论文标题
线性代数中的硬性问题的量子近似优化
Quantum Approximate Optimization for Hard Problems in Linear Algebra
论文作者
论文摘要
Farhi等人的量子近似优化算法（QAOA）。是解决量子或经典优化任务的量子计算框架。在这里，我们使用QAOA进行二进制线性最小二乘（BLL）探索；一个可以用作线性代数中其他几个硬问题的问题，例如非负二进制矩阵分解（NBMF）和其他非负矩阵分解（NMF）问题的其他变体。以前的大多数用于解决这些问题的量子计算方面的工作都是使用量子退火范式完成的。对于这项工作的范围，我们的实验是在无噪声量子模拟器，包括设备真实噪声模型的模拟器和两台IBM Q 5 Qubit机器上进行的。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，在这些问题中可以直接作为样品获得试验溶液，而不是在量子波函数中进行振幅编码。我们的数字显示，模拟退火可以在$ p \ leq3 $的QAOA深度上胜过BLL的表现，以进行采样基态的概率。最后，我们指出了该技术对基于云的量子计算机的当今实验实现所涉及的一些挑战。
The Quantum Approximate Optimization Algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for Binary Linear Least Squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the Non-negative Binary Matrix Factorization (NBMF) and other variants of the Non-negative Matrix Factorization (NMF) problem. 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 noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our numerics show that Simulated Annealing can outperform QAOA for BLLS at a QAOA depth of $p\leq3$ for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on cloud-based quantum computers.
