Controllable coupling between a nanomechanical resonator and a coplanar-waveguide resonator via a superconducting flux qubit

We study a tripartite quantum system consisting of a coplanar-waveguide (CPW) resonator and a nanomechanical resonator (NAMR) connected by a flux qubit, where the flux qubit has a large detuning from both resonators. By a unitray transformation and a second-order approximation, we obtain a strong and controllable (i.e., magnetic-field-dependent) effective coupling between the NAMR and the CPW resonator. Due to the strong coupling, vacuum Rabi splitting can be observed from the voltage-fluctuation spectrum of the CPW resonator. We further study the properties of single photon transport as inferred from the reflectance or equivalently the transmittance. We show that the reflectance and the corresponding phase shift spectra both exhibit doublet of narrow spectral features due to vacuum Rabi splitting. By tuning the external magnetic field, the reflectance and the phase shift can be varied from 0 to 1 and $-\pi$ to $\pi$, respectively. The results indicate that this hybrid quantum system can act as a quantum router.Comment: 8 pages, 6 figure

Reward Teaching for Federated Multi-armed Bandits

Most of the existing federated multi-armed bandits (FMAB) designs are based on the presumption that clients will implement the specified design to collaborate with the server. In reality, however, it may not be possible to modify the clients' existing protocols. To address this challenge, this work focuses on clients who always maximize their individual cumulative rewards, and introduces a novel idea of ``reward teaching'', where the server guides the clients towards global optimality through implicit local reward adjustments. Under this framework, the server faces two tightly coupled tasks of bandit learning and target teaching, whose combination is non-trivial and challenging. A phased approach, called Teaching-After-Learning (TAL), is first designed to encourage and discourage clients' explorations separately. General performance analyses of TAL are established when the clients' strategies satisfy certain mild requirements. With novel technical approaches developed to analyze the warm-start behaviors of bandit algorithms, particularized guarantees of TAL with clients running UCB or epsilon-greedy strategies are then obtained. These results demonstrate that TAL achieves logarithmic regrets while only incurring logarithmic adjustment costs, which is order-optimal w.r.t. a natural lower bound. As a further extension, the Teaching-While-Learning (TWL) algorithm is developed with the idea of successive arm elimination to break the non-adaptive phase separation in TAL. Rigorous analyses demonstrate that when facing clients with UCB1, TWL outperforms TAL in terms of the dependencies on sub-optimality gaps thanks to its adaptive design. Experimental results demonstrate the effectiveness and generality of the proposed algorithms.Comment: Accepted to IEEE Transactions on Signal Processin

5-(2-Methyl-5-nitro­phen­yl)-1H-tetra­zole

In the title compound, C8H7N5O2, the benzene ring makes a dihedral angle of 45.7 (2)° with the tetra­zole ring. In the crystal structure, the mol­ecules are linked into a chain running along the a axis by N—H⋯N hydrogen bonds, and the chains are linked through π–π inter­actions between the tetra­zole rings [centroid–centroid distance = 3.450 (2) Å]

N-(1H-1,2,4-Triazol-5-yl)pyridine-2-carboxamide

In the structure of the title compound, C8H7N5O, the pyridine ring and the imidazole ring are nearly coplanar, making a dihedral angle of 2.97 (15)°. An intra­molecular N—H⋯O hydrogen bond occurs. In the crystal mol­ecules are connected by inter­molecular hydrogen bonds and π–π stacking inter­actions between neighboring imidazole rings [centroid–centroid distance = 3.5842 (5) Å and off-set angle = 21.77°], leading to the formation of a two-dimensional supra­molecular sheet