Eigenstate extraction with neural-network tomography

Melkani, Abhijeet; Gneiting, Clemens; Nori, Franco

doi:10.48550/arxiv.1911.07506

Cited by 4 publications

(4 citation statements)

References 34 publications

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“…Realtime tomography could be useful in QKD protocols resistant to "trojan-horse attacks" [85] or any SPD platform subject to time-dependent environmental parameter fluctuations: for instance, atmospheric turbulence in MDI-QKD [86] or interplanetary medium in deep space classical communications [87]. Recently tomography speedups have been achieved using machine learning assisted tomography protocols [88]. The POVMs derived in this paper provide priors which can further speed up detector tomography [89].…”

Section: Applicationsmentioning

confidence: 99%

How to Project onto an Arbitrary Single-Photon Wavepacket

Propp,

van Enk

2020

Preprint

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The time-frequency degree of freedom of the electromagnetic field is the final frontier for singlephoton measurements. The temporal and spectral distribution a measurement retrodicts (that is, the state it projects onto) is determined by the detector's intrinsic resonance structure. In this paper, we construct ideal and more realistic positive operator-valued measures (POVMs) that project onto arbitrary single-photon wavepackets with high efficiency and low noise. We discuss applications to super-resolved measurements and quantum communication. In doing so we will give a fully quantum description of the entire photo detection process, give prescriptions for (in principle) performing single-shot Heisenberg-limited time-frequency measurements of single photons, and discuss fundamental limits and trade-offs inherent to single-photon detection.

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Section: Applicationsmentioning

confidence: 99%

How to Project onto an Arbitrary Single-Photon Wavepacket

Propp,

van Enk

2020

Preprint

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“…This approach has culminated in the recent demonstration of the reconstruction of a Rydberg atom quantum simulator from experimental data [7]. Methods for quantum state reconstruction with generative models are advancing rapidly and are capable of learning both pure state wave functions and mixed state density matrices [6,8,9]. Reconstruction is driven by projective qubit measurement data in a variety of bases or more general positive operator valued measures (POVMs) [10].…”

Section: Introductionmentioning

confidence: 99%

Reconstructing quantum molecular rotor ground states

et al. 2020

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Nanomolecular assemblies of C 60 can be synthesized to enclose dipolar molecules. The low-temperature states of such endofullerenes are described by quantum mechanical rotors, which are candidates for quantum information devices with higher-dimensional local Hilbert spaces. The experimental exploration of endofullerene arrays comes at a time when machine learning techniques are rapidly being adopted to characterize, verify, and reconstruct quantum states from measurement data. In this paper, we develop a strategy for reconstructing the ground state of chains of dipolar rotors using restricted Boltzmann machines (RBMs) adapted to train on data from higher-dimensional Hilbert spaces. We demonstrate accurate generation of energy expectation values from an RBM trained on data in the free-rotor eigenstate basis and explore the learning resources required for various chain lengths and dipolar interaction strengths. Finally, we show evidence for fundamental limitations in the accuracy achievable by RBMs due to the difficulty in imposing symmetries in the sampling procedure. We discuss possible avenues to overcome this limitation in the future, including the further development of autoregressive models such as recurrent neural networks for the purposes of quantum state reconstruction.

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“…This approach has culminated in the recent demonstration of the reconstruction of a Rydberg atom quantum simulator from experimental data 7 . Methods for quantum state reconstruction with generative models are advancing rapidly, and are capable of learning both pure state wavefunctions and mixed state density matrices 6,8,9 . Reconstruction is driven by projective qubit measurement data in a variety of bases, or more general positive operator valued measures (POVMs) 10 .…”

Section: Introductionmentioning

confidence: 99%

Reconstructing quantum molecular rotor ground states

De Vlugt,

Iouchtchenko,

Merali

et al. 2020

Preprint

View full text Add to dashboard Cite

Nanomolecular assemblies of C60 can be synthesized to enclose dipolar molecules. The lowtemperature states of such endofullerenes are described by quantum mechanical rotors, which are candidates for quantum information devices with higher-dimensional local Hilbert spaces. The experimental exploration of endofullerene arrays comes at a time when machine learning techniques are rapidly being adopted to characterize, verify, and reconstruct quantum states from measurement data. In this paper, we develop a strategy for reconstructing the ground state of chains of dipolar rotors using restricted Boltzmann machines (RBMs) adapted to train on data from higherdimensional Hilbert spaces. We demonstrate accurate generation of energy expectation values from an RBM trained on data in the free-rotor eigenstate basis, and explore the learning resources required for various chain lengths and dipolar interaction strengths. Finally, we show evidence for fundamental limitations in the accuracy achievable by RBMs due to the difficulty in imposing symmetries in the sampling procedure. We discuss possible avenues to overcome this limitation in the future, including the further development of autoregressive models such as recurrent neural networks for the purposes of quantum state reconstruction.

show abstract

Eigenstate extraction with neural-network tomography

Cited by 4 publications

References 34 publications

How to Project onto an Arbitrary Single-Photon Wavepacket

How to Project onto an Arbitrary Single-Photon Wavepacket

Reconstructing quantum molecular rotor ground states

Reconstructing quantum molecular rotor ground states

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