少数约束多数：多体量子系统的关联增强学习
A Few Constrain Many: Correlation-Enhanced Learning of Many-Body Quantum Systems
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中文总结 AI 辅助
本文证明量子可观测量间的关联可降低多体量子系统学习复杂度，利用多项式测量约束指数级未测量量，设计关联信息算法高效估计100量子比特系统的纠缠和魔法等资源，优于现有方法。
中文摘要 AI 辅助
发现多体量子系统的性质具有挑战性，因为需要确定大量参数。在此，我们证明量子可观测量之间的关联有助于降低量子学习的复杂度。多项式数量的选定测量可以约束指数多个依赖但未测量的量的值，从而实现对量子态一般函数的高效估计。我们利用这一结果设计了关联信息学习算法，用于估计100量子比特系统中诸如纠缠和魔法等关键量子资源。通过利用多项式数量的测量泡利字符串的信息，这些算法比阴影层析成像和神经态方法实现了更低的相对误差。这些协议可直接在当今量子计算机上测试，因为它们不需要测量前的纠缠门。因此，量子约束本身是探索大型量子系统的资源。
英文摘要
Discovering properties of many-body quantum systems is challenging because of the large number of parameters to determine. Here, we show that correlations among quantum observables help reduce the complexity of quantum learning. A polynomial number of selected measurements can bound the values of exponentially many dependent yet unmeasured quantities, enabling efficient estimation of general functions of quantum states. We leverage this result to design correlation-informed learning algorithms that estimate key quantum resources, such as entanglement and magic, in systems of 100 qubits. They achieve a lower relative error than shadow tomography and neural-state methods by using information about a polynomial number of measured Pauli strings. These protocols are readily testable with today's quantum computers, as they do not require premeasurement entangling gates. Quantum constraints themselves are therefore a resource for exploring large quantum systems.
发表机构
- Politecnico di Torino（都灵理工大学）
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