Contraction Heuristics for Tensor Decision Diagrams.

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.