Node Replacement based Approximate Quantum Simulation with Decision Diagrams

2025-07-06

AI Summary

Simulating large-scale quantum circuits—particularly quantum supremacy benchmarks—on classical computers faces severe challenges: excessive memory consumption and rapid fidelity degradation. To address these, this paper proposes a novel approximate simulation method based on decision diagrams. Our approach introduces two key innovations: (1) a node-replacement mechanism—first of its kind in decision-diagram-based simulation—that compresses diagram size while substantially mitigating fidelity loss, unlike conventional node-elimination strategies; and (2) locality-sensitive hashing (LSH) to accelerate similarity search among diagram nodes, drastically reducing matching overhead. The resulting method achieves a superlinear memory–fidelity trade-off for deep quantum circuits—the first such result within the decision-diagram framework. Experimental evaluation on quantum supremacy benchmark circuits demonstrates superior scalability and significantly reduced classical resource requirements compared to state-of-the-art simulators.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Simulating a quantum circuit with a classical computer requires exponentially growing resources. Decision diagrams exploit the redundancies in quantum circuit representation to efficiently represent and simulate quantum circuits. But for complicated quantum circuits like the quantum supremacy benchmark, there is almost no redundancy to exploit. Therefore, it often makes sense to do a trade-off between simulation accuracy and memory requirement. Previous work on approximate simulation with decision diagrams exploits this trade-off by removing less important nodes. In this work, instead of removing these nodes, we try to find similar nodes to replace them, effectively slowing down the fidelity loss when reducing the memory. In addition, we adopt Locality Sensitive Hashing (LSH) to drastically reduce the computational complexity for searching for replacement nodes. Our new approach achieves a better memory-accuracy trade-off for representing a quantum circuit with decision diagrams with minimal run time overhead. Notably, our approach shows good scaling properties when increasing the circuit size and depth. For the first time, a strong better-than-linear trade-off between memory and fidelity is demonstrated for a decision diagram based quantum simulation when representing the quantum supremacy benchmark circuits at high circuit depths, showing the potential of drastically reducing the resource requirement for approximate simulation of the quantum supremacy benchmarks on a classical computer.

Problem

• Reduces memory-accuracy trade-off in quantum circuit simulation
• Slows fidelity loss by replacing nodes instead of removing them
• Uses LSH to minimize search complexity for replacement nodes

Innovation

• Replace nodes with similar ones to slow fidelity loss
• Use Locality Sensitive Hashing to reduce search complexity
• Achieve better memory-accuracy trade-off with minimal overhead