arXiv:2607.07338quant-phcs.AI2026-07

用量子电路模拟复杂非线性系统,突破传统限制。

Quantum simulation of real-world nonlinear dynamics via Koopman method

论文配图:Quantum simulation of real-world nonlinear dynamics via Koopman method
图 1 · 摘自论文原文
  • 将非线性系统转为线性表示,用浅层量子电路实现演化。
  • 在超导处理器上成功模拟三类系统,最高用32条并行10量子比特电路。
  • 揭示了量子模拟性能受噪声与表示精度双重制约的边界,适合中等非线性场景。

非线性动力学广泛存在于自然界,从化学图案形成到海洋环流,但量子计算机的幺正演化特性使其模拟面临根本限制。本文提出量子柯普曼方法,一种数据驱动框架,将非线性动力学嵌入学习得到的线性表示,并通过浅层量子电路实现演化。该方法从轨迹数据学习柯普曼观测量,将提升后的动力学投影到有限维子空间,并将对应的非幺正传播算子分解为并行谱通道。我们在超导处理器上模拟了三类非线性系统:反应-扩散动力学、球面上流体运动及卫星观测的墨西哥湾流,最多使用32条并行10量子比特电路。量子模拟准确捕捉了系统的主导多尺度模式与统计特征,揭示了弱非线性系统性能受限于硬件噪声,而随着非线性尺度相互作用增强,性能转向受限于有限维柯普曼表示。这一转变界定了可被量子设备有效模拟的非线性动力学实用边界,为近中期量子硬件上模拟中等非线性系统提供了经硬件验证的路径。

原文摘要 · Abstract (English)

Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation and implements the resulting evolution using shallow quantum circuits. This method learns Koopman observables from trajectory data, projects the lifted dynamics onto a finite-dimensional subspace, and decomposes the corresponding non-unitary propagator into parallel spectral channels. We utilize the Koopman method on a superconducting processor to simulate three distinct nonlinear systems, comprising reaction-diffusion dynamics, fluid motion on a sphere, and satellite-derived observations of Gulf Stream currents, employing up to 32 parallel circuits of 10 qubits. These quantum simulations capture the dominant multiscale patterns and statistical signatures of the underlying dynamics, and reveal a transition from performance limited by hardware noise in weakly nonlinear systems to performance limited by finite-dimensional Koopman representations as nonlinear scale interactions increase. This transition identifies a practical boundary for quantum-amenable nonlinear dynamics, establishing a hardware-validated route for simulating moderately nonlinear dynamics on near-term quantum hardware.

量子模拟非线性系统柯普曼方法近中期量子

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