Quantum neural networks (QNNs) use parameterized quantum circuits with data-dependent inputs and generate outputs through the evaluation of expectation values. Calculating these expectation values necessitates repeated circuit evaluations, thus introducing fundamental finite-sampling noise even on error-free quantum computers. We reduce this noise by introducing the variance regularization, a technique for reducing the variance of the expectation value during the quantum model training. This technique requires no additional circuit evaluations if the QNN is properly constructed. Our empirical findings demonstrate the reduced variance speeds up the training and lowers the output noise as well as decreases the number of measurements in the gradient circuit evaluation. This regularization method is benchmarked on the regression of multiple functions. We show that in our examples, it lowers the variance by an order of magnitude on average and leads to a significantly reduced noise level of the QNN. We finally demonstrate QNN training on a real quantum device and evaluate the impact of error mitigation. Here, the optimization is practical only due to the reduced number shots in the gradient evaluation resulting from the reduced variance.

翻译：量子神经网络（QNNs）使用参数化量子电路，这些电路具有数据依赖的输入，并通过期望值的评估生成输出。计算这些期望值需要重复进行电路评估，因此即使在无误差的量子计算机上也会引入基本的有限采样噪声。我们通过引入方差正则化来降低这种噪声，这是一种在量子模型训练期间减少期望值方差的技术。如果QNN构建得当，该技术无需额外的电路评估。我们的实证发现表明，降低的方差能够加速训练，降低输出噪声，并减少梯度电路评估中的测量次数。这种正则化方法在多个函数的回归任务上进行了基准测试。我们证明，在我们的示例中，它平均将方差降低了一个数量级，并显著降低了QNN的噪声水平。最后，我们在真实量子设备上演示了QNN训练，并评估了误差缓解的影响。在此，由于方差降低导致梯度评估中所需的测量次数减少，优化才得以实际实现。