论文标题
神经网络优化问题的量子退火：通过张量网络模拟的一种新方法
Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations
论文作者
论文摘要
量子退火（QA）是量子优化的最有希望的框架之一。在这里，我们关注的问题是最大程度地减少与原型离散神经网络有关的复杂经典成本功能，特别是范式Hopfield模型和二元感知。我们表明，质量保证的绝热时间演变可以有效地表示为合适的张量网络。这种表示允许简单的经典模拟，适合精确的对角线化技术的小小的小尺寸。我们表明，以矩阵乘积状态（MP）表示的优化状态可以重铸到量子电路中，量子电路的深度仅与系统大小线性地缩放，并与MPS键尺寸四倍地缩放。这可能代表一个有价值的起点，允许在近期量子设备上进行进一步的电路优化。
Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.
