利用量子储层计算中的对称性
Exploiting Symmetry in Quantum Reservoir Computing
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中文总结 AI 辅助
研究量子储层计算中对称性的利用，提出可观测轨道补全方法，通过对齐编码、动力学、测量和读出四个接口来提升循环预测任务的性能。
中文摘要 AI 辅助
对称性是一种强大的归纳偏置，但在量子储层计算（QRC）中，仅通过使储层对称并不能施加对称性。QRC通过固定的量子动力学将输入映射为非线性期望值特征，并仅训练经典读出层，因此相关对称性必须在测量的特征图中可见。我们研究循环预测任务，例如围绕涡轮机的传感器或沿纬度圈的气象站，其中相同的局部模式应通过相同的规则进行预测，无论它出现在环上的哪个位置。因此，将输入旋转一个位置应使预测场旋转，而非改变。我们证明，对称哈密顿量是不够的：即使是大规模的泡利测量集，如果其通道与数据对称性不匹配，也可能失败，因为优化无法恢复从未测量过的通道。我们通过可观测轨道补全来解决这一问题，该方法测量与对称性相关的可观测通道，并对齐编码、动力学、测量和读出。最强的增益来自同时对齐所有四个接口，匹配的自旋环、真实天气和IBM硬件检查支持相同的测量跨度机制。
英文摘要
Quantum reservoir computing (QRC) uses a quantum processor without training it. The input is encoded into a quantum state, a fixed random circuit evolves it, selected observables are measured, and only a simple linear readout is trained on the measured values. We study QRC for forecasting on a ring of sensors, such as weather stations around a circle of latitude. On such a ring, the same physical rule governs every position, so a model that respects this symmetry can learn one shared local rule from all sensors at once instead of a separate rule per sensor. This is especially valuable when data is scarce. Because the readout sees only the measured numbers, the symmetry can be lost even when the quantum state respects it. We show how to preserve the symmetry by measuring every observable together with all its shifted copies and by using one shared rule for encoding, circuit, and readout, and we prove that this construction is sufficient. In a controlled audit the aligned design consistently outperforms misaligned alternatives, and the advantage persists in noisy simulations, on IBM hardware, and on real weather data.
