度条件退火偏移重塑最小顶点覆盖的认证最优采样

中文摘要 AI 辅助

量子退火器对简并最优解的采样可能不均匀，因此在寻求多个解时，有限读取输出的组成至关重要。我们研究了问题结构能否通过节点相关的退火偏移来引导这种输出，以解决最小顶点覆盖（MVC）问题。在MVC中，顶点度数等于其关联的边覆盖约束数量，因此度量了局部约束参与度。我们利用这一关系定义了度条件偏移调度量子退火（DC-OSQA），这是一种静态规则，为具有更大最大归一化度数的顶点分配更负的偏移。实验使用了D-Wave Advantage2系统1量子处理单元（QPU）。对于每个图，DC-OSQA与使用相同MVC编码、固定物理嵌入、多数投票链解码和1000次读取预算的零偏移基线进行了比较。只有当采样的比特串表示一个可行的顶点覆盖，且其基数与整数线性规划独立认证的最小基数相匹配时，该采样比特串才被计为认证候选。在稀疏的Barabasi-Albert图（每个新增顶点附带两个连接，图大小N=70-150）上的120次配对比较中，DC-OSQA将不同认证候选的平均数量从171.7增加到455.8，并将完全连接汉明距离族的平均数量从22.5增加到80.0；在每个测试大小下，配对增益均为正。这些变化连同较低的实证集中度，表明观测到的认证支持集的组成发生了变化。在N=150时，度对齐分配在20个图中的19个图中，认证支持集大小超过了相同偏移值的20次随机重新分配内的实例内平均值，而汉明距离族在所有20个图中均超过。在测试的集合内，这些结果表明，针对MVC的度规则改变了在固定QPU读取预算内观测到的认证最优解。

英文摘要

Quantum annealers can sample degenerate optima unevenly, so the composition of finite-read output matters when multiple solutions are sought. We investigate whether problem structure can steer this output through node-dependent anneal offsets for Minimum Vertex Cover (MVC). In MVC, vertex degree equals the number of incident edge-cover constraints and therefore measures local constraint participation. We use this relation to define degree-conditioned offset-scheduled quantum annealing (DC-OSQA), a static rule assigning more negative offsets to vertices with larger max-normalized degree. Experiments used a D-Wave Advantage2 system1 quantum processing unit (QPU). For each graph, DC-OSQA was compared with a zero-offset baseline using the same MVC encoding, fixed physical embedding, majority-vote chain decoding, and 1000-read budget. A sampled bitstring was counted as a certified candidate only if it represented a feasible vertex cover and its cardinality matched the minimum independently certified by integer linear programming. Across 120 paired comparisons on sparse Barabasi-Albert graphs with two attachments per added vertex and graph sizes N = 70-150, DC-OSQA increased the mean number of distinct certified candidates from 171.7 to 455.8 and the mean number of complete-linkage Hamming-distance families from 22.5 to 80.0; paired gains were positive at every tested size. These shifts, together with lower empirical concentration, indicate a change in the composition of the observed certified support. At N = 150, the degree-aligned assignment exceeded the within-instance mean over 20 random reassignments of the same offset values in 19 of 20 graphs for certified-support size and all 20 graphs for Hamming families. Within the tested ensemble, these results show that an MVC-specific degree rule changes the certified optima observed within a fixed QPU read budget.

发表机构

• Yonsei University（延世大学）
• University of Cambridge（剑桥大学）

机构由 AI 辅助整理，请以论文原文为准。