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

TL;DR

ZX-DB introduces a graph database system leveraging ZX-calculus for efficient quantum circuit simplification and rewriting, enabling scalable quantum compilation with significant speedups over existing frameworks.

Contribution

It presents a novel database-native approach to quantum circuit optimization using ZX-calculus, integrating correctness validation and demonstrating improved performance.

Findings

ZX-DB achieves up to 10x speedup in circuit rewriting.

It exposes pattern-matching bottlenecks in graph database engines.

ZX-DB outperforms the PyZX framework in efficiency.

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.