Approximability of Connected Factors

Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte's reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard - finding a minimal connected 2-factor is just the traveling salesman problem (TSP). Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected $d$-factor. We give a 3-approximation for all $d$ and improve this to an (r+1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r+1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP. Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.Comment: To appear in the proceedings of WAOA 201

Giant Nonlinear Optical Activity from Planar Metasurfaces

Second harmonic generation circular dichroism (CD) is more sensitive to the handedness of chiral materials than its linear optical counterpart. In this work, we show that 3D chiral structures are not necessary for introducing strong CD for harmonic generations. Specifically, we demonstrate giant CD for both second harmonic generation and third harmonic generation on suitably designed ultrathin plasmonic metasurfaces. It is experimentally and theoretically verified that the overwhelming contribution to this nonlinear CD is of achiral origin. The results shed new light on the origin of the nonlinear CD effect in achiral planar surfaces

Flip-chip-based fast inductive parity readout of a planar superconducting island

Properties of superconducting devices depend sensitively on the parity (even or odd) of the quasiparticles they contain. Encoding quantum information in the parity degree of freedom is central in several emerging solid-state qubit architectures. Yet, accurate, non-destructive, and time-resolved parity measurement is a challenging and long-standing issue. Here we report on control and real-time parity measurement in a superconducting island embedded in a superconducting loop and realized in a hybrid two-dimensional heterostructure using a microwave resonator. Device and readout resonator are located on separate chips, connected via flip-chip bonding, and couple inductively through vacuum. The superconducting resonator detects the parity-dependent circuit inductance, allowing for fast and non-destructive parity readout. We resolved even and odd parity states with signal-to-noise ratio SNR $\approx3$ with an integration time of $20~\mu$s and detection fidelity exceeding 98%. Real-time parity measurement showed state lifetime extending into millisecond range. Our approach will lead to better understanding of coherence-limiting mechanisms in superconducting quantum hardware and provide novel readout schemes for hybrid qubits

Zeeman and Orbital Driven Phase Transitions in Planar Josephson Junctions

We perform supercurrent and tunneling spectroscopy measurements on gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field, and report on phase shifts in the current-phase relation measured with respect to an absolute phase reference. The impact of orbital effects is investigated by studying multiple devices with different superconducting lead sizes. At low fields, we observe gate-dependent phase shifts of up to ${\varphi_{0}=0.5\pi}$ which are consistent with a Zeeman field coupling to highly-transmissive Andreev bound states via Rashba spin-orbit interaction. A distinct phase shift emerges at larger fields, concomitant with a switching current minimum and the closing and reopening of the superconducting gap. These signatures of an induced phase transition, which might resemble a topological transition, scale with the superconducting lead size, demonstrating the crucial role of orbital effects. Our results elucidate the interplay of Zeeman, spin-orbit and orbital effects in InAs/Al JJs, giving new understanding to phase transitions in hybrid JJs and their applications in quantum computing and superconducting electronics

Spin-degeneracy breaking and parity transitions in three-terminal Josephson junctions

Harnessing spin and parity degrees of freedom is of fundamental importance for the realization of emergent quantum devices. Nanostructures embedded in superconductor--semiconductor hybrid materials offer novel and yet unexplored routes for addressing and manipulating fermionic modes. Here we spectroscopically probe the two-dimensional band structure of Andreev bound states in a phase-controlled hybrid three-terminal Josephson junction. Andreev bands reveal spin-degeneracy breaking, with level splitting in excess of 9 GHz, and zero-energy crossings associated to ground state fermion parity transitions, in agreement with theoretical predictions. Both effects occur without the need of external magnetic fields or sizable charging energies and are tuned locally by controlling superconducting phase differences. Our results highlight the potential of multiterminal hybrid devices for engineering quantum states

Dipeptidyl peptidase IV (DPP IV) inhibitory activity screening of Momordica charantia, Taraxacum officinale and Trigonella foenum-graecumextracts in vitro

Diabetes, a globally popular disease which attracted the attention of many researches worldwide to discover a non-toxic and side effect free remedy for this disease. Inhibition of DPP IV enzymes has been adopted as one of the strategies in recent years in controlling diabetes. DPP IV inhibitor inhibits the dipeptidyl peptidase enzyme which degrades several incretin hormones that are vital in the production of insulin and managing the blood glucose level.Thus, the present study was designed to investigate the DPP IV inhibitory effects of plants having antidiabetic property. In vitro DPP IV inhibition was evaluated by the specific inhibitory activity of Momordica charantia (whole fruit), Taraxacum officinale (whole plant) and Trigonella foenum-graecum (seed) extracts prepared with heat treatment using petroleum ether, acetone, ethanol and water as solvents. Among the tested plants T. officinale and M. charantia acetone extracts exhibited strong DPP IV activity inhibition, with 78.88% and 54.13% respectively. The present study is the first report on screening of DPP IV inhibitory activity of T. officinale, M. charantiaand T. foenum-graecum extracts. This could provide a new insight into DPP IV inhibitors from plants that could be useful for treatment of type 2 diabetes