Quantum circuit synthesis is a crucial task in quantum computing, aiming to transform a given high-level logic quantum operation into a sequence of elementary quantum gates. Traditional synthesis methods often rely on special characteristics of quantum operations or complex mathematical operations. While effective, they tend to incur high computational costs because they do not fully exploit the underlying structure of the quantum operation. In this work, we introduce a novel synthesis approach leveraging the LimTDD (Local Invertible Map Tensor Decision Diagram) data structure, known for its high compression efficiency and ability to identify isomorphic structures within tensors.By utilising LimTDD, our algorithm achieves efficient synthesis for specific types of quantum circuits, significantly reducing computational overhead. Moreover, the ability to extract isomorphic operators allows for reducing the entanglements, making our method particularly effective in accelerating other synthesis algorithms. We demonstrate the efficacy of our approach through experiments, showing substantial improvements in gate count and synthesis time compared to existing methods. Our work not only provides a powerful tool for quantum circuit synthesis but also highlights the potential of LimTDD in advancing the field of quantum computing.

Quantum state preparation is a fundamental task in quantum computing and quantum information processing. With the rapid advancement of quantum technologies, efficient quantum state preparation has become increasingly important. This paper proposes a novel approach for quantum state preparation based on the Local Invertible Map Tensor Decision Diagram (LimTDD). LimTDD combines the advantages of tensor networks and decision diagrams, enabling efficient representation and manipulation of quantum states. Compared with the state-of-the-art quantum state preparation method, LimTDD demonstrates substantial improvements in efficiency when dealing with complex quantum states, while also reducing the complexity of quantum circuits. Examples indicate that, in the best-case scenario, our method can achieve exponential efficiency gains over existing methods. This study not only highlights the potential of LimTDD in quantum state preparation but also provides a robust theoretical and practical foundation for the future development of quantum computing technologies.

Abstract We present QReach, the first reachability analysis tool for quantum Markov chains based on decision diagrams CFLOBDD (presented at CAV 2023). QReach provides a novel framework for finding reachable subspaces, as well as a series of model-checking subprocedures like image computation. Experiments indicate its practicality in verification of quantum circuits and algorithms. QReach is expected to play a central role in future quantum model checkers.