arXiv:2502.05264quant-phcs.AI2025-02被引 8

提出无梯度量子学习新方法,可证明收敛且解释性强。

Quantum automated learning with provable and explainable trainability

  • 用量子态演化替代参数优化,通过单元操作编码数据并迭代演进。
  • 在合理假设下证明训练过程指数级收敛至全局最优解。
  • 适用于大规模量子机器学习,适合关注可证明性与可解释性的研究者。

机器学习被认为是量子计算最具前景的实际应用之一。现有量子机器学习方案多采用依赖参数梯度的量子-经典混合方法,缺乏全局最优收敛保证,且在模型规模扩大时将不可行。本文提出量子自动学习,完全不涉及变分参数,将训练过程转化为量子态制备。具体地,将训练数据编码为单元操作,对随机初始态交替施加这些单元操作及其逆操作,并在中间插入面向目标的扰动以提升预测精度。在合理假设下,严格证明该演化过程能指数级收敛至对应损失函数全局最小的期望量子态。从虚时间演化视角看,数据编码单元操作与目标扰动协同实现模型自动化训练。进一步证明该范式具有良好的泛化能力,泛化误差上界由希尔伯特空间维数的对数函数与训练样本数之比决定。我们在真实图像和量子数据上进行了大量数值模拟,验证了方法的有效性与假设合理性。结果建立了一种无梯度、可证明且可解释的量子学习新策略,对量子计算在机器学习中的大规模实际应用至关重要。

原文摘要 · Abstract (English)

Machine learning is widely believed to be one of the most promising practical applications of quantum computing. Existing quantum machine learning schemes typically employ a quantum-classical hybrid approach that relies crucially on gradients of model parameters. Such an approach lacks provable convergence to global minima and will become infeasible as quantum learning models scale up. Here, we introduce quantum automated learning, where no variational parameter is involved and the training process is converted to quantum state preparation. In particular, we encode training data into unitary operations and iteratively evolve a random initial state under these unitaries and their inverses, with a target-oriented perturbation towards higher prediction accuracy sandwiched in between. Under reasonable assumptions, we rigorously prove that the evolution converges exponentially to the desired state corresponding to the global minimum of the loss function. We show that such a training process can be understood from the perspective of preparing quantum states by imaginary time evolution, where the data-encoded unitaries together with target-oriented perturbations would train the quantum learning model in an automated fashion. We further prove that the quantum automated learning paradigm features good generalization ability with the generalization error upper bounded by the ratio between a logarithmic function of the Hilbert space dimension and the number of training samples. In addition, we carry out extensive numerical simulations on real-life images and quantum data to demonstrate the effectiveness of our approach and validate the assumptions. Our results establish an unconventional quantum learning strategy that is gradient-free with provable and explainable trainability, which would be crucial for large-scale practical applications of quantum computing in machine learning scenarios.

量子机器学习无梯度训练可证明性状态制备

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