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There has been an increasing research focus on quantum algorithms for condensed matter systems recently, particularly on calculating energy band structures. Here, we propose a quantum algorithm, the powered full quantum eigensolver(P-FQE), by using the exponentiation of operators of the full quantum eigensolver(FQE). This leads to an exponential increase in the success probability of measuring the target state in certain circumstances where the number of generating elements involved in the exponentiation of operators exhibit a log polynomial dependence on the number of orbitals. Furthermore, we conduct numerical calculations for band structure determination of the twisted double-layer graphene. We experimentally demonstrate the feasibility and robustness of the P-FQE algorithm using superconducting quantum computers for graphene and Weyl semimetal. One significant advantage of our algorithm is its ability to reduce the requirements of extremely high-performance hardware, making it more suitable for energy spectra determination on noisy intermediate-scale quantum (NISQ) devices.

The Tangle-based structure becomes one of the most promising solutions when designing DAG-based blockchain systems. The approach improves the scalability by directly confirming multiple transactions in parallel instead of single blocks in linear. However, the performance gain may bring potential security risks. In this paper, we construct three types of attacks with comprehensive evaluations, namely parasite attack (PS), double spending attack (DS), and hybrid attack (HB). To achieve that, we deconstruct the Tangle-based projects (e.g. IOTA) and abstract the main components to rebuild a simple but flexible network for the simulation. Then, we informally define three smallest actions to build up the attack strategies layer by layer. Based on that, we provide analyses to evaluate different types of attacks. To the best of our knowledge, this is the first study to provide a comprehensive security analysis of Tangle-based blockchains., Comment: Full version with 22pages. The conference version has been published at ACISP'20