Eigenstate extraction with neural-network tomography

Melkani, Abhijeet; Gneiting, Clemens; Nori, Franco

doi:10.1103/physreva.102.022412

Cited by 36 publications

(14 citation statements)

References 41 publications

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“…The concept of random-coefficient pure states may be summarized as follows (see [51] for more details). Whereas the coefficients c k in (27) are fixed parameters for deterministic-coefficient pure states, they become complex-valued random variables for random-coefficient pure states. Therefore, the probabilities P(A k ) in ( 28) also become random variables for random-coefficient pure states.…”

Section: A Single-preparation Qip Based On Probability Expectationsmentioning

confidence: 99%

“…Classical machine learning is currently a booming field [1], and various quantum machine learning extensions are also being considered [2]- [5]. The processing tasks that involve data-driven learning include not only widespread classification/clustering [1], [3], [6]- [10] and regression [6], [7], [9] but also especially: 1) classical system identification [11]- [13] and its quantum extension, called (nonblind [14]- [23] or blind [24]- [26]) quantum process tomography (QPT) 1 ; 2) system inversion and signal restoration; and 3) blind source separation (BSS), e.g., based on independent component analysis (ICA) [30]- [36] (with a close connection with principal component analysis (PCA) [37]- [39]) and quantum 1 Methods based on machine learning with neural networks have also been proposed for a partly related task, namely, quantum state tomography [27]- [29]. extensions of BSS/ICA [40]- [45].…”

Section: Introductionmentioning

confidence: 99%

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New Single-Preparation Methods for Unsupervised Quantum Machine Learning Problems

Deville

2021

IEEE Trans. Quantum Eng.

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The term "machine learning" especially refers to algorithms that derive mappings, i.e., inputoutput transforms, by using numerical data that provide information about considered transforms. These transforms appear in many problems related to classification/clustering, regression, system identification, system inversion, and input signal restoration/separation. We here analyze the connections between all these problems in the classical and quantum frameworks. We then focus on their most challenging versions, involving quantum data and/or quantum processing means, and unsupervised, i.e., blind, learning. We consider the general single-preparation quantum information processing (SIPQIP) framework that we have recently proposed. It involves methods that can work with a single instance of each (unknown) state, whereas usual methods are quite cumbersome because they have to very accurately create many copies of each (known) state. In our previous papers, we applied the SIPQIP approach to only one task [blind quantum process tomography (BQPT)], but it opens the way to a large range of other types of methods. In this article, we, therefore, propose various new SIPQIP methods that efficiently perform tasks related to system identification (blind Hamiltonian parameter estimation (BHPE), blind quantum channel identification/estimation, and blind phase estimation), system inversion and state estimation (blind quantum source separation (BQSS), blind quantum entangled state restoration (BQSR), and blind quantum channel equalization), and classification. Numerical tests show that our SIPQIP framework, moreover, yields much more accurate estimation than the usual multiple-preparation approach. Our methods are especially useful in a quantum computer, which we propose to more briefly call a "quamputer": BQPT and BHPE simplify the characterization of quamputer gates; BQSS and BQSR yield quantum gates that may be used to compensate for the nonidealities that alter states stored in quantum registers and open the way to very general self-adaptive quantum gates.INDEX TERMS Blind Hamiltonian parameter estimation (BHPE), blind quantum process tomography (BQPT), blind quantum source separation (BQSS), blind quantum state restoration (BQSR), blind/unsupervised quantum machine learning, Heisenberg exchange coupling, quantum classification, quantum computer (quamputer), single-preparation quantum information processing (SIPQIP), spin-based qubits. Engineering uantum Transactions on IEEEDeville and Deville: NEW SINGLE-PREPARATION METHODS FOR UNSUPERVISED (QM) LEARNING PROBLEMS

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Section: A Single-preparation Qip Based On Probability Expectationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Single-Preparation Methods for Unsupervised Quantum Machine Learning Problems

Deville

2021

IEEE Trans. Quantum Eng.

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show abstract

“…Some recent proposals for quantum state tomography include self-guided quantum tomography (SGQT), practical adaptive quantum tomography (PAQT), and state tomography through eigenstate extraction with neural networks [17][18][19][20][21][22]. SGQT employs a stochastic approximation optimization technique known as simultaneous perturbation stochastic approximation (SPSA) [23] to learn an unknown pure state.…”

Section: Introductionmentioning

confidence: 99%

Self-Guided Quantum State Learning for Mixed States

Farooq¹,

Ullah²,

Ramadhani³

et al. 2021

Preprint

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We provide an adaptive learning algorithm for tomography of general quantum states. Our proposal is based on the simultaneous perturbation stochastic approximation algorithm and is applicable on mixed qudit states. The salient features of our algorithm are efficient (O d 3 ) post-processing in the dimension d of the state, robustness against measurement and channel noise, and improved infidelity performance as compared to the contemporary adaptive state learning algorithms. A higher resilience against measurement noise makes our algorithm suitable for noisy intermediate-scale quantum applications.

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“…The exploration of NQS is motivated by universal approximation theorems [17,18] and the observation that many NQS can efficiently encode volume-law entanglement and thereby have higher representational power compared to most tensor-network based approaches [19,20] as well as a favorable generalization to higher dimensions. These emerging neural network QST (NN-QST) approaches [15,16,[21][22][23][24][25][26] are starting to receive attention from the experimental communities with applications to Rydberg-, trapped-ion and optical systems [27][28][29][30].…”

mentioning

confidence: 99%

Scalable quantum state tomography with artificial neural networks

Schmale,

Reh,

Gärttner

2021

Preprint

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Eigenstate extraction with neural-network tomography

Cited by 36 publications

References 41 publications

New Single-Preparation Methods for Unsupervised Quantum Machine Learning Problems

New Single-Preparation Methods for Unsupervised Quantum Machine Learning Problems

Self-Guided Quantum State Learning for Mixed States

Scalable quantum state tomography with artificial neural networks

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