论文标题
用于解决线性代数问题的量子退火如何可行？
How viable is quantum annealing for solving linear algebra problems?
论文作者
论文摘要
随着量子计算的日益普及，特别是量子退火，越来越多的研究来评估线性代数的各种问题的元效力：从线性最小二乘到矩阵到矩阵和张量分解。这项工作的核心是评估解决线性最小二乘和线性方程式的量子退火。在这项工作中，我们专注于使用量子退火解决这些问题的可行性。我们使用基于绝热原理的模拟为先前观察到的现象提供了新的见解，例如，量子退火对方程不良的条件系统具有鲁棒性，并且可以很好地缩放系统中的行数。然后，我们提出了一种混合方法，该方法使用量子退火器来提供解决方案$ x_0 $的初始猜测，然后使用经典的固定点迭代方法进行迭代改进。
With the increasing popularity of quantum computing and in particular quantum annealing, there has been growing research to evaluate the meta-heuristic for various problems in linear algebra: from linear least squares to matrix and tensor factorization. At the core of this effort is to evaluate quantum annealing for solving linear least squares and linear systems of equations. In this work, we focus on the viability of using quantum annealing for solving these problems. We use simulations based on the adiabatic principle to provide new insights for previously observed phenomena with the D-wave machines, such as quantum annealing being robust against ill-conditioned systems of equations and scaling quite well against the number of rows in a system. We then propose a hybrid approach which uses a quantum annealer to provide a initial guess of the solution $x_0$, which would then be iteratively improved with classical fixed point iteration methods.
