Quantum

Fast Template Matching for Quantum Circuits Using Hypergraph

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Briefings

A new hypergraph-based template matching algorithm for quantum circuits achieves 11 to 606x speed-ups over DAG-based methods in Qiskit benchmarks, while maintaining optimization quality. The approach collapses commuting gates into super-nodes to preserve local connectivity, enabling incremental updates limited to the immediate neighborhood. Results show acceleration increases with circuit size, confirming locality is key to scalability.

Key points

• The hypergraph-based template matching algorithm achieves 11 to 606x speed-ups over DAG-based methods in Qiskit benchmarks.
• The algorithm collapses commuting gates into super-nodes to preserve local connectivity, enabling incremental updates limited to the immediate neighborhood.

Context

Quantum circuit optimization is a key step toward efficient algorithm execution. Template matching is a dominant approach for simplifying circuits, but DAG-based techniques fail to preserve local connectivity, leading to high matching complexity. This paper introduces a commutativity-aware hypergraph representation that addresses these limitations.

Limitations

Experimental results are limited to Qiskit benchmarks on random and arithmetic circuits. The specific circuit sizes tested are not detailed, and the exact upper bound of the speed-up ratio (606x) is not confirmed for all cases.

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