论文标题
量子启发的搜索方法，用于古典伊辛岛的低能状态
Quantum-inspired search method for low-energy states of classical Ising Hamiltonians
论文作者
论文摘要
我们开发了一种量子启发的数值程序，用于搜索由两体完全连接的随机ISING相互作用和随机局部纵向磁场组成的经典哈密顿量的低能状态。在这种方法中，我们引入了无限的量子相互作用，这些相互作用不与原始的Ising Hamiltonian通勤，并反复生成和截断直接产物状态，灵感来自Krylov子空间方法，以获得原始经典的Issing Ising Hamiltonian的低能状态。计算成本受到无穷小量子相互作用的形式（例如，一身或两体相互作用）以及引入了不同的初始状态以及在迭代期间保持的低能状态的无限相互作用项的数量。为了证明该方法，我们将其作为无限量子交互作用对Pauli $ x $运算符的无限量子交互产品，这些产品在不同的站点和现场Pauli $ x $运算符上作用于随机的Ising Hamiltonian，其中数值成本为$ O（N^3），每个ITITERANION，系统尺寸为$ n $ n $ n $ n $。我们考虑120个随机耦合实现的实例，用于随机的Ising Hamiltonian，$ n $最高600美元，并为每个实例搜索120个最低能量的状态。我们发现，这里提出的量子启发方法的时间溶液，与不同的初始状态有关，用于搜索随机的伊斯丁·哈密顿量表的基础状态，大约为$ n^5 $ for $ n $ for $ n $ to $ n $ 600。我们还检查了基本的物理特性，例如基本的物理特性，例如随机的范围和首先要验证的范围，并在随机的情况下，以随机的态度和最低态度的数量来看，以实现随机的范围。 Ising Hamiltonian。
We develop a quantum-inspired numerical procedure for searching low-energy states of a classical Hamiltonian composed of two-body fully-connected random Ising interactions and a random local longitudinal magnetic field. In this method, we introduce infinitesimal quantum interactions that do not commute with the original Ising Hamiltonian, and repeatedly generate and truncate direct product states, inspired by the Krylov subspace method, to obtain the low-energy states of the original classical Ising Hamiltonian. The computational cost is controlled by the form of infinitesimal quantum interactions (e.g., one-body or two-body interactions) and the numbers of infinitesimal interaction terms introduced, different initial states considered, and low-energy states kept during the iteration. For a demonstrate of the method, here we introduce as the infinitesimal quantum interactions pair products of Pauli $X$ operators acting on different sites and on-site Pauli $X$ operators into the random Ising Hamiltonian, in which the numerical cost is $O(N^3)$ per iteration with the system size $N$. We consider 120 instances of the random coupling realizations for the random Ising Hamiltonian with $N$ up to 600 and search the 120 lowest-energy states for each instance. We find that the time-to-solution by the quantum-inspired method proposed here, with parallelization in terms of the different initial states, for searching the ground state of the random Ising Hamiltonian scales approximately as $N^5$ for $N$ up to 600. We also examine the basic physical properties such as the ensemble-averaged ground-state and first-excited energies and the ensemble-averaged number of states in the low-energy region of the random Ising Hamiltonian.
