论文标题
量子天然梯度的有效经典计算
Efficient classical calculation of the Quantum Natural Gradient
论文作者
论文摘要
量子天然梯度已成为量子变异算法中的最小化技术。经典地模拟在近距离量子硬件上运行的算法在其研究中至关重要，因为它适用于所有变分算法。在这种情况下，P-参数/门ANSATZ电路的状态矢量模拟不会主导运行时。取而代之的是，Fisher信息矩阵的计算成为瓶颈，涉及O（p^3）门评估，尽管可以使用O（p）临时状态矢量将其简化为O（p^2）门。这类似于梯度计算子例程的主导量子梯度下降的模拟，量子梯度下降吸引了HPC策略和定制模拟算法，并具有渐近速度。我们在这里提出了一种新颖的模拟策略，以精确计算O（p^2）门和O（1）状态向量中的量子天然梯度。尽管更复杂，但我们的策略与参考文献6中梯度的策略具有相同的精神，并且涉及迭代评估Fisher信息矩阵的经常性形式。我们的策略仅使用“应用门”，“克隆状态”和“内部产品”操作，这些操作实际上存在于所有量子计算模拟器中。此外，它与平行化方案兼容，例如硬件加速度和分布。由于我们的方案利用Fisher信息矩阵的一种形式进行严格的统一Ansatz电路，因此不能简单地扩展到具有非单身电路的量子天然梯度的密度矩阵模拟。
Quantum natural gradient has emerged as a superior minimisation technique in quantum variational algorithms. Classically simulating the algorithm running on near-future quantum hardware is paramount in its study, as it is for all variational algorithms. In this case, state-vector simulation of the P-parameter/gate ansatz circuit does not dominate the runtime; instead, calculation of the Fisher information matrix becomes the bottleneck, involving O(P^3) gate evaluations, though this can be reduced to O(P^2) gates by using O(P) temporary state-vectors. This is similar to the gradient calculation subroutine dominating the simulation of quantum gradient descent, which has attracted HPC strategies and bespoke simulation algorithms with asymptotic speedups. We here present a novel simulation strategy to precisely calculate the quantum natural gradient in O(P^2) gates and O(1) state-vectors. While more complicated, our strategy is in the same spirit as that presented for gradients in Reference 6, and involves iteratively evaluating recurrent forms of the Fisher information matrix. Our strategy uses only "apply gate", "clone state" and "inner product" operations which are present in practically all quantum computing simulators. It is furthermore compatible with parallelisation schemes, like hardware acceleration and distribution. Since our scheme leverages a form of the Fisher information matrix for strictly unitary ansatz circuits, it cannot be simply extended to density matrix simulation of quantum natural gradient with non-unitary circuits.
