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

TL;DR

ZX-db addresses scalable quantum circuit compilation by leveraging ZX-calculus as a rewrite framework implemented inside a graph database. It encodes ZX rules as openCypher queries and runs on Memgraph, translating circuits to ZX diagrams via PyZX to enable database-native transformations. Correctness is validated via tensor-network and graph-isomorphism checks, and performance is benchmarked against PyZX, showing up to an order-of-magnitude speedup for independent rewrites and revealing pattern-matching bottlenecks in current graph databases. The work evidences a data-management-oriented direction for quantum software pipelines and outlines future improvements like DAG support and broader rewrite coverage.

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.

Figures (16)

• Figure 1: A random circuit generated with Qiskit
• Figure 2: Compiled circuit in Fig. \ref{['fig:example_circuit']}
• Figure 3: Generators for $Z$- and $X$-spiders with phase $\alpha$
• Figure 4: Identity removal
• Figure 5: Spiders with the same color can be fused and their phases add