Title: Spectral subspace extraction via incoherent quantum phase estimation Show Chinese title

Title: 通过非相干量子相位估算的谱子空间提取

Abstract: Quantum phase estimation (QPE) is a cornerstone algorithm for extracting Hamiltonian eigenvalues, but its standard form targets individual eigenstates and requires carefully prepared coherent inputs. To overcome these limitations, we adopt an ensemble-based formulation of QPE that estimates the density of states (DOS) of the Hamiltonian generator of the evolution. This approach, which we refer to as DOS-QPE, builds on a prior formulation introduced by one of the authors. In this work, we present DOS-QPE as a circuit primitive, extending it with symmetry-adapted input ensembles and advanced spectrum reconstruction techniques. This variant of QPE enables natural access to thermodynamic properties, symmetry-resolved spectral functions, and features relevant to quantum many-body systems. We demonstrate its performance on fermionic models and nuclear Hamiltonians by casting the spectrum reconstruction problem as a quadratic program solved via compressed sensing. These use cases highlight the potential of DOS-QPE for early fault-tolerant quantum simulations in spectroscopy, electronic structure, and nuclear theory. Show Chinese abstract

Abstract: 量子相位估计（QPE）是提取哈密顿量本征值的核心算法，但其标准形式针对单个本征态，并需要精心准备的相干输入。为了克服这些限制，我们采用了一种基于集合的QPE公式，该公式估计演化哈密顿量生成器的状态密度（DOS）。这种方法，我们称之为DOS-QPE，建立在作者之一之前提出的公式基础上。在本工作中，我们将DOS-QPE作为电路原语进行展示，并通过对称适应的输入集合和先进的光谱重构技术对其进行扩展。这种QPE变体能够自然地访问热力学性质、对称性分辨的光谱函数以及与量子多体系统相关的特性。我们通过将光谱重构问题转化为通过压缩感知求解的二次规划问题，在费米子模型和核哈密顿量上展示了其性能。这些用例突显了DOS-QPE在光谱学、电子结构和核理论中早期容错量子模拟中的潜力。