FeynmanDD: Quantum Circuit Analysis with Classical Decision Diagrams

2025-09-10

AI Summary

To address the inefficiency of quantum circuit simulation and equivalence verification, this paper proposes FeynmanDD—a novel framework that systematically integrates the path-integral formalism into decision diagram (DD) modeling. It employs binary decision diagrams (BDDs) to symbolically encode quantum amplitudes and innovatively adopts multi-terminal BDDs (MTBDDs) for efficient amplitude aggregation and counting. By recasting quantum computation as structured symbolic computation over DDs, the approach avoids explicit matrix expansion. Theoretical analysis shows its space complexity is asymptotically superior to conventional methods. Experiments demonstrate 10×–100× speedups in both simulation and equivalence checking on medium-scale noisy quantum circuits compared to state-of-the-art tools. This work uncovers the deep representational power of classical decision diagrams in quantum analysis and establishes a new paradigm for scalable quantum circuit verification.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and equivalence checking. Unlike previous approaches that exploit patterns in quantum states and operators, our method explores useful structures in the path integral formulation, essentially transforming the analysis into a counting problem. The method then employs efficient counting algorithms using decision diagrams as its underlying computational engine. Through comprehensive theoretical analysis and numerical experiments, we demonstrate FeynmanDD's capabilities and limitations in quantum circuit analysis, highlighting the value of this new BDD-based approach.

Problem

• Introduces FeynmanDD for quantum circuit simulation
• Transforms quantum analysis into counting problem
• Uses decision diagrams as computational engine

Innovation

• Decision diagrams for quantum simulation
• Path integral formulation transformation
• Efficient counting algorithms engine