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Recently, the BESIII Collaboration has observed three-body decays $D_s^+\to \eta \omega\pi^+$, $D^+\to K^0_S\pi^+\omega$ and $D^0\to K^-\pi^+\omega$. In this work, we investigate the contributions of the subprocesses $\rho^+\to \omega\pi^+$ in these Cabibbo-favored decays $D \to h\omega\pi$, with $\rho^+= \{\rho(770)^+, \rho(1450)^+, \rho(770)^+\&\rho(1450)^+\}$ and $h=\{ \eta, K^0_S, K^-\}$, by introducing these subprocesses into the decay amplitudes of the relevant decay processes via the vector form factor $F_{\omega\pi}$ measured in the related $\tau$ and $e^+e^-$ processes; we provide the first theoretical predictions for the branching fractions of the quasi-two-body decays $D_s^+\to\eta[\rho^+\to]\omega\pi^+$, $D^+\to K^0_S[\rho^+\to]\omega\pi^+$ and $D^0\to K^-[\rho^+\to]\omega\pi^+$. Our findings reveal that the contributions from the subprocess $\rho(770)^+\to\omega\pi^+$ are significant in these observed three-body decays $D_s^+\to\eta \omega\pi^+$, $D^+\to K^0_S \omega\pi^+$ and $D^0\to K^- \omega\pi^+$, notwithstanding the contributions originating from the Breit-Wigner tail effect of $\rho(770)^+$. The numerical results of this study suggest that these Cabibbo-favored three-body decays are dominated by the contributions come from the $P$-wave intermediate states $\rho(770)^+$, $\rho(1450)^+$ and their interference effects., Comment: 9 pages, 2 figures

Three-qubit gates can be constructed using combinations of single-qubit and two-qubit gates, making their independent realization unnecessary. However, direct implementation of three-qubit gates reduces the depth of quantum circuits, streamlines quantum programming, and facilitates efficient circuit optimization, thereby enhancing overall performance in quantum computation. In this work, we propose and experimentally demonstrate a high-fidelity scheme for implementing a three-qubit controlled-controlled-Z (CCZ) gate in a flip-chip superconducting quantum processor with tunable couplers. This direct CCZ gate is implemented by simultaneously leveraging two tunable couplers interspersed between three qubits to enable three-qubit interactions, achieving an average final state fidelity of $97.94\%$ and a process fidelity of $93.54\%$. This high fidelity cannot be achieved through a simple combination of single- and two-qubit gate sequences from processors with similar performance levels. Our experiments also verify that multi-layer direct implementation of the CCZ gate exhibits lower leakage compared to decomposed gate approaches. To further showcase the versatility of our approach, we construct a Toffoli gate by combining the CCZ gate with Hadamard gates. As a showcase, we utilize the CCZ gate as an oracle to implement the Grover search algorithm on three qubits, demonstrating high performance with the target probability amplitude significantly enhanced after two iterations. These results highlight the advantage of our approach, and facilitate the implementation of complex quantum circuits., Comment: main text: 8 pages, 4 figures; supp: 11 pages, 11 figures, 2 tables

For superconducting quantum processors, stable high-fidelity two-qubit operations depend on precise flux control of the tunable coupler. However, the pulse distortion poses a significant challenge to the control precision. Current calibration methods, which often rely on microwave crosstalk or additional readout resonators for coupler excitation and readout, tend to be cumbersome and inefficient, especially when couplers only have flux control. Here, we introduce and experimentally validate a novel pulse calibration scheme that exploits the strong coupling between qubits and couplers, eliminating the need for extra coupler readout and excitation. Our method directly measures the short-time and long-time step responses of the coupler flux pulse transient, enabling us to apply predistortion to subsequent signals using fast Fourier transformation and deconvolution. This approach not only simplifies the calibration process but also significantly improves the precision and stability of the flux control. We demonstrate the efficacy of our method through the implementation of diabatic CZ and iSWAP gates with fidelities of $99.61\pm0.04\%$ and $99.82\pm0.02\%$, respectively, as well as a series of diabatic CPhase gates with high fidelities characterized by cross-entropy benchmarking. The consistency and robustness of our technique are further validated by the reduction in pulse distortion and phase error observed across multilayer CZ gates. These results underscore the potential of our calibration and predistortion method to enhance the performance of two-qubit gates in superconducting quantum processors., Comment: 16 pages, 11 figures, 7 tables

Motived by the accumulated experimental results on three-body charmed $B$ decays with resonance contributions in Babar, LHCb and Belle (II), we systematically analyze $B_{(s)} \to D_{(s)} (V \to) P_1 P_2 $ decays with $V$ representing a vector resonance ($\rho, K^*, \omega$ or $\phi$) and $P_{1,2}$ as a light pseudoscalar meson (pion or kaon). The intermediate subprocesses $B_{(s)} \to D_{(s)} V$ are calculated with the factorization-assisted topological-amplitude (FAT) approach and the intermediate resonant states $V$ described by the relativistic Breit-Wigner distribution successively decay to $P_1 P_2$ via strong interaction. Taking all lowest resonance states ($\rho, K^*, \omega, \phi$) into account, we calculate the branching fractions of these decay modes as well as the Breit-Wigner-tail effects for $B_{(s)} \to D_{(s)} (\rho ,\omega \to) KK$. Our results agree with the data by Babar, LHCb and Belle (II). Among the predictions that are still not observed, there are some branching ratios of order $10^{-6}-10^{-4}$ which are hopeful to be measured by LHCb and Belle II. Our approach and the perturbative QCD approach (PQCD) adopt the compatible theme to deal with the resonance contributions. What's more, our data for the intermediate two-body charmed $B$-meson decays in FAT approach are more precise. As a result, our results for branching fractions have smaller uncertainties, especially for color-suppressed emission diagram dominated modes., Comment: 23 pages, 2 figures

High-order topological phases of matter refer to the systems of $n$-dimensional bulk with the topology of $m$-th order, exhibiting $(n-m)$-dimensional boundary modes and can be characterized by topological pumping. Here, we experimentally demonstrate two types of second-order topological pumps, forming four 0-dimensional corner localized states on a 4$\times$4 square lattice array of 16 superconducting qubits. The initial ground state of the system for half-filling, as a product of four identical entangled 4-qubit states, is prepared using an adiabatic scheme. During the pumping procedure, we adiabatically modulate the superlattice Bose-Hubbard Hamiltonian by precisely controlling both the hopping strengths and on-site potentials. At the half pumping period, the system evolves to a corner-localized state in a quadrupole configuration. The robustness of the second-order topological pump is also investigated by introducing different on-site disorder. Our work studies the topological properties of high-order topological phases from the dynamical transport picture using superconducting qubits, which would inspire further research on high-order topological phases.

Thouless pumping, a dynamical version of the integer quantum Hall effect, represents the quantized charge pumped during an adiabatic cyclic evolution. Here we report experimental observations of nontrivial topological pumping that is induced by disorder even during a topologically trivial pumping trajectory. With a 41-qubit superconducting quantum processor, we develop a Floquet engineering technique to realize cycles of adiabatic pumping by simultaneously varying the on-site potentials and the hopping couplings. We demonstrate Thouless pumping in the presence of disorder and show its breakdown as the strength of disorder increases. Moreover, we observe two types of topological pumping that are induced by on-site potential disorder and hopping disorder, respectively. Especially, an intrinsic topological pump that is induced by quasi-periodic hopping disorder has never been experimentally realized before. Our highly controllable system provides a valuable quantum simulating platform for studying various aspects of topological physics in the presence of disorder.

We analyze quasi-two-body charmless $B$ decays $B_{(s)} \to P_1 V \to P_1 P_2 P_3$ with $V$ representing a vector resonant, and $P_{1,2,3}$ as a light pseudo-scalar meson, pion, kaon or $\eta^{(\prime)}$. The intermediate processes $B_{(s)} \to P_1 V $ are calculated in the factorization-assisted topological-amplitude approach and the vector resonant effects are described by the Breit-Wigner propagator, which successively decay to $P_1 P_2$ via strong interaction. Taking into account of all vector resonances in ground state, $\rho, K^*, \omega, \phi$, we present the related branching fractions, and calculate the virtual effects for $B_{(s)} \to \pi, K (\rho ,\omega \to) KK$. We also predict direct $\it{CP}$ asymmetries of three body B decay modes with $\rho, K^*$ resonances as intermediate states. Our predicted branching fractions of decay modes dominated by the color-favored tree diagram or the color-favored penguin diagram are consistent with the perturbative QCD approach's predictions as well as QCD factorization approach. While for those nonperturbative contribution dominated decay modes, the branching ratios in this work are in better agreement with current experimental data than the PQCD predictions and the QCD factorization results due to their shortage of the nonperturbative contributions or $1/m_b$ power corrections. Many of the decays channels, especially for direct $\it{CP}$ asymmetries, are waiting for the future experiments., Comment: 28 pages, 2 figures

Motivated by a dynamical enhancement of the electromagnetic corrections by a power of $\Lambda_{\mathrm{QCD}}/m_b$ in $B_{d,s}\, \to\, \mu^+\, \mu^-$ at next-to-leading order (NLO), we extend the QED factorization effects on the leptonic $B$ meson decays with light muon leptons to tauonic final states, $B_{d,s} \, \to\, \tau^+\, \tau^-$, using soft-collinear effective theory (SCET). This extension is necessary owing to the appearance of the large $\tau$ mass, which will lead to different power counting in SCET and also different results. We provide a complete NLO electromagnetic corrections to $B_{d,s} \, \to\, \tau^+\, \tau^-$, which include hard functions and hard-collinear functions below the bottom quark mass scale $\mu_b$. The power enhanced electromagnetic effects from hard-collinear contributions on $B_{d,s}\, \to\, \mu^+\, \mu^-$ discussed before also exist in $B_{d,s} \, \to\, \tau^+\, \tau^-$. However the logarithm term arising from contributions of hard-collinear photon and lepton virtualities for $B_{d,s}\, \to\, \tau^+\, \tau^-$ is not large as it is in muon case due to the hard-collinear scale of $\tau$ mass, which lead to only approximately $0.04\%$ QED corrections to the branching fraction of $B_{d,s} \, \to\, \tau^+\, \tau^-$ compared with overall reduction about $0.5\%$ in $B_{d,s}\, \to\, \mu^+\, \mu^-$., Comment: 29 pages, 3 figures

Heavy meson decays provide an important platform for studies of both QCD and electroweak dynamics, which may contain some portals to understanding of nonperturbative QCD and physics beyond the Standard Model. The factorization-assisted topological-amplitude approach was proposed to study two-body non-leptonic $D$ meson decays, where a promising QCD inspired approach from first principles is still missing. It was also applied to $B$ meson decays whose subleading power contributions are difficult to calculate. By factorizing topological amplitudes into short distance Wilson coefficients and long distance hadronic matrix elements either to be calculated or to be parameterized, it provides an effective framework to extract information of nonperturbative dynamics involved. With important flavor SU(3) breaking effects taken into account, the data of the decay branching ratios (and also CP asymmetries in $B$ decays) can be fitted well. The extracted amplitudes were further applied to make predictions for other observables, such as CP asymmetries in $D$ decays, mixing parameters in the $D^0-\bar{D}^0$ system, and so on. By this review, we will describe the formulation of the factorization-assisted topological-amplitude approach and summarize its applications in $D$ and $B$ meson decays and highlight some of its achievements., Comment: Invited review paper for the special issue "Heavy Flavor Physics and CP Violation" of Advances in High Energy Physics