Compressed representation of quantum states via orthogonal polynomials for flow field analysis

Abstract

Quantum computing promises exponential acceleration for fluid flow simulations, yet the measurement overhead required to extract classical information from the resulting quantum states fundamentally undermines this advantage—a challenge termed the “output problem”. To address this, we propose an orthogonal-polynomial-based quantum neural network (OP-QNN) that generates a compressed, low-dimensional representation of these states, enabling the efficient extraction of classical information with significantly reduced measurement overhead. Within OP-QNN, we develop an orthogonal-polynomial-based variational quantum circuit as a core component, which embeds trainable parameters into orthogonal basis transformations to enhance expressivity and generate compressed coefficients. We evaluate the compressed representation through two critical post-processing tasks on fluid flow data: reconstruction and classification, demonstrating exceptional performance in both areas. The high reconstruction fidelity confirms that the compressed data preserves the state’s global structure, while the high classification accuracy proves that it retains key discriminative features. Achieved with significantly reduced computational complexity and parameter counts compared to benchmarks, these results validate OP-QNN as an effective solution to the output problem—bridging quantum simulation outputs with practical fluid analysis and offering a scalable pathway to exploit quantum advantages in computational fluid dynamics.

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