observed in the system with multiphoton excitations, and the corresponding spreading velocity is equal to that of quantum walk. Our results indicate that the method has a high potential for simulating a variety of quantum many-body systems and their dynamics, which is also scalable to more qubits and higher dimensional circuits.

Metrological characterisation of non-Gaussian entangled states of superconducting qubits

  1. Kai Xu,
  2. Yu-Ran Zhang,
  3. Zheng-Hang Sun,
  4. Hekang Li,
  5. Pengtao Song,
  6. Zhongcheng Xiang,
  7. Kaixuan Huang,
  8. Hao Li,
  9. Yun-Hao Shi,
  10. Chi-Tong Chen,
  11. Xiaohui Song,
  12. Dongning Zheng,
  13. Franco Nori,
  14. H. Wang,
  15. and Heng Fan
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to
achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterises the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalisation of the RSP with respect to nonlinear observables, and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, here we report the characterisation of multiparticle entangled states generated during its nonlinear dynamics. First, selecting 10 qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89[Math Processing Error] dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Demonstration of a non-Abelian geometric controlled-Not gate in a superconducting circuit

  1. Kai Xu,
  2. Wen Ning,
  3. Xin-Jie Huang,
  4. Pei-Rong Han,
  5. Hekang Li,
  6. Zhen-Biao Yang,
  7. Dongning Zheng,
  8. Heng Fan,
  9. and Shi-Biao Zheng
Holonomies, arising from non-Abelian geometric transformations of quantum states in Hilbert space, offer a promising way for quantum computation. The non-community of these holonomies
renders them suitable for realization of a universal set of quantum logic gates, while the global geometric feature may result in some noise-resilient advantages. Here we report on the first on-chip realization of the non-Abelian geometric controlled-Not gate, which is a buidling block for constructing a holonomic quantum computer. The conditional dynamics is achieved in an all-to-all connected architecture involving multiple frequency-tunable superconducting qubits controllably coupled to a resonator; a holonomic gate between any two qubits can be implemented by tuning their frequencies on resonance with the resonator and applying a two-tone drive to one of them. The combination of the present gate and previously demonstrated holonomic single-qubit operations represents an all-holonomic approach to scalable quantum computation on a superconducting platform.

Observation of Bloch Oscillations and Wannier-Stark Localization on a Superconducting Processor

  1. Xue-Yi Guo,
  2. Zi-Yong Ge,
  3. Hekang Li,
  4. Zhan Wang,
  5. Yu-Ran Zhang,
  6. Peangtao Song,
  7. Zhongcheng Xiang,
  8. Xiaohui Song,
  9. Yirong Jin,
  10. Kai Xu,
  11. Dongning Zheng,
  12. and Heng Fan
In a crystal lattice system, a conduction electron can exhibit Bloch oscillations and Wannier-Stark localization (WSL) under a constant force, which has been observed in semiconductor
superlattice, photonic waveguide array and cold atom systems. Here, we experimentally investigate the Bloch oscillations on a 5-qubit superconducting processor. We simulate the electron movement with spin (or photon) propagation. We find, in the presence of a linear potential, the propagation of a single spin charge is constrained. It tends to oscillate near the neighborhood of initial positions, which is a strong signature of Bloch oscillations and WSL. In addition, we use the maximum probability that a spin charge can propagate from one boundary to another boundary to represent the WSL length, and it is verified that the localization length is inversely correlated to the potential gradient. Remarkably, benefiting from the precise simultaneous readout of the all qubits, we can also study the thermal transport of this system. The experimental results show that, similar to the spin charges, the thermal transport is also blocked under a linear potential. Our work demonstrates possibilities for further simulation and exploration of the Bloch oscillation phenomena and other quantum physics using multiqubit superconducting quantum processor.

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.

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.