Tangent Space Excitation Ansatz for Quantum Circuits

Computing the excitation spectra of quantum many-body systems on noisy quantum devices is a promising avenue to demonstrate the practical utility of current quantum processors, especially as we move toward the ``megaquop'' regime. For this task, here we introduce a \textit{tangent-space excitation ansatz} for quantum circuits, motivated by the quasi-particle picture of many-body systems and the structural similarity between quantum circuits and classical tensor networks. Increasing the circuit depth by one layer to construct the tangent space around the variational optimum of a parametrized quantum circuit, we show that a large number of low-energy states can be accurately captured. We demonstrate this ansatz using various models in both one and two spatial dimensions, including the challenging kagome Heisenberg antiferromagnet. We further provide evidence that this approach, implementable using Hadamard test, is stable in the presence of measurement noise and scalable to large system size.在含噪量子器件上计算量子多体系统的激发谱，是展现当前量子处理器实用价值的颇具前景的路径，尤其当我们迈向「兆库普（megaquop）」时代之际。针对该任务，本文基于多体系统的准粒子图像，以及量子电路与经典张量网络间的结构相似性，提出了一款面向量子电路的切空间激发试探方案（tangent-space excitation ansatz）。通过在参数化量子电路的变分最优解周围新增一层电路以构建切空间，我们证明该方案可精准捕获大量低能态。我们通过一维和二维空间下的多款模型验证了该方案的有效性，其中包括极具挑战性的笼目海森堡反铁磁体（kagome Heisenberg antiferromagnet）。我们进一步提供证据表明，该方案可通过哈达玛测试（Hadamard test）实现，且在存在测量噪声的场景下仍保持稳定，同时可扩展至大规模系统。