The Quantum Approximate Optimization Algorithm (QAOA) by Farhi et al. is a framework for hybrid quantum/classical optimization. In this paper, we explore using QAOA for binary linear least squares; a problem that can serve as a building block of several other hard problems in linear algebra. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on the QISKIT simulator and an IBM Q 5 qubit machine. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where the result outputs produced are classical. We find promising numerical results, and point out some of the challenges involved in current-day experimental implementations of this technique on a cloud-based quantum computer.

中文翻译：

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线性代数难题的量子近似优化

Farhi 等人的量子近似优化算法 (QAOA)。是一个混合量子/经典优化的框架。在本文中，我们探索使用 QAOA 进行二元线性最小二乘；一个可以作为线性代数中其他几个难题的构建块的问题。以前在量子计算中解决这些问题的大部分工作都是使用量子退火范式完成的。对于这项工作，我们的实验是在 QISKIT 模拟器和 IBM Q 5 量子位机上完成的。我们强调了使用 QAOA 和类似 QAOA 的变分算法来解决此类问题的可能性，其中产生的结果输出是经典的。我们发现了有希望的数值结果，