AI 中文总结
本文提出CAMERA方法，在里德堡原子阵列上以远低于传统CNF编码的原子成本实现Circuit-SAT编码，验证了全加器等算术块的编码并完成端到端实例求解，为求解组合问题提供了新路径。
AI 中文摘要
里德堡原子阵列通过阻塞机制天然编码最大权独立集（MWIS）问题，因此一旦电路可满足性问题（Circuit-SAT）被归约为MWIS，便可在该平台上实现。传统的Circuit-SAT在里德堡原子阵列中的编码通过合取范式（CNF）进行，会产生大量原子开销。本文提出CAMERA（Circuit-SAT Atom-efficient MWIS Encoding for Rydberg Arrays，面向里德堡阵列的Circuit-SAT高效MWIS编码方法），该方法针对阵列的王点子图几何结构提供Circuit-SAT实例的MWIS编码。CAMERA将每个逻辑门表示为紧凑的加权小工具，并借助受超大规模集成电路（VLSI）设计启发的布局布线编译器组装这些小工具。在随机多门基准测试中，直接编码路径相比CNF路径的原子成本平均降低$22.4 \boldsymbol{\times} 1.8$倍。为验证该编码可从单个加权小工具扩展至多门算术块，本文编译了全加器和乘法器，通过精确经典基态计算对照其完整真值表完成验证。本文还展示了端到端求解一个代表性Circuit-SAT实例的过程：从门级编译开始，对编码后的30原子实例执行硬件兼容退火协议的闭系统张量网络模拟，直至读出满足赋值。这些结果确立了一套完整的编码与模拟工作流，作为原理验证，也为在里德堡原子阵列上求解更广泛的组合问题提供了具体路径。
英文摘要
Rydberg atom arrays natively encode the maximum-weight independent set (MWIS) problem through the blockade mechanism, so the Boolean circuit satisfiability problem (Circuit-SAT) can be brought onto the platform once it is reduced to MWIS. The conventional encoding of Circuit-SAT in the Rydberg atom array proceeds through conjunctive normal form (CNF) and incurs a substantial atom overhead. We introduce CAMERA (Circuit-SAT Atom-efficient MWIS Encoding for Rydberg Arrays), a method that provides MWIS encodings of Circuit-SAT instances on the king subgraph geometry of the array. CAMERA represents each logic gate as a compact weighted gadget and assembles the gadgets with a placement and routing compiler inspired by very large scale integration (VLSI) design. On random multi-gate benchmarks, the direct encoding route lowers the atom cost relative to the CNF route by an average factor of $22.4 \pm 1.8$. To demonstrate that the encoding extends from individual weighted gadgets to multi-gate arithmetic blocks, we compile a full adder and a multiplier, verifying each against its complete truth table by exact classical ground state calculations. We further showcase solving a representative Circuit-SAT instance end-to-end, from gate level compilation through a closed-system tensor-network simulation of a hardware-compatible annealing protocol on the encoded 30-atom instance to readout of a satisfying assignment. These results establish a complete encoding and simulation workflow as a proof of principle, and a concrete route toward solving a broader family of combinatorial problems on Rydberg atom arrays.
