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Relational Quantum Circuit Compilation via Tensor Networks

Jincheng Zhang

Published Sep 3, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.22274880

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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 compilation is a critical step in realizing quantum computation, aiming to translate high-level quantum algorithms into a sequence of gates executable on a specific quantum hardware. However, traditional compilation methods often struggle with the inherent complexities of quantum circuits, including their high dimensionality, susceptibility to noise, and the diverse characteristics of different quantum devices. This work proposes a novel approach to adaptive quantum circuit compilation that leverages the power of tensor networks (TNs) and reinforcement learning (RL). The core idea is to represent quantum circuits as TNs, dynamically adjusting the network's structure to capture the relevant circuit features while minimizing computational overhead and mitigating noise effects. A reinforcement learning agent is trained to iteratively construct and refine these TN representations, guided by feedback signals derived from circuit fidelity metrics and computational cost estimates. This dynamic adaptation allows for a more efficient and robust compilation process, potentially leading to improved performance and reduced error rates in quantum computations. The key contribution lies in the integration of TNs with RL for a self-optimizing compilation pipeline. This approach offers a promising direction for tackling the challenges inherent in quantum hardware limitations and diverse quantum device architectures.
Quantum circuit compilation is a crucial step in realizing quantum algorithms on near-term quantum hardware. Traditional compilation methods often employ static circuit representations, limiting their ability to adapt to the fluctuating coherence properties and connectivity constraints of actual quantum devices. This research introduces a novel approach utilizing tensor network representations for dynamic quantum circuit compilation. The core idea is to leverage the inherent entanglement and superposition present in quantum systems to create adaptive circuit layouts. Our method employs an iterative tensor network algorithm that continuously refines circuit representations, prioritizing coherence preservation and minimizing gate count, while incorporating real-time qubit state estimations. This dynamic adaptation directly addresses the challenges posed by the limitations of current quantum hardware, offering a pathway to more efficient and robust quantum algorithm execution. The key innovation lies in the application of tensor networks, a powerful mathematical tool, to the optimization problem of quantum circuit compilation.
Quantum circuits, fundamental to quantum computation, represent quantum states through a sequence of unitary transformations. The exponential growth in the Hilbert space dimension with increasing circuit size presents a significant challenge to simulation and analysis. This work introduces a novel tensor network approach to formally model and manipulate quantum circuits, specifically designed to mitigate this exponential scaling issue. The core idea is to represent the circuit's state vector as a tensor network, leveraging techniques for efficient compression and expansion. We explore the application of variational tensor networks (VTNs) to approximate the dynamics of quantum circuits, offering a pathway towards more scalable simulations. The effectiveness of this method is demonstrated through theoretical analysis and conceptual design, focusing on key aspects of tensor network construction and manipulation tailored to quantum circuit representations. This approach aims to provide a more scalable representation compared to existing methods.
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Quantum circuit compilation is a crucial step in transforming a high-level quantum algorithm description into a sequence of gates executable on a specific quantum hardware platform. Traditional compilation methods predominantly focus on minimizing gate count and circuit depth, often overlooking the significant impact of quantum coherence on the overall fidelity of the computation. This paper introduces an adaptive quantum circuit compilation algorithm designed to mitigate this limitation. The algorithm dynamically analyzes the coherence properties of the quantum circuit during the compilation process, aiming to preserve coherence while simultaneously minimizing detrimental decoherence effects. This approach represents a fundamental shift in the compilation paradigm, directly addressing the critical challenge of coherence maintenance in quantum computing. The proposed methodology utilizes a novel metric for coherence analysis and employs an adaptive optimization strategy to achieve superior circuit fidelity compared to conventional compilation techniques. The effectiveness of the algorithm is demonstrated through theoretical analysis and a detailed explanation of its components, paving the way for more robust and accurate quantum circuit implementations.