用于稀疏连接量子退火器上VQE测量缩减的Pauli字符串分组
Pauli-string grouping for VQE measurement reduction on a sparse-connectivity quantum annealer
- Quantum Technologies Department, ITECAM（ITECAM量子技术部）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本研究将VQE测量缩减中的Pauli字符串分组问题建模为QUBO着色模型，在D-Wave量子退火器上评估其可扩展性，量化嵌入开销并确定硬件可行性阈值。
中文摘要 AI 辅助
变分量子本征求解器（VQE）需要大量测量来评估分子哈密顿量。将分子哈密顿量表示为Pauli字符串的线性组合会产生测量瓶颈：非对易的Pauli字符串无法同时测量。因此，必须将对易的Pauli字符串分组并一起测量，以最小化量子态制备的次数。该任务映射为对易图上的最小团覆盖问题，这是一个NP难问题，通常使用经典启发式算法解决。尽管最近已在全连接CMOS Ising机器上探索了Ising模型公式，并仅在物理量子退火器上进行了小规模演示，但控制其在稀疏连接硬件上行为的嵌入成本（其中每个逻辑变量必须由一串物理量子比特表示）尚未被表征。在本工作中，我们将Pauli分组问题表述为标准QUBO着色模型，并研究其在D-Wave量子退火器上的可扩展性。在一系列分子系统中，对于量子比特级和完全对易两种情况，我们量化了逻辑变量数量和QUBO交互密度的增长，表征了在Zephyr拓扑上嵌入所需的物理量子比特和链长开销，并将退火器的求解时间和解质量与启发式经典基线进行了比较。该分析确定了分子复杂度的阈值，超过该阈值硬件连接性会阻止可行的嵌入，并表明第二个实际限制会更早达到。因此，该阈值衡量了当前退火器距离在硬件上预优化VQE测量方案值得考虑的体制还有多远。
英文摘要
The Variational Quantum Eigensolver (VQE) requires a large number of measurements to evaluate molecular Hamiltonians. Expressing a molecular Hamiltonian as a linear combination of Pauli strings creates a measurement bottleneck: non-commuting Pauli strings cannot be measured simultaneously. Consequently, mutually commuting Pauli strings must be grouped and measured together to minimise the number of quantum-state preparations. This task maps to the minimum clique cover problem on a commutativity graph, an NP-hard problem typically addressed using classical heuristics. Although an Ising-model formulation has recently been explored on fully connected CMOS Ising machines and demonstrated on physical quantum annealers only at small scale, the embedding cost that governs its behaviour on hardware with sparse connectivity, where each logical variable must be represented by a chain of physical qubits, has not been characterised. In this work, we formulate the Pauli-grouping problem as a standard QUBO colouring model and study its scalability on a D-Wave quantum annealer. Across a series of molecular systems and for both qubit-wise and full commutativity, we quantify the growth in the number of logical variables and the QUBO interaction density, characterise the physical-qubit and chain-length overhead required for embedding on the Zephyr topology, and compare the annealer's time-to-solution and solution quality with those of heuristic classical baselines. This analysis identifies the threshold of molecular complexity beyond which hardware connectivity prevents viable embedding, and shows that a second, practical limit is reached earlier. The threshold therefore measures how far current annealers are from the regime in which pre-optimising a VQE measurement scheme on hardware would be worth considering.
