Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement

Zhang, Mengshi; Ni, Guyan

doi:10.1007/s10589-019-00126-5

Cited by 9 publications

(8 citation statements)

References 43 publications

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“…Moreover, we have observed a linear increase on the generation time with the dimension. Here we used pure four-to ten-qubit states for training because the test samples of mixed states (mixed entangled states) are hard to label for high-dimensional system, while we have developed an efficient algorithm [42] that can tell whether a randomly generated ten-qubit pure state is entangled or not within 5 s. However, test samples are just used to measure the accuracy of the model. The model is trained using the separable samples only, which can be generated efficiently.…”

Section: Scalability Up To Ten-qubit Statesmentioning

confidence: 99%

Detecting quantum entanglement with unsupervised learning

Chen

Pan

Cheng

2021

Quantum Sci. Technol.

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Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features especially for high-dimensional and multipartite quantum systems. In this work, we exploit the convexity of samples without the desired quantum features and design an unsupervised machine learning method to detect the presence of such features as anomalies. Particularly, in the context of entanglement detection, we propose a complex-valued neural network composed of pseudo-siamese network and generative adversarial net, and then train it with only separable states to construct non-linear witnesses for entanglement. It is shown via numerical examples, ranging from two-qubit to ten-qubit systems, that our network is able to achieve high detection accuracy which is above 97.5% on average. Moreover, it is capable of revealing rich structures of entanglement, such as partial entanglement among subsystems. Our results are readily applicable to the detection of other quantum resources such as Bell nonlocality and steerability, and thus our work could provide a powerful tool to extract quantum features hidden in multipartite quantum data.

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Section: Scalability Up To Ten-qubit Statesmentioning

confidence: 99%

Detecting quantum entanglement with unsupervised learning

Chen

Pan

Cheng

2021

Quantum Sci. Technol.

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“…The unsupervised learning method is applied on 5-and 10-qubit states to study its scalability. Without loss of generality, we focus on the classification of pure states for which geometrical entanglement measure can be computed [34]. Note that the geometrical measure is only used to label the entangled states for the test dataset.…”

Section: Scalability Up To 10-qubit Statesmentioning

confidence: 99%

“…The training dataset is composed of 160000 separable states, and the test dataset is composed of 40000 separable and 40000 entangled states. The entangled states are found by randomly generating 5-and 10-qubit pure states and computing their entanglement measures using the numerical method from [34]. See Appendix B for the details of the algorithm.…”

Section: Scalability Up To 10-qubit Statesmentioning

confidence: 99%

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Detecting quantum entanglement with unsupervised learning

Chen,

Pan,

Zhang

et al. 2021

Preprint

Self Cite

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Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features especially for high-dimensional quantum systems. In this work, we exploit the convexity of normal samples without quantum features and design an unsupervised machine learning method to detect the presence of quantum features as anomalies. Particularly, given the task of entanglement detection, we propose a complex-valued neural network composed of pseudo-siamese network and generative adversarial net, and then train it with only separable states to construct non-linear witnesses for entanglement. It is shown via numerical examples, ranging from 2-qubit to 10-qubit systems, that our network is able to achieve high detection accuracy with above 97.5% on average. Moreover, it is capable of revealing rich structures of entanglement, such as partial entanglement among subsystems. Our results are readily applicable to the detection of other quantum resources such as Bell nonlocality and steerability, indicating that our work could provide a powerful tool to extract quantum features hidden in high-dimensional quantum data.

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“…Ni et al [33] proposed the unitary eigenvalues and unitary symmetric eigenvalues for complex tensors and symmetric complex tensors, respectively, and demonstrated a relation to the geometric measure of quantum entanglement. Zhang et al [44] studied the unitary eigenvalues of non-symmetric complex tensors. Jiang et al [24] characterized real-valued complex polynomial functions and their symmetric tensor representations, which naturally led to the definition of CPS tensors as well as its generalization called conjugate super-symmetric tensors.…”

Section: Introductionmentioning

confidence: 99%

On decompositions and approximations of conjugate partial-symmetric tensors

Fu¹,

Jiang

2021

Calcolo

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Hermitian matrices have played an important role in matrix theory and complex quadratic optimization. The high-order generalization of Hermitian matrices, conjugate partial-symmetric (CPS) tensors, have shown growing interest recently in tensor theory and computation, particularly in application-driven complex polynomial optimization problems. In this paper, we study CPS tensors with a focus on ranks, computing rank-one decompositions and approximations, as well as their applications. We prove constructively that any CPS tensor can be decomposed into a sum of rank-one CPS tensors, which provides an explicit method to compute such rank-one decompositions. Three types of ranks for CPS tensors are defined and shown to be different in general. This leads to the invalidity of the conjugate version of Comon’s conjecture. We then study rank-one approximations and matricizations of CPS tensors. By carefully unfolding CPS tensors to Hermitian matrices, rank-one equivalence can be preserved. This enables us to develop new convex optimization models and algorithms to compute best rank-one approximations of CPS tensors. Numerical experiments from data sets in radar wave form design, elasticity tensor, and quantum entanglement are performed to justify the capability of our methods.

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Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement

Cited by 9 publications

References 43 publications

Detecting quantum entanglement with unsupervised learning

Detecting quantum entanglement with unsupervised learning

Detecting quantum entanglement with unsupervised learning

On decompositions and approximations of conjugate partial-symmetric tensors

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