We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial state with non-trivial overlap with the target eigenstate and have a reasonable lower bound for the spectral gap. We apply this algorithm to the quantum linear system problem (QLSP), and present two algorithms based on quantum adiabatic computing (AQC) and quantum Zeno effect respectively. Both algorithms prepare the final solution as a pure state, and achieves the near optimal $\mathcal{\widetilde{O}}(dκ\log(1/ε))$ query complexity for a $d$-sparse matrix, where $κ$ is the condition number, and $ε$ is the desired precision. Neither algorithm uses phase estimation or amplitude amplification.
Eigenstate Preparation Through Near-Optimal Eigenprobability Filtering
Mathematical Institute, University of Oxford（牛津大学数学研究所）；Quantum Motion（量子运动）；HUN-REN Wigner Research Centre for Physics（匈牙利科学院维格纳物理研究中心）；Faculty of Informatics, Eötvös Loránd University（罗兰大学信息学院）
Dynamic Programming Principle and Stabilization for Mean-Field Quantum Filtering Systems
Université Paris-Saclay, CentraleSupélec（巴黎萨克雷大学，中央理工-高等电力学院）；University of Florida（佛罗里达大学）；CNRS, L2S, Université Paris-Saclay, CentraleSupélec（法国国家科学研究中心，L2S实验室，巴黎萨克雷大学，中央理工-高等电力学院）；Shanghai Frontiers Science Center of AI and DL NYU-ECNU Institute of Mathematical Sciences NYU Shanghai（上海人工智能前沿科学中心，纽约大学-华东师范大学数学科学研究所，纽约大学上海校区）
Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits
马约拉纳零模（Majorana zero modes，MZM）被预测为一个被称为Kitaev链的物理系统的边缘状态。MZM应该拥有自己的反粒子，并且可以用作对噪声鲁棒的量子比特的基础。然而，所有试图证明它们存在的努力都没有得出结论。在这里，Kitaev链是精确地解决了量子计算方法和MZM的性质，通过产生本征态的Kitev哈密顿量上的3个噪声量子比特的公开可用的量子计算机。经过本体论的阐述，我表明，两个本征态的Kitaev哈密顿表现出八个签名归因于MZMs。这里提供的结果是在实际物理系统中进行的最全面的MZM验证集。此外，该手稿的发现对于公开可用的量子计算机的任何用户来说都是容易重现的，解决了MZM研究的另一个重要问题-结果重现性危机。
Rodeo Filtering for Direct Steady-State Estimation in Open Quantum Systems
Seoul National University（首尔大学）；Pusan National University（釜山国立大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Kyung Hee University（庆熙大学）
Imaginary-time nonuniform mesh method for solving the multidimensional Schrodinger equation: Fermionization and melting of quantum Lennard-Jones crystals
