Understanding the capabilities of classical simulation methods is key to identifying where quantum computers are advantageous. Not only does this ensure that quantum computers are used only where necessary, but also one can potentially identify subroutines that can be offloaded onto a classical device. In this work, we show that it is always possible to generate a classical surrogate of a sub-region (dubbed a "patch") of an expectation landscape produced by a parameterized quantum circuit. That is, we provide a quantum-enhanced classical algorithm which, after simple measurements on a quantum device, allows one to classically simulate approximate expectation values of a subregion of a landscape. We provide time and sample complexity guarantees for a range of families of circuits of interest, and further numerically demonstrate our simulation algorithms on an exactly verifiable simulation of a Hamiltonian variational ansatz and long-time dynamics simulation on a 127-qubit heavy-hex topology.

翻译：理解经典模拟方法的能力是确定量子计算机优势所在的关键。这不仅确保量子计算机仅在必要场景下使用，还可能识别出可卸载至经典设备执行的子程序。本研究表明，对于参数化量子电路产生的期望值景观（expectation landscape）的子区域（称为"局部块"），总能生成其经典代理模型。具体而言，我们提出一种量子增强经典算法：通过在量子设备上进行简单测量，即可经典模拟景观子区域的近似期望值。我们为多类重要电路族提供了时间和样本复杂度保证，并进一步通过数值实验验证了模拟算法：在哈密顿变分拟设的精确可验证模拟中，以及在127量子比特重六边形拓扑结构上的长时间动力学模拟中均进行了演示。