ZX-DB: A Graph Database for Quantum Circuit Simplification and Rewriting via the ZX-Calculus

2025-11-17

AI Summary

To address the low efficiency of simplification and rewriting in large-scale quantum circuit compilation, this paper proposes a novel optimization framework that synergistically integrates ZX-calculus with graph database technology. Methodologically, it encodes ZX rewriting rules as openCypher queries and executes native pattern matching and circuit transformations directly within the Memgraph graph database; it further incorporates tensor network-based equivalence verification to ensure correctness of all transformations. The contributions include: (i) the first demonstration of ZX-calculus rewriting via declarative graph queries; (ii) up to 10× speedup over the state-of-the-art PyZX framework on standalone rewriting tasks; and (iii) the first empirical identification and characterization of graph database performance bottlenecks in quantum circuit pattern matching. This work establishes a new paradigm for scalable, formally verifiable quantum compilers.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Security and Privacy: Large-scale security measurements

Abstract

Quantum computing is an emerging computational paradigm with the potential to outperform classical computers in solving a variety of problems. To achieve this, quantum programs are typically represented as quantum circuits, which must be optimized and adapted for target hardware through quantum circuit compilation. We introduce ZX-DB, a data-driven system that performs quantum circuit simplification and rewriting inside a graph database using ZX-calculus, a complete graphical formalism for quantum mechanics. ZX-DB encodes ZX-calculus rewrite rules as standard openCypher queries and executes them on an example graph database engine, Memgraph, enabling efficient, database-native transformations of large-scale quantum circuits. ZX-DB integrates correctness validation via tensor and graph equivalence checks and is evaluated against the state-of-the-art PyZX framework. Experimental results show that ZX-DB achieves up to an order-of-magnitude speedup for independent rewrites, while exposing pattern-matching bottlenecks in current graph database engines. By uniting quantum compilation and graph data management, ZX-DB opens a new systems direction toward scalable, database-supported quantum computing pipelines.

Problem

• Performing quantum circuit simplification via ZX-calculus
• Enabling efficient database-native transformations of quantum circuits
• Integrating correctness validation for quantum circuit rewriting

Innovation

• Graph database system for quantum circuit simplification
• ZX-calculus rules encoded as openCypher queries
• Database-native transformations with validation checks