具有编码数据结构的可解释量子回归算法
Explainable quantum regression algorithm with encoded data structure
AI总结：
本文构建了首个可解释的量子回归算法，通过量子态精确编码经典数据表并使变分参数直接对应实数回归系数，实现了高可解释性与低优化成本，并利用编码数据结构降低计算复杂度，支持非线性扩展。
摘要：
混合变分量子算法（VQAs）有望在含噪量子计算机上解决实际问题，如组合优化、量子化学模拟、量子机器学习和量子纠错。然而，使用典型的随机拟设或量子交替算子拟设，导出的变分量子算法变成了一个无法信任以进行模型解释的黑盒，更不用说部署为应用以指导关键决策：这些变分参数的结果仅仅是量子门的旋转角度，与模型可以直接提供的可解释值无关。在本文中，我们构建了首个可解释的量子回归算法，其中量子态精确编码了经典数据表，且变分参数直接对应于回归系数，这些系数在构造上为实数，提供了高度的模型可解释性，并且由于适当的表达能力，优化成本极低。我们还利用编码数据结构来降低计算回归映射的时间复杂度。为了缩短非线性回归的电路深度，我们的算法可以通过经典预处理构建非线性特征作为独立编码列向量进行扩展。尽管作者最近已通过较低噪声的压缩编码实现了超导量子比特中的压缩编码，我们仍设想通过在中性冷原子和离子中实现多量子比特门来获得潜在的量子效用。
英文摘要：
Hybrid variational quantum algorithms (VQAs) are promising for solving practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers. However, with typical random ansatz or quantum alternating operator ansatz, derived variational quantum algorithms become a black box that cannot be trusted for model interpretation, not to mention deploying as applications in informing critical decisions: the results of these variational parameters are just rotational angles for the quantum gates and have nothing to do with interpretable values that a model can provide directly. In this paper, we construct the first interpretable quantum regression algorithm, in which the quantum state exactly encodes the classical data table and the variational parameters correspond directly to the regression coefficients, which are real numbers by construction, providing a high degree of model interpretability and minimal cost to optimize due to the right expressiveness. We also take advantage of the encoded data structure to reduce the time complexity of computing the regression map. To shorten the circuit depth for nonlinear regression, our algorithm can be extended by building nonlinear features by classical preprocessing as the independent encoded column vectors. Even though the realization of compressed encoding in superconducting qubits has been achieved by the less noisy compressed encoding recently by the authors, we envision potential quantum utilities with multi-qubit gates implemented in neutral cold atoms and ions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
