Complete Characterization of the Ground Space Structure of Two-Body Frustration-Free Hamiltonians for Qubits

The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is always a ground state that is a product of single- or two-qubit states. However, it remains unclear whether the whole ground space is of any succinct structure. Here, we give a complete characterization of the ground space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a span of tree tensor network states of the same tree structure. This characterization allows us to show that the problem of determining the ground state degeneracy is as hard as, but no harder than, its classical analog.Comment: 5pages, 3 figure

Quantum Capacity Approaching Codes for the Detected-Jump Channel

The quantum channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known. Given the quantum capacity of a degradable channel, it remains challenging to find a practical coding scheme which approaches capacity. Here we discuss code designs for the detected-jump channel, a degradable channel with practical relevance describing the physics of spontaneous decay of atoms with detected photon emission. We show that this channel can be used to simulate a binary classical channel with both erasures and bit-flips. The capacity of the simulated classical channel gives a lower bound on the quantum capacity of the detected-jump channel. When the jump probability is small, it almost equals the quantum capacity. Hence using a classical capacity approaching code for the simulated classical channel yields a quantum code which approaches the quantum capacity of the detected-jump channel

STAR-RIS Enabled Heterogeneous Networks: Ubiquitous NOMA Communication and Pervasive Federated Learning

This paper integrates non-orthogonal multiple access (NOMA) and over-the-air federated learning (AirFL) into a unified framework using a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). The STAR-RIS plays an important role in adjusting the decoding order of hybrid users for efficient interference mitigation and omni-directional coverage extension. To capture the impact of non-ideal wireless channels on AirFL, a closed-form expression for the optimality gap (a.k.a. convergence upper bound) between the actual loss and the optimal loss is derived. This analysis reveals that the learning performance is significantly affected by active and passive beamforming schemes as well as wireless noise. Furthermore, when the learning rate diminishes as the training proceeds, the optimality gap is explicitly characterized to converge with a linear rate. To accelerate convergence while satisfying QoS requirements, a mixed-integer non-linear programming (MINLP) problem is formulated by jointly designing the transmit power at users and the configuration mode of STAR-RIS. Next, a trust region-based successive convex approximation method and a penalty-based semidefinite relaxation approach is proposed to handle the decoupled non-convex subproblems iteratively. An alternating optimization algorithm is then developed to find a suboptimal solution for the original MINLP problem. Extensive simulation results show that i) the proposed framework can efficiently support NOMA and AirFL users via concurrent uplink communications, ii) our algorithms can achieve a faster convergence rate on the IID and non-IID settings as compared to baselines, and iii) both the spectrum efficiency and learning performance can be significantly improved with the aid of the well-tuned STAR-RIS.Comment: 16 pages, 8 figure

SnTox3 Acts in Effector Triggered Susceptibility to Induce Disease on Wheat Carrying the Snn3 Gene

The necrotrophic fungus Stagonospora nodorum produces multiple proteinaceous host-selective toxins (HSTs) which act in effector triggered susceptibility. Here, we report the molecular cloning and functional characterization of the SnTox3-encoding gene, designated SnTox3, as well as the initial characterization of the SnTox3 protein. SnTox3 is a 693 bp intron-free gene with little obvious homology to other known genes. The predicted immature SnTox3 protein is 25.8 kDa in size. A 20 amino acid signal sequence as well as a possible pro sequence are predicted. Six cysteine residues are predicted to form disulfide bonds and are shown to be important for SnTox3 activity. Using heterologous expression in Pichia pastoris and transformation into an avirulent S. nodorum isolate, we show that SnTox3 encodes the SnTox3 protein and that SnTox3 interacts with the wheat susceptibility gene Snn3. In addition, the avirulent S. nodorum isolate transformed with SnTox3 was virulent on host lines expressing the Snn3 gene. SnTox3-disrupted mutants were deficient in the production of SnTox3 and avirulent on the Snn3 differential wheat line BG220. An analysis of genetic diversity revealed that SnTox3 is present in 60.1% of a worldwide collection of 923 isolates and occurs as eleven nucleotide haplotypes resulting in four amino acid haplotypes. The cloning of SnTox3 provides a fundamental tool for the investigation of the S. nodorum-wheat interaction, as well as vital information for the general characterization of necrotroph-plant interactions.This work was supported by USDA-ARS CRIS projects 5442-22000-043-00D and 5442-22000-030-00D