Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolver (VQE). These coupled quantum-classical algorithms leverage the ability to perform many repeated measurements to avoid the currently prohibitive gate depths often required for exact quantum algorithms, with the restriction of a parametrized circuit to describe the states of interest. In this work, we show how the calculation of zero-temperature dynamic correlation functions defining the linear response characteristics of quantum systems can also be recast into a modified VQE algorithm, which can be incorporated into the current variational quantum infrastructure. This allows for these important physical expectation values describing the dynamics of the system to be directly converged on the frequency axis, and they approach exactness over all frequencies as the flexibility of the parametrization increases. The frequency resolution hence does not explicitly scale with gate depth, which is approximately twice as deep as a ground-state VQE. We apply the method to compute the single-particle Green's function of ab initio dihydrogen and lithium hydride molecules, and demonstrate the use of a practical active space embedding approach to extend to larger systems. While currently limited by the fidelity of two-qubit gates, whose number is increased compared to the ground-state algorithm on current devices, we believe the approach shows potential for the extraction of frequency dynamics of correlated systems on near-term quantum processors.

中文翻译：

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动态相关函数的变分量子特征求解器

最近在模拟量子多体问题中使用当前一代有噪声的量子设备的实用方法主要是使用变分量子本征求解器 (VQE)。这些耦合的量子经典算法利用执行多次重复测量的能力来避免精确量子算法通常需要的当前令人望而却步的门深度，同时限制参数化电路来描述感兴趣的状态。在这项工作中，我们展示了定义量子系统线性响应特性的零温度动态相关函数的计算如何也可以重新转换为修改后的 VQE 算法，该算法可以合并到当前的变分量子基础设施中。这允许这些描述系统动态的重要物理期望值直接收敛在频率轴上，并且随着参数化灵活性的增加，它们在所有频率上都接近精确性。因此，频率分辨率没有明确地与门深度成比例，门深度大约是基态 VQE 的两倍。我们应用该方法计算单粒子格林函数ab initio二氢和氢化锂分子，并演示使用实用的主动空间嵌入方法扩展到更大的系统。虽然目前受限于双量子位门的保真度，与当前设备上的基态算法相比，其数量有所增加，但我们相信该方法显示了在近期量子处理器上提取相关系统频率动态的潜力。