An online optimization algorithm for the real-time quantum state tomography

Zhang, Kun; Cong, Shuang; Li, Kezhi; Wang, Tao

doi:10.1007/s11128-020-02866-4

Cited by 11 publications

(7 citation statements)

References 28 publications

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“…For example, dynamical maps can be utilized to generate an informationally complete set of measurement operators [24]. There have also been proposals involving continuous measurement defined in the time domain, for example, by performing a weak (non-projective) continuous measurement on an ensemble of systems [25][26][27], including numerical optimization algorithms to reduce the influence of experimental noise [28].…”

Section: Introductionmentioning

confidence: 99%

Quantum tomography of entangled qubits by time-resolved single-photon counting with time-continuous measurements

Czerwinski

2022

Quantum Inf Process

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In this article, we introduce a framework for entanglement characterization by time-resolved single-photon counting with measurement operators defined in the time domain. For a quantum system with unitary dynamics, we generate time-continuous measurements by shifting from the Schrödinger picture to the Heisenberg representation. In particular, we discuss this approach in reference to photonic tomography. To make the measurement scheme realistic, we impose timing uncertainty on photon counts along with the Poisson noise. Then, the framework is tested numerically on quantum tomography of qubits. Next, we investigate the accuracy of the model for polarization-entangled photon pairs. Entanglement detection and precision of state reconstruction are quantified by figures of merit and presented on graphs versus the amount of time uncertainty.

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Section: Introductionmentioning

confidence: 99%

Quantum tomography of entangled qubits by time-resolved single-photon counting with time-continuous measurements

Czerwinski

2022

Quantum Inf Process

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“…Both these scenarios require online QST-learning algorithms that continuously update the estimate of the state description [5], and thus enable real-time control and diagnosis of errors. Recent proposals for this include Bayesian approaches [6,7], adaptive measurements [8][9][10][11], and machine learning techniques [11][12][13][14][15]. All these techniques are also closely related to continuous learning [16,17]weak measurements over time to characterise a systems evolution, motivated by feedback control to correct errors-and Hamiltonian identification/learning [18,19]-algorithms to determine Hamiltonian parameters governing the dynamics or unknown structures in the system, motivated by distinguishing and quantification of errors.…”

Section: Introductionmentioning

confidence: 99%

Efficient Quantum State Tracking in Noisy Environments

Rambach¹,

Youssry²,

Tomamichel³

et al. 2022

Preprint

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Quantum state tomography, which aims to find the best description of a quantum state-the density matrix, is an essential building block in quantum computation and communication. Standard techniques for state tomography are incapable of tracking changing states and often perform poorly in the presence of environmental noise. Although there are different approaches to solve these problems theoretically, experimental demonstrations have so far been sparse. Our approach, matrix-exponentiated gradient tomography, is an online tomography method that allows for state tracking, updates the estimated density matrix dynamically from the very first measurements, is computationally efficient, and converges to a good estimate quickly even with noisy data. The algorithm is controlled via a single parameter, its learning rate, which determines the performance and can be tailored in simulations to the individual experiment. We present an experimental implementation of matrix-exponentiated gradient tomography on a qutrit system encoded in the transverse spatial mode of photons. We investigate the performance of our method on stationary and evolving states, as well as significant environmental noise, and find fidelities of around 95% in all cases.

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“…[29]. There have also been proposals involving continuous measurement defined in the time domain [30][31][32][33]. Special attention should be paid to the methods, both theoretical and experimental, which demonstrate the possibility to obtain the complete information about an unknown quantum state from a single measurement setup [34,35].…”

Section: Introductionmentioning

confidence: 99%

Quantum state tomography with informationally complete POVMs generated in the time domain

Czerwinski

2021

Quantum Inf Process

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The article establishes a framework for dynamic generation of informationally complete POVMs in quantum state tomography. Assuming that the evolution of a quantum system is given by a dynamical map in the Kraus representation, one can switch to the Heisenberg picture and define the measurements in the time domain. Consequently, starting with an incomplete set of positive operators, one can obtain sufficient information for quantum state reconstruction by multiple measurements. The framework has been demonstrated on qubits and qutrits. For some types of dynamical maps, it suffices to initially have one measurement operator. The results demonstrate that quantum state tomography is feasible even with limited measurement potential.

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An online optimization algorithm for the real-time quantum state tomography

Cited by 11 publications

References 28 publications

Quantum tomography of entangled qubits by time-resolved single-photon counting with time-continuous measurements

Quantum tomography of entangled qubits by time-resolved single-photon counting with time-continuous measurements

Efficient Quantum State Tracking in Noisy Environments

Quantum state tomography with informationally complete POVMs generated in the time domain

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