发表机构
University of Seoul; Singularity Quantum Inc.; Sogang University（首尔大学; 奇点量子公司; 延世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对无固有对称性约束的特征值问题，引入码空间恢复方法，通过双轨表示编码使违规可检测修复，结合自洽恢复，经伊辛模型测试，虽电路开销增加，但能降低投影里兹能量，扩展了基于样本的量子对角化应用范围。
AI 中文摘要
基于样本的量子对角化（SQD）在由量子样本构建的紧凑子空间中对哈密顿量进行对角化，其性能通常依赖于利用诸如粒子数对称性等固有约束的恢复过程。然而，对于一大类特征值问题，不存在类似的约束，限制了SQD型恢复的适用性。在此，我们引入码空间恢复，它通过编码而非在目标问题中假设可恢复结构来设计可恢复结构。使用双轨表示，每个逻辑量子比特映射到一个物理对，$|0\rangle \to |01\rangle$且$|1\rangle \to |10\rangle$，使有噪声样本中的码空间违规可检测和修复。我们将此编码与自洽恢复相结合，并在具有多达36个自旋位点的横向和混合场伊辛模型上进行基准测试。尽管电路开销增加，但即使在较小的投影基维度下，码空间恢复产生的投影里兹能量也比未编码的样本支持对角化更低，这表明设计的可恢复结构可以将SQD扩展到超越固有约束的范围。
英文摘要
Quantum algorithms that sample basis states and diagonalize a Hamiltonian in their span depend on repairing noisy measurement outcomes, using a constraint native to the target problem$\unicode{x2014}$typically particle-number symmetry. Many eigenvalue problems possess no such constraint. Here we show that the constraint can instead be engineered into the sampling representation. Using dual-rail encoding, $|0\rangle\to|01\rangle$ and $|1\rangle\to|10\rangle$, we implement sampling operations in encoded form, making code-space violations local recovery signals for self-consistent, reference-based repair. On transverse- and mixed-field Ising models of up to 36 spin sites, which lack a $U(1)$ symmetry usable for recovery, code-space recovery reached lower Ritz energies than diagonalization over the full observed support of matched unencoded samples while using 38-84% fewer basis states, despite a twofold qubit overhead. The margin was largest for the two-dimensional and 36-site systems and was already present in the first recovery iteration. Recoverable structure can be engineered rather than inherited.
Comments18 pages, 4 figures; supplementary information provided as an ancillary file
