Experimental quantum homodyne tomography via machine learning

Tiunov, Egor; Tiunova, Vera; Ulanov, Alexander E.; Lvovsky, A. I.; Fedorov, Aleksey K.

doi:10.1364/optica.389482

Cited by 74 publications

(60 citation statements)

References 54 publications

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“…Moreover, the promising direction of the research is employing the precision guaranteed tomography in self-calibrating protocols [28]. Another interesting point is to use this technique for investigating possible advantages of machine learning approaches for tomography of quantum states and processes [29,30].…”

Section: Discussionmentioning

confidence: 99%

Estimating the precision for quantum process tomography

2020

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Quantum tomography is a widely applicable tool for complete characterization of quantum states and processes. In the present work, we develop a method for precision-guaranteed quantum process tomography. With the use of the Choi-Jamiokowski isomorphism, we generalize the recently suggested extended norm minimization estimator for the case of quantum processes. Our estimator is based on the Hilbert-Schmidt distance for quantum processes. Specifically, we discuss the application of our method for characterizing quantum gates of a superconducting quantum processor in the framework of the IBM Q Experience.

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Section: Discussionmentioning

confidence: 99%

Estimating the precision for quantum process tomography

2020

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“…With the recent success in the field of deep learning, tools other than those based on tensor networks work as well as an ansatz. Restricted Boltzmann machine has been successfully applied as an ansatz to a ground state search, dynamics calculation, and quantum tomography [ 58 , 59 , 60 ], as well as convolution neural network to the two-dimensional frustrated

model [ 61 ]. The deep autoregressive model was applied very efficiently and elegantly to a ground state search of many-body quantum system and to classical statistical physics as well [ 62 , 63 ].…”

Section: Introductionmentioning

confidence: 99%

Variational Autoencoder Reconstruction of Complex Many-Body Physics

Luchnikov

Ryzhov

Stas

et al. 2019

Entropy

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2The empirical development of the dynamical theory of heat or classical equilibrium thermodynamics as we know it, was only possible because of the definition through a phenomenological approach of two fundamental physical concepts, which are the actual pillars of the theory: energy and entropy [1]. It is with these two concepts that the laws (or principles) of thermodynamics could be stated and the absolute temperature be given a first proper definition. Though energy remains as fully enigmatic as entropy from the ontological viewpoint, the latter concept is not completely understood from the physical viewpoint. This of course did not preclude the success of equilibrium thermodynamics as evidenced not only by the development of thermal sciences and engineering, but also because of its cognate fields that owe it, at least partly or as an indirect consequence, their birth, from quantum physics to information theory.Early attempts to refine and give thermodynamics solid grounds started with the development of the kinetic theory of gases and of statistical physics, which in turn permitted studies of irreversible processes with the development of nonequilibrium thermodynamics [2-5] and later on finite-time thermodynamics [6,7] thus establishing closer ties between the concrete notion of irreversibility and the more abstract entropy, notably with Boltzmann's statistical definition [8] and Gibbs' ensemble theory [9]. Notwithstanding conceptual difficulties inherent to the foundations of statistical physics such as, e.g., irreversibility and the ergodic hypothesis [10,11], entropy acquired a meaningful statistical character and the scope of its definitions could be extended beyond thermodynamics, thus paving the way to information theory, as information content became a physical quantity per se, i.e. something that can be measured [12]. And, while quantum physics developed independently from thermodynamics, it extended the scope of statistical physics with the introduction of quantum statistics, led to the definition of the von Neumann entropy [13], and also introduced new problems related to small, i.e. mesoscopic and nanoscopic, systems [14,15], down to nuclear matter [16], where the concepts of thermodynamic limit and ensuing standard definitions of thermodynamic quantities may be put at odds.Quantum physics problems that overlap with thermodynamics, are typically classified into different categories: ground state characterization [17], thermal state characterization at finite temperature [18], calculation of the dynamics of either closed or open systems [19,20], state reconstruction from tomographic data [21], and quantum system control, which, given the complexity for its implementation, requires the development of new methods [22]. There are essentially two large families of techniques applicable to such problems: One is based on the quantum Monte Carlo (QMC) framework [23], which is powerful to overcome the curse of dimensionality by using the stochastic estimation of high-dimensional integrals; the other family e...

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“…In particular, artificial neural networks (NNs) already offer an alternative and efficient strategy to represent quantum many-body states, enabling us to perform quantum state tomography for high dimensional states from a limited number of experimental data [40,41]. Most of the protocols have been implemented in a discrete variables framework, one approach for quantum homodyne tomography has been proposed [42], and experimentally tested in the single-mode configuration. Our algorithm allows, in a supervised learning approach, the discrimination between multimode optical states presenting negative or positive Wigner function and it is the first application of a machine learning algorithm to CV multimode optical states.…”

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confidence: 99%

Neural Networks for Detecting Multimode Wigner Negativity

et al. 2020

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The characterization of quantum features in large Hilbert spaces is a crucial requirement for testing quantum protocols. In the continuous variable encoding, quantum homodyne tomography requires an amount of measurement that increases exponentially with the number of involved modes, which practically makes the protocol intractable even with few modes. Here, we introduce a new technique, based on a machine learning protocol with artificial neural networks, that allows us to directly detect negativity of the Wigner function for multimode quantum states. We test the procedure on a whole class of numerically simulated multimode quantum states for which the Wigner function is known analytically. We demonstrate that the method is fast, accurate, and more robust than conventional methods when limited amounts of data are available. Moreover, the method is applied to an experimental multimode quantum state, for which an additional test of resilience to losses is carried out.

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Experimental quantum homodyne tomography via machine learning

Cited by 74 publications

References 54 publications

Estimating the precision for quantum process tomography

Estimating the precision for quantum process tomography

Variational Autoencoder Reconstruction of Complex Many-Body Physics

Neural Networks for Detecting Multimode Wigner Negativity

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