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Design, Automation, and Test in Europe

Quantum Circuit Synthesis Based on LimTDD

Xin Hong, Chenjian Li, Aochu Dai, Runhong He, Shenggang Ying

Published Apr 20, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.23919/date69613.2026.11539289

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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.
Tensor networks serve as a powerful tool for efficiently representing and manipulating high-dimensional data in applications such as quantum physics, machine learning, and data compression. Tensor Decision Diagrams (TDDs) offer an efficient framework for tensor representation by leveraging decision diagram techniques. However, the current implementation of TDDs and other decision diagrams fail to exploit tensor isomorphisms, limiting their compression potential. This paper introduces Local Invertible Map Tensor Decision Diagrams (LimTDDs), an extension of TDDs that incorporates local invertible maps (LIMs) to achieve more compact representations. Unlike LIMDD, which uses Pauli operators for quantum states, LimTDD employs the XPXPXP-stabilizer group, enabling broader applicability across tensor-based tasks. We present efficient algorithms for normalization, slicing, addition, and contraction, critical for tensor network applications. Theoretical analysis demonstrates that LimTDDs achieve greater compactness than TDDs and, in best-case scenarios and for quantum state representations, offer exponential compression advantages over both TDDs and LIMDDs. Experimental results in quantum circuit tensor computation and simulation confirm LimTDD's superior efficiency. Open-source code is available at https://github.com/Veriqc/LimTDD.
Quantum circuit synthesis, the process of mapping logical operations onto a quantum hardware architecture, presents a significant bottleneck in the development of practical quantum computers. Traditional methods often suffer from exponential computational complexity, rendering them unsuitable for circuits of even moderate size. This work introduces a novel approach to quantum circuit synthesis leveraging topological optimization, a technique rooted in condensed matter physics. We represent quantum circuits as topological phases on a graph, where gate operations are encoded as transitions between these phases. An iterative optimization process then refines the graph structure, minimizing circuit complexity (represented as energy) while maintaining the desired quantum operations. The core of our method lies in the application of gradient-based optimization algorithms to this topological graph, driving the system towards a low-energy state representing an optimal quantum circuit. Preliminary results demonstrate the potential of this approach to significantly reduce gate count and improve fidelity compared to conventional synthesis methods. The proposed framework offers a scalable solution to the challenges inherent in quantum circuit design, paving the way for more efficient and reliable quantum computation.
Quantum state preparation (QSP) is a fundamental task in quantum computing and quantum information processing. It is critical to the execution of many quantum algorithms, including those in quantum machine learning. In this paper, we propose a family of efficient QSP algorithms tailored to different numbers of available ancilla qubits — ranging from no ancilla qubits, to a single ancilla qubit, to a sufficiently large number of ancilla qubits. Our approach exploits the power of Local Invertible Map Tensor Decision Diagrams (LimTDDs) — a highly compact representation of quantum states that combines tensor networks and decision diagrams to reduce quantum circuit complexity. Extensive experiments demonstrate that our methods significantly outperform existing approaches and exhibit better scalability for large-scale quantum states, both in terms of runtime and gate complexity. Furthermore, our method shows exponential improvement in best-case scenarios.
Quantum circuit compilation is a critical step in realizing quantum computation, aiming to translate high-level quantum algorithms into a sequence of low-level gate operations executable on a quantum hardware. Traditional compilation methods often suffer from exponential scaling in the representation of the quantum state space, leading to prohibitive computational costs. This work introduces a novel approach to quantum circuit compilation utilizing tensor networks. We represent quantum circuits and their resulting states as higher-order tensor networks, enabling efficient manipulation and contraction of these representations. Our algorithm leverages tensor contraction and permutation techniques specifically tailored to the inherent structure of quantum circuits, minimizing the rank of the tensor networks and, consequently, reducing computational overhead. This approach offers the potential for significant speedups compared to conventional compilation techniques, addressing the core challenge of exponential scaling in quantum state representation. The method's effectiveness is demonstrated through theoretical analysis and a novel compilation algorithm.
Quantum circuit compression is a crucial step towards realizing scalable quantum computing. Current methods often rely on approximations or heuristics, leading to significant information loss and reduced circuit fidelity. This paper presents a novel adaptive approach to quantum circuit compression leveraging tensor decomposition. The core idea is to decompose the unitary evolution operators within a quantum circuit into lower-rank tensors, effectively capturing the essential dynamics while drastically reducing the circuit's complexity. The adaptive nature of the method stems from dynamically adjusting the tensor rank based on the circuit's characteristics and desired compression level. This approach minimizes information loss by intelligently selecting the rank that best represents the circuit's unitary evolution. We demonstrate the effectiveness of this method through theoretical analysis and illustrate its potential with a simplified example, showcasing the ability to achieve substantial gate count reduction without compromising circuit performance significantly. The framework offers a promising direction for reducing the resource demands of quantum algorithms and contributing to the practical realization of quantum computation.