Quantum Pure State Tomography via Variational Hybrid Quantum-Classical Method

Xin, Tao; Nie, Xinfang; Kong, Xiangyu; Wen, Jingwei; Lu, Dawei; Li, Jun

doi:10.1103/physrevapplied.13.024013

Cited by 25 publications

(9 citation statements)

References 60 publications

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“…Machine learning is a possible approach to solve the entanglement structure problem. Myriad investigations toward quantum correlation problems by machine learning have been reported, such as representation of quantum states, [57][58][59][60][61] entanglement detection, [56,62] steerability detection, [63] and Bell nonlocality detection. [64,65] Here, we review how to establish a machine learning model for characterizing entanglement intactness and depth in ref.…”

Section: Entanglement Intactness and Depthmentioning

confidence: 99%

Machine Learning Experimental Multipartite Entanglement Structure

et al. 2022

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With the rapid growth of controllable qubits in recent years, experimental multipartite entangled states can be created with high fidelity in various moderate-and large-scale physical systems. However, the characterization of multipartite entanglement structure remains a formidable challenge, as traditionally it requires exponential number of local measurements to realize the identification. Machine learning is demonstrated to be an efficient tool to detect the underlying entanglement structure for ideal states, but it has non-negligible underperformance when tackling imperfect experimental data in reality. Here, a modified classifier based on feed-forward neural network to predict experimental entanglement structure in terms of entanglement intactness and depth is proposed. By preprocessing the input data, the classifier maintains efficiency and reliability against experimental noises, with the accuracy being enhanced from 69.7% to 91.2% for 6-qubit entangled states in spin systems. This method is anticipated to shed light on future studies of entanglement structure, in particular when the number of controlled qubits reaches explosive growth in practice.

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Section: Entanglement Intactness and Depthmentioning

confidence: 99%

Machine Learning Experimental Multipartite Entanglement Structure

et al. 2022

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“…Thus, developing novel algorithms which are friendly to imperfect NISQ simulators and capable of achieving quantum advantage has attracted a lot of attention in recent years [19]. An important class of these algorithms are variational methods which are performed on a hybrid of NISQ simulators and classical optimizers [20][21][22][23][24]. In such algorithms, a cost function is measured on a parameterized quantum circuit.…”

Section: Introductionmentioning

confidence: 99%

Symmetry enhanced variational quantum spin eigensolver

Lyu¹,

Xu²,

Yung³

et al. 2022

Preprint

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The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.

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“…Several QST protocols have been extended to perform QPT, which include MLE-based QPT [9], LS-based QPT [10], simplified QPT [11], convex optimization-based QPT [12], selective and efficient QPT [13], adaptive QPT [14], and ancillaassisted QPT [15]. These protocols have been successfully demonstrated on various physical systems such as NMR [16][17][18][19][20], NV-centers [21], linear optics [22], superconducting qubits [23][24][25] and ion trap-based quantum processors [26].…”

Section: Introductionmentioning

confidence: 99%

Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor

Gaikwad¹,

Arvind²,

Dorai³

2021

Preprint

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We employ the compressed sensing (CS) algorithm and a heavily reduced data set to experimentally perform true quantum process tomography (QPT) on an NMR quantum processor. We obtain the estimate of the process matrix χ corresponding to various two-and three-qubit quantum gates with a high fidelity. The CS algorithm is implemented using two different operator bases, namely, the standard Pauli basis and the Pauli-error basis. We experimentally demonstrate that the performance of the CS algorithm is significantly better in the Pauli-error basis, where the constructed χ matrix is maximally sparse. We compare the standard least square (LS) optimization QPT method with the CS-QPT method and observe that, provided an appropriate basis is chosen, the CS-QPT method performs significantly better as compared to the LS-QPT method. In all the cases considered, we obtained experimental fidelities greater than 0.9 from a reduced data set, which was approximately five to six times smaller in size than a full data set. We also experimentally characterized the reduced dynamics of a two-qubit subsystem embedded in a three-qubit system, and used the CS-QPT method to characterize processes corresponding to the evolution of two-qubit states under various J-coupling interactions.

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Quantum Pure State Tomography via Variational Hybrid Quantum-Classical Method

Cited by 25 publications

References 60 publications

Machine Learning Experimental Multipartite Entanglement Structure

Machine Learning Experimental Multipartite Entanglement Structure

Symmetry enhanced variational quantum spin eigensolver

Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor

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