Importance Sampling of Randomized Measurements for Probing Entanglement

Rath, Aniket; Bijnen, Rick van; Elben, Andreas; Zoller, P.; Vermersch, Benoît

doi:10.1103/physrevlett.127.200503

Cited by 33 publications

(18 citation statements)

References 36 publications

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“…Recently, there are enhancements of the error scaling of the shadow protocol by using prior knowledge of the observable [59][60][61], or the intrinsic tensor-product structure of the underlying state for the nonlinear function estimation [51]. It would be interesting to ascertain if these methodologies could provide further enhancement to estimating the total correlation measurement here, in situations where one has additional knowledge of the NISQ device [62].…”

Section: Discussionmentioning

confidence: 99%

Characterizing correlation within multipartite quantum systems via local randomized measurements

et al. 2022

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Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics, plays an important role in understanding multipartite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be non-linear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography, and obviates the need to coherently interfere multiple copies of a given state. Thus we provide a tool for proving multipartite correlations that can be applied to near-term quantum devices.

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Section: Discussionmentioning

confidence: 99%

Characterizing correlation within multipartite quantum systems via local randomized measurements

et al. 2022

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“…Compared to alternative methods based on implementing multiple copies to measure Rényi entropies [122][123][124][125], negativities [126], (and also the ES [108]), the protocols presented above involve single instances of the quantum states and appear thus as more experimentally friendly. Finally, protocols based on measuring statistical correlations between randomized measurements have been also devised to measure entanglement entropies [115,[127][128][129][130][131], and entanglement negativities [132,133]. These protocols have the advantage of not making assumptions on the state, and of not requiring multiple copies.…”

Section: Summary Of the Experimental Section And Comparisons With Oth...mentioning

confidence: 99%

Entanglement Hamiltonians: from field theory, to lattice models and experiments

Dalmonte,

Eisler,

Falconi

et al. 2022

Preprint

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“…The exact value of b and the optimal ratio N U /N meas depends on the state of interest and the required precision. The scaling of statistical errors with system size can furthermore be substantially improved via importance sampling [35].…”

Section: B Purity Estimationmentioning

confidence: 99%

A randomized measurement toolbox for Rydberg quantum technologies

Notarnicola¹,

Elben²,

Lahaye³

et al. 2021

Preprint

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We present a toolbox to probe quantum many-body states implemented on Rydberg-atoms quantum hardware via randomized measurements. We illustrate the efficacy of this measurement toolbox in the context of probing entanglement, via the estimation of the purity, and of verifying a groundstate preparation using measurements of the Hamiltonian variance. To achieve this goal, we develop and discuss in detail a protocol to realize independent, local unitary rotations. We benchmark the protocol by investigating the ground state of the one-dimensional SSH model, recently realized on a chain of Rydberg atom. We probe the robustness of our toolbox by taking into account experimental imperfections, such as pulse fluctuations and measurement errors.

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Importance Sampling of Randomized Measurements for Probing Entanglement

Cited by 33 publications

References 36 publications

Characterizing correlation within multipartite quantum systems via local randomized measurements

Characterizing correlation within multipartite quantum systems via local randomized measurements

Entanglement Hamiltonians: from field theory, to lattice models and experiments

A randomized measurement toolbox for Rydberg quantum technologies

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