标题： 基于量子初级数的子空间扩展：用于高效量子测量的短路酉变换线性组合 显示英文标题

标题： Quantum Seniority-based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for Efficient Quantum Measurements

摘要： 量子 SENiority 基础子空间扩展（Q-SENSE）是一种混合量子经典算法，它在变分量子本征求解器（VQE）和组态相互作用（CI）方法之间进行插值。它在量子设备上构建哈密顿矩阵元素，并在经典上解决由此产生的本征值问题。这种基于seniority对称性的方法通过将较低的电路复杂度与需要计算额外矩阵元素的需求进行交换，减少了近期内量子硬件上VQE的主要限制之一——电路深度。与其他基于展开的方法不同，如量子子空间扩展（QSE）、量子Krylov子空间扩展和非正交量子本征求解器，Q-SENSE利用对称性诱导的正交性在不同的对称性子空间中构建基态。这不仅保证了正交性，还减少了必须测量的哈密顿项的数量，因为许多项在不同的对称性子空间之间为零。通过系统地将对称性原理与基于矩阵的技术相结合，Q-SENSE为在近期量子设备和早期容错阶段实现量子优势提供了一种可扩展且资源高效的潜在途径。 显示英文摘要

摘要： Quantum SENiority-based Subspace Expansion (Q-SENSE) is a hybrid quantum-classical algorithm that interpolates between the Variational Quantum Eigensolver (VQE) and Configuration Interaction (CI) methods. It constructs Hamiltonian matrix elements on a quantum device and solves the resulting eigenvalue problem classically. This seniority-symmetry-based approach reduces one of the primary limitations of VQE on near-term quantum hardware - circuit depth - by exchanging lower circuit complexity for the need to compute additional matrix elements. Unlike other expansion-based methods - such as Quantum Subspace Expansion (QSE), Quantum Krylov Subspace Expansion, and the Non-orthogonal Quantum Eigensolver - Q-SENSE leverages symmetry-induced orthogonality to construct basis states in distinct symmetry sectors. This not only guarantees orthogonality but also reduces the number of Hamiltonian terms that must be measured, as many terms are zero between different symmetry subspaces. By systematically combining symmetry principles with matrix-based techniques, Q-SENSE offers a scalable and resource-efficient potential route to quantum advantage on near-term quantum devices and in the early fault-tolerant regime.