Finite edge-transitive dihedrant graphs

AbstractIn this paper, we first prove that each biquasiprimitive permutation group containing a regular dihedral subgroup is biprimitive, and then give a classification of such groups. The classification is then used to classify vertex-quasiprimitive and vertex-biquasiprimitive edge-transitive dihedrants. Moreover, a characterization of valencies of normal edge-transitive dihedrants is obtained, and some classes of examples with certain valences are constructed

Quantum Approximate Optimization Algorithm in Non-Markovian Quantum Systems

Quantum Approximate Optimization Algorithm(QAOA) is a promising quantum algorithm that can demonstrate quantum supremacy. The performance of QAOA on noisy intermediate-scale quantum (NISQ) devices degrades due to decoherence. In this paper, we present a framework for running QAOA on non-Markovian quantum systems which are represented by an augmented system model. In this model, a non-Markovian environment is modelled as an ancillary system driven by quantum white noises and the corresponding principal system is the computational unit for the algorithm. With this model, we mathematically formulates QAOA as piecewise control of the augmented system. To reduce the effect of non-Markovian decoherence, the above basic algorithm is modified for obtaining an efficient depth by a proximal gradient descent algorithm. Finally, in an example of the Max-Cut problem, we find non-Markovianity can help to achieve a good performance of QAOA, which is characterized by an exploration rate.Comment: 13 pages, 7 figure

Quantum simulation of ZnO nanowire piezotronics

We address the problem of quantum transport in a nanometre sized two-terminal ZnO device subject to an external strain. The two junctions formed between the electrodes and the ZnO are generally taken as Ohmic and Schottky type, respectively. Unlike the conventional treatment to the piezopotential, we treat it as a potential barrier which is only induced at the interfaces. By calculating the transmission coefficient of a Fermi-energized electron that flows from one end to the other, it is found that the piezopotential has the effect of modulating the voltage threshold of the current flowing. The calculations are based on the quantum scattering theory. The work is believed to pave the way for investigating the quantum piezotronics

Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition

Over the past few decades, tremendous efforts have been devoted to understanding self-duality at the quantum critical point, which enlarges the global symmetry and constrains the dynamics. In this letter, we employ large-scale density matrix renormalization group simulations to investigate the critical spin chain with long-range interaction $V(r) \sim 1/r^{\alpha}$. Remarkably, we reveal that the long-range interaction drives the deconfined criticality towards a first-order phase transition as $\alpha$ decreases. More strikingly, the emergent self-duality leads to an emergent symmetry and manifests at these first-order critical points. This discovery is reminiscent of self-duality protected multicritical points and provides the example of the critical line with generalized symmetry. Our work has far-reaching implications for ongoing experimental efforts in Rydberg atom quantum simulators.Comment: 5 + 10 pages, 9 figures. Any comments or suggestions are welcome

Local to Global: A Distributed Quantum Approximate Optimization Algorithm for Pseudo-Boolean Optimization Problems

With the rapid advancement of quantum computing, Quantum Approximate Optimization Algorithm (QAOA) is considered as a promising candidate to demonstrate quantum supremacy, which exponentially solves a class of Quadratic Unconstrained Binary Optimization (QUBO) problems. However, limited qubit availability and restricted coherence time challenge QAOA to solve large-scale pseudo-Boolean problems on currently available Near-term Intermediate Scale Quantum (NISQ) devices. In this paper, we propose a distributed QAOA which can solve a general pseudo-Boolean problem by converting it to a simplified Ising model. Different from existing distributed QAOAs' assuming that local solutions are part of a global one, which is not often the case, we introduce community detection using Louvian algorithm to partition the graph where subgraphs are further compressed by community representation and merged into a higher level subgraph. Recursively and backwards, local solutions of lower level subgraphs are updated by heuristics from solutions of higher level subgraphs. Compared with existing methods, our algorithm incorporates global heuristics into local solutions such that our algorithm is proven to achieve a higher approximation ratio and outperforms across different graph configurations. Also, ablation studies validate the effectiveness of each component in our method.Comment: 12 pages, 6 figure

A New ZrCuSiAs-Type Superconductor: ThFeAsN

We report the first nitrogen-containing iron-pnictide superconductor ThFeAsN, which is synthesized by a solid-state reaction in an evacuated container. The compound crystallizes in a ZrCuSiAs-type structure with the space group P4/nmm and lattice parameters a=4.0367(1) {\AA} and c=8.5262(2) {\AA} at 300 K. The electrical resistivity and dc magnetic susceptibility measurements indicate superconductivity at 30 K for the nominally undoped ThFeAsN.Comment: 6 pages, 4 figures, 1 tabl