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基于二元决策图的大模型驱动量子电路综合算法设计

文章背景与核心概要

本文介绍了 QuantumEvo，这是一个利用大语言模型（LLM）自动为量子电路综合中的二元决策图（BDD）变量排序生成启发式算法的进化框架。传统的基于 BDD 的综合方法通常通过最小化 BDD 大小来减小电路规模，但 BDD 大小并不是量子成本感知电路（QCC）指标的完美代理。QuantumEvo 通过下游的 QCC 性能评估，在多个启发式函数族中进行搜索。最终发现的启发式算法（HGA-QE）修改了遗传算法内部的筛选步骤，使其与 QCC 目标更加契合。它在标准基准测试中取得了 70.9% 的平局或胜率，并在分布外（out-of-domain）基准测试集中展现出显著的优越性。

文章背景与核心概要

本文介绍了 QuantumEvo，这是一个利用大语言模型（LLM）自动为量子电路综合中的二元决策图（BDD）变量排序生成启发式算法的进化框架。传统的基于 BDD 的综合方法通常通过最小化 BDD 大小来减小电路规模，但 BDD 大小并不是量子成本感知电路（QCC）指标的完美代理。QuantumEvo 通过下游的 QCC 性能评估，在多个启发式函数族中进行搜索。最终发现的启发式算法（HGA-QE）修改了遗传算法内部的筛选步骤，使其与 QCC 目标更加契合。它在标准基准测试中取得了 70.9% 的平局或胜率，并在分布外（out-of-domain）基准测试集中展现出显著的优越性。

LLM-Driven Algorithm Design for Quantum Circuit Synthesis based on Binary Decision Diagrams

LLM-Driven Algorithm Design for Quantum Circuit Synthesis based on Binary Decision Diagrams

Summary

Summary

This paper introduces QuantumEvo, an evolutionary framework that leverages Large Language Models (LLMs) to automatically generate heuristics for Binary Decision Diagram (BDD) variable ordering in quantum circuit synthesis. While traditional BDD-based synthesis minimizes BDD size to reduce circuit size, BDD size remains an imperfect proxy for Quantum Cost-aware Circuit (QCC) metrics. QuantumEvo searches over multiple heuristic families using downstream QCC performance for evaluation. The resulting discovered heuristic (HGA-QE) modifies the sifting step inside a genetic algorithm to align more closely with QCC, achieving a 70.9% tie-or-win rate across standard benchmarks and showing notable superiority on out-of-domain benchmark suites.

This paper introduces QuantumEvo, an evolutionary framework that leverages Large Language Models (LLMs) to automatically generate heuristics for Binary Decision Diagram (BDD) variable ordering in quantum circuit synthesis. While traditional BDD-based synthesis minimizes BDD size to reduce circuit size, BDD size remains an imperfect proxy for Quantum Cost-aware Circuit (QCC) metrics. QuantumEvo searches over multiple heuristic families using downstream QCC performance for evaluation. The resulting discovered heuristic (HGA-QE) modifies the sifting step inside a genetic algorithm to align more closely with QCC, achieving a 70.9% tie-or-win rate across standard benchmarks and showing notable superiority on out-of-domain benchmark suites.

Paper Metadata

Paper Metadata

  • arXiv ID: arXiv:2609.05327
  • Primary Subject: Artificial Intelligence (cs.AI)
  • Secondary Subject: Hardware Architecture (cs.AR)
  • Submission Date: September 4, 2026
  • Authors:
  • Yoonju Sim
  • Federico Berto
  • Chuanbo Hua
  • Jinkyoo Park
  • Changhyun Kwon
  • arXiv ID: arXiv:2609.05327
  • Primary Subject: Artificial Intelligence (cs.AI)
  • Secondary Subject: Hardware Architecture (cs.AR)
  • Submission Date: September 4, 2026
  • Authors:
  • Yoonju Sim
  • Federico Berto
  • Chuanbo Hua
  • Jinkyoo Park
  • Changhyun Kwon

Abstract

Abstract

Quantum circuits are central to implementing quantum algorithms on quantum devices, where quantum gates must be reversible. Many quantum algorithms rely on Boolean functions, which must therefore be implemented reversibly within quantum circuits. Reversible circuit synthesis provides a way to translate such Boolean functions into reversible circuits.

Quantum circuits are central to implementing quantum algorithms on quantum devices, where quantum gates must be reversible. Many quantum algorithms rely on Boolean functions, which must therefore be implemented reversibly within quantum circuits. Reversible circuit synthesis provides a way to translate such Boolean functions into reversible circuits.

Binary decision diagrams (BDDs) offer a scalable approach to this task, but the resulting BDDs and circuits depend heavily on variable ordering. Existing ordering heuristics commonly minimize BDD size because it is closely tied to the circuit size. However, BDD size is an imperfect proxy for the quantum cost of the synthesized circuit (QCC).

Binary decision diagrams (BDDs) offer a scalable approach to this task, but the resulting BDDs and circuits depend heavily on variable ordering. Existing ordering heuristics commonly minimize BDD size because it is closely tied to the circuit size. However, BDD size is an imperfect proxy for the quantum cost of the synthesized circuit (QCC).

We propose QuantumEvo, an evolutionary framework that uses an LLM as a heuristic generator for QCC-aware BDD variable ordering. Instead of predicting orderings directly, QuantumEvo searches over ordering heuristics initialized from multiple heuristic families. Candidate heuristics directly manipulate variable orderings using standard BDD operations and are selected by downstream QCC.

We propose QuantumEvo, an evolutionary framework that uses an LLM as a heuristic generator for QCC-aware BDD variable ordering. Instead of predicting orderings directly, QuantumEvo searches over ordering heuristics initialized from multiple heuristic families. Candidate heuristics directly manipulate variable orderings using standard BDD operations and are selected by downstream QCC.

The discovered heuristic, HGA-QE, modifies the sifting step inside a genetic algorithm so that the procedure is better aligned with QCC. Across the benchmark set, HGA-QE achieves a 70.9% tie-or-win rate against the per-function best baseline and is strictly best on 13.5% of the functions. The results demonstrate broadly competitive QCC performance, with HGA-QE showing a clearer relative advantage in strict wins on the two benchmark suites drawn from sources different from the data used for heuristic discovery.

The discovered heuristic, HGA-QE, modifies the sifting step inside a genetic algorithm so that the procedure is better aligned with QCC. Across the benchmark set, HGA-QE achieves a 70.9% tie-or-win rate against the per-function best baseline and is strictly best on 13.5% of the functions. The results demonstrate broadly competitive QCC performance, with HGA-QE showing a clearer relative advantage in strict wins on the two benchmark suites drawn from sources different from the data used for heuristic discovery.