Quantifying entanglement is an important task by which the resourcefulness of a state can be measured. Here we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state, by making use of the quantum steering effect. Our first separability test consists of a distributed quantum computation involving two parties: a computationally limited client, who prepares a purification of the state of interest, and a computationally unbounded server, who tries to steer the reduced systems to a probabilistic ensemble of pure product states. To design a practical algorithm, we replace the role of the server by a combination of parameterized unitary circuits and classical optimization techniques to perform the necessary computation. The result is a variational quantum steering algorithm (VQSA), which is our second separability test that is better suited for the capabilities of quantum computers available today. This VQSA has an additional interpretation as a distributed variational quantum algorithm (VQA) that can be executed over a quantum network, in which each node is equipped with classical and quantum computers capable of executing VQA. We then simulate our VQSA on noisy quantum simulators and find favorable convergence properties on the examples tested. We also develop semidefinite programs, executable on classical computers, that benchmark the results obtained from our VQSA. Our findings here thus provide a meaningful connection between steering, entanglement, quantum algorithms, and quantum computational complexity theory. They also demonstrate the value of a parameterized mid-circuit measurement in a VQSA and represent a first-of-its-kind application for a distributed VQA. Finally, the whole framework generalizes to the case of multipartite states and entanglement.
翻译:量化纠缠是一个重要的任务,可以据此测量一个国家的智慧。 在这里, 我们开发了量子算法, 通过使用量子方向效应测试和量化一个普通两边状态的分离性。 我们的第一次分离性测试包括一个分布式量子计算, 涉及两个方面: 一个计算有限的客户, 负责准备净化利息状态, 以及一个计算上不受约束的服务器, 试图将降低的系统引导到一个纯产品状态的概率性混合。 为了设计一个实用的算法, 我们用一个参数化的线性平均电路和经典优化技术组合来取代服务器的作用, 以进行必要的计算。 结果是一个可变式的量子方向算法( VQSA) 。 这个VQSA 的额外解释是, 一个分布式的分布式量子计算法( VQA ), 一个用于测试性能的经典和量子计算法( VQA ) 。 我们然后将我们VSA 的精度的精度数据转换结果, 一个用于测试的量子计算机的精度 。</s>