AI 中文总结
开发用于评估量子电路参数梯度的反向传播算法，利用泡利传播模拟，计算复杂度与标准技术相当，内存成本降低，函数评估更高效，可用于量子电路经典优化及相关复杂度度量监测正则化。
AI 中文摘要
我们开发了一种反向传播算法，用于使用泡利传播模拟来评估量子电路中的参数梯度。该方法的计算复杂度与标准稀疏泡利模拟技术相当，同时产生的梯度精度与相应可观测量期望值的精度处于同一量级。通过利用量子电路的可逆性，与传统的反向模式自动微分相比，该算法将内存成本降低了\(\mathcal{O}(n_\text{param})\)倍，其中\(n_\text{param}\)表示电路中的参数数量。与有限差分方法相比，该算法在函数评估方面效率提高了\(\mathcal{O}(n_\text{param})\)倍。这些特性使得能够对量子电路进行高效且准确的经典优化，用于诸如状态制备和时间演化压缩等应用，同时还允许在优化过程中监测和正则化诸如算子稳定器雷尼熵等算子复杂度度量。我们通过优化一维、二维和三维横向场伊辛模型以及三维海森堡模型的低能状态制备电路，以及压缩二维时间演化电路来演示该方法。
英文摘要
We develop a backpropagation algorithm for evaluating parameter gradients in quantum circuits using Pauli propagation simulation. The method has computational complexity comparable to that of standard sparse Pauli simulation techniques, while producing gradients whose accuracy is of the same order as the corresponding observable expectation values. By exploiting the reversibility of quantum circuits, the algorithm reduces the memory cost by a factor of $\mathcal{O}(n_\text{param})$ compared with conventional reverse-mode automatic differentiation, where $n_\text{param}$ denotes the number of parameters in the circuit. Compared with finite difference methods, the algorithm is $\mathcal{O}(n_\text{param})$ more efficient in function evaluations. These features enable efficient and accurate classical optimization of quantum circuits for applications such as state preparation and time-evolution compression, while also allowing operator-complexity measures such as the operator stabilizer Rényi entropy to be monitored and regularized during optimization. We demonstrate the method by optimizing low-energy state-preparation circuits for transverse-field Ising models in one, two, and three dimensions and for the three-dimensional Heisenberg model, and by compressing two-dimensional time-evolution circuits.
Comments14+6 pages, 10 figures
