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Contraction Heuristics for Tensor Decision Diagrams.

Christian Bøgh Larsen¹, Simon Brun Olsen¹, Kim Guldstrand Larsen¹

¹Department of Computer Science, Aalborg University, 9220 Aalborg, Denmark.

Entropy (Basel, Switzerland)

|January 8, 2025

Summary

This summary is machine-generated.

This study introduces new tensor contraction heuristics for efficiently checking quantum circuit equivalence. Our novel methods significantly outperform existing approaches, improving the state-of-the-art in quantum computing verification.

Keywords:

contraction planning equivalence checking heuristics quantum circuit tensor decision diagram tensor network

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Area of Science:

Quantum Computing
Computational Complexity
Tensor Networks

Background:

The equivalence problem for quantum circuits is computationally challenging.
Efficiently contracting tensor networks is crucial for solving this problem.
Existing contraction heuristics struggle with tensor decision diagrams.

Purpose of the Study:

To develop efficient tensor contraction heuristics for quantum circuit equivalence checking.
To improve the performance of equivalence checking frameworks.
To address the limitations of current heuristics with tensor decision diagrams.

Main Methods:

Reducing quantum circuit equivalence to tensor network contraction.
Utilizing tensor decision diagrams for efficient tensor representation.
Proposing and implementing two novel tensor contraction heuristics.

Main Results:

The proposed heuristics outperform existing state-of-the-art methods.
Experimental validation confirms the superiority of the new heuristics.
The framework achieves state-of-the-art performance in equivalence checking.

Conclusions:

Novel tensor contraction heuristics enhance quantum circuit equivalence checking.
Tensor decision diagrams combined with new heuristics offer a powerful approach.
This work advances the verification of quantum algorithms and circuits.