通用纠缠见证生成器
A Universal Entanglement Witness Generator
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中文总结 AI 辅助
本文提出一种机器学习方法，可生成适用于多体量子系统的通用纠缠见证，其噪声鲁棒性优于现有方法，且已在多种量子态及不同实验平台上得到验证。
中文摘要 AI 辅助
纠缠见证是验证纠缠的关键工具，但构建兼具噪声鲁棒性与测量设置经济性的纠缠见证颇具挑战，尤其针对量子比特之外的系统及非稳定器（“ magic”）态。本文提出一种机器学习方法，给定目标态与用户指定的测量设置数量，生成仅需局域测量、针对该态邻域噪声鲁棒性优化的纠缠见证。该方法具有普适性，适用于多体量子比特与量子维数（qudit）系统，包括非稳定器态。对于维数为 d 的 N 个量子维数，我们针对每个量子维数的 SU(d) 生成元的完全可分本征态进行训练以得到原型见证，再通过梯度下降调整见证的偏置项以最大化噪声鲁棒性。对抗训练进一步增强了见证的性能，在更少设置下实现了更高的噪声鲁棒性；关键的是，该方案下所需训练集规模与系统大小无关。我们将整个流程封装为自动化脚本，在所有测试案例中，生成的见证在噪声鲁棒性和/或测量设置数量上均优于现有所有方法。我们在贝尔态、GHZ 态、W 态、超图态及一系列量子维数态上验证了该方法，涵盖 2-6 量子比特、二分量子维数至 d=10、三分 qutrit。我们的见证在物理实验测试态与大规模数值可分混合态集上均达到完美准确率，包括 3 量子比特 W 态见证的 3000 万个测试态、4 量子比特超图态见证的 1000 万个测试态；我们还分别在光子平台和超导平台上实验验证了贝尔态与超图态见证的噪声鲁棒性。
英文摘要
Entanglement witnesses are essential for certifying entanglement, yet constructing ones that are both noise-robust and economical in measurement settings remains challenging - particularly beyond qubits and for non-stabilizer ("magic") states. We present a machine-learning method that, given a target state and a user-specified number of measurement settings, generates an entanglement witness optimized for noise tolerance in the neighborhood of that state, requiring only local measurements. The approach is fully general, applying to multipartite qubit and qudit systems alike, including non-stabilizer states. For N qudits of dimension d, we train on the fully-separable eigenstates of each qudit's SU(d) generators to find a prototype witness, then tune the witness's bias term via gradient descent to maximize noise tolerance. Adversarial training further strengthens the witnesses, delivering greater noise tolerance with even fewer settings; critically, under this scheme the required training-set size becomes independent of system size. We package the entire pipeline as an automated script that, in every case we tested, produces witnesses surpassing all existing methods in noise tolerance and/or number of measurement settings. We demonstrate the method on Bell, GHZ, W, and hypergraph states, along with a range of qudit states, spanning 2-6 qubits, bipartite qudits up to d=10, and tripartite qutrits. Our witnesses achieve perfect accuracy across both physical experimental test states and large numerical sets of separable mixed states-including 30 million test states for a 3-qubit W-state witness and 10 million for a 4-qubit hypergraph-state witness-and we experimentally confirm the noise tolerance of Bell- and hypergraph state witnesses on both photonic and superconducting platforms, respectively.
