面向量子-经典工作流的张量网络可满足性（SAT）求解器
Towards Tensor-Network SAT-Solvers for Quantum-Classical Workflows
浏览论文内容
中文总结 AI 辅助
本研究针对集成HPC/QC系统的需求，以张量网络基态搜索为优化代理，对比不同Max-3-SAT编码形式的性能，发现二次化会降低解质量、SA表现优于DMRG，为HPC/QC运行时的代理选择提供了经验基础。
中文摘要 AI 辅助
集成式高性能计算（HPC）/量子计算（QC）系统旨在将经典高性能计算与量子处理器结合，但其不能简化为仅调度量子核的机制。集成架构必须支持可观测性等方面（仅用量子处理单元无法实现）、回退执行，以及关于是否用经典代理替代量子任务的成本感知决策。这类机制必须是近似的，或能利用问题结构以缓解不可避免的经典最坏情况指数复杂度。本研究将张量网络基态搜索作为优化问题的代理，该方法结合了关键量子基元与先进经典模拟，为代理选择标准提供了初步经验指标，并揭示了端到端工具链效应——若孤立研究变换步骤则可能忽略这些效应。针对最大3-可满足性（Max-3-SAT），我们将原生多项式无约束优化的高阶伊辛（higher-order-Ising）形式，与二次化无约束二元优化的二次伊辛（quadratic-Ising）形式进行对比，两者均编码为矩阵乘积算符，并用密度矩阵重整化群（DMRG）方法优化，以模拟退火（SA）作为经典性能基准。结果显示，二次化并非中性变换步骤：与原生高阶表示相比，辅助变量和成对耦合会大幅降低解的质量，而在所有测试实例中SA的表现与DMRG相当或更优。由于可满足性（SAT）衍生问题的最优解是经典乘积态，DMRG的优势在此无法体现。这些发现表明，HPC/QC运行时的代理选择必须感知编码方式与实例，并为回退策略及架构协同设计的合理决策提供经验基础。
英文摘要
Integrated HPC/QC systems aim to combine classical high-performance computing with quantum processors, but cannot be reduced to mechanisms for dispatching quantum kernels. An integrated architecture must support aspects such as observability, which cannot be implemented using QPUs alone, as well as fallback execution and cost-aware decisions on whether to replace quantum tasks with classical surrogates. Such mechanisms must be approximate or benefit from problem structure to soften the inescapable exponential classical worst-case complexity. In this work, we study tensor-network ground-state search, as such a surrogate, for optimisation problems. This combines key quantum primitives with advanced classical simulation. It provides initial empirical indicators for surrogate selection criteria, and exposes end-to-end toolchain effects that may be missed when transformation steps are studied in isolation. We compare a native polynomial unconstrained optimisation to-higher-order-Ising and a quadratised quadratic unconstrained binary optimization to-quadratic-Ising formulation for Max-3-SAT. Both are encoded as matrix product operator and optimised using density matrix renormalisation group approaches, with simulated annealing (SA) as classical performance baseline. Our results show that quadratisation is not a neutral transformation step: auxiliary variables and pairwise couplings substantially degrade solution quality relative to the native higher-order representation, while SA matches or outperforms DMRG across all tested instances. Since the optima of Boolean satisfiability (SAT)-derived problems are classical product states, DMRGs advantages dont materialise here. These findings suggest that surrogate selection in HPC/QC runtimes must be encoding- and instance-aware and provide empirical groundwork for informed decisions on fallback strategies and architecture co-design.
