Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

European Signal Processing Conference (EUSIPCO)

An Efficient Online Estimation Algorithm for Evolving Quantum States

Kun Zhang, Shuang Cong, Yaru Tang, Nikolaos M. Freris

Published Dec 18, 2020• 4 citations
Publisher

Abstract

In this paper, we propose an online optimization algorithm for estimating state density in free evolution quantum systems from noisy continuous weak measurements. The problem is formulated via sparsity-promoting semidefinite programming, and an online quantum state estimation algorithm is developed based on online proximal gradient and alternating direction multiplier method. The proposed algorithm is computationally efficient and further features high robustness to measurement noise. The merits of the approach are illustrated by numerical experiments in 1-, 2-, 3-, and 4-qubit systems.

DOI
10.23919/eusipco47968.2020.9287682

Related papers

A Comparative Study on the Convergence Rate of Two Online Quantum State Reconstruction Algorithms

Shuang Cong, Weiyi Qin

In this paper, the convergence rates of two algorithms for the online quantum states reconstruction with Gaussian measurement noise in continuous weak measurement are studied, one is the online proximal gradient-based alternating direction method of multipliers (OPG-ADMM) algorithm, and another is Kalman fitering-based quantum state estimation (KF-QSE) algorithm. For the OPG-ADMM algorithm, by defining the loss function of the optimization function and the constraint condition in the times T tracking process, the convergence rate theorem of the two loss functions is obtained and proved. Then, the convergence order of the normalized distance of the density matrix under the OPG-ADMM algorithm is derived from the conclusion of the theorem. For the KF-QSE algorithm, after defining the loss function of the optimization function, the theorem of the convergence order of the loss function is investigated. Then, the convergence order of the normalized distance of the KF-QSE algorithm is deduced from the conclusion of the theorem. Finally, in the numerical simulation experiments, we use the normalized distance of density matrix as the indicator and use two algorithms for online reconstruction of the 4-bit quantum system. The derived performance of algorithm convergence rates are verified by the comparison and analysis of the results.

arXiv:2410.09056•International Conference on Intelligent Control and Information Processing•Feb 21, 2026•0 citations

Online quantum state tomography of N-qubit via continuous weak measurement and compressed sensing

Sajede Harraz, Shuang Cong, Kezhi Li

In this paper, we propose an online state tomography method for [Formula: see text]-qubit quantum system based on the continuous weak measurement and compressed sensing (CS). The quantum system is described by stochastic master equation. The continuous weak measurement operators for the [Formula: see text]-qubit quantum system, which are indirectly acted on the quantum system, are derived according to the measurement operator results of two-level quantum system. The online time-varying measurement operators are obtained by means of the dynamic evolution equation of the system. The quantum state is online estimated by solving the optimization problem of minimizing the two-norm with the positive definite constraints of density matrix, and we use the nonnegative least squares algorithm to solve the optimization problem. CS theory is used to reduce the number of the measurements in the process of online state estimation. In the numerical experiments, we study the effects of external control field, measurement rate and the different numbers of qubits on the performance in the proposed method. The minimum required numbers of measurements for 2, 3, 4 and 5 qubits are found. The normalized distance and fidelity of our proposed method can achieve satisfying accuracy with small number of measurements.

International Journal of Quantum Information•Oct 30, 2020•2 citations

Efficient online quantum state estimation using a matrix-exponentiated gradient method

Akram Youssry, Christopher Ferrie, Marco Tomamichel

In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that determines how much weight is given to the new measurement results obtained in each step. We show convergence of the running state estimate in probability to the true state for both noiseless and noisy measurements. We find that in the latter case the learning rate has to be chosen adaptively and decreasing to guarantee convergence beyond the noise threshold. As a practical alternative we then propose to use running averages of the measurement statistics and a constant learning rate to overcome the noise problem. The proposed algorithm is numerically compared with batch maximum-likelihood and least-squares estimators. The results show a superior performance of the new algorithm in terms of accuracy and runtime complexity.

arXiv:1807.01852•New Journal of Physics•Feb 4, 2019•27 citations

Fast algorithm of high-dimensional quantum state estimation via low measurement rates

Jiaojiao Zhang, Kezhi Li, Shuang Cong

Based on the theoretical lower bounds of the number of measurements given by Compressive Sensing (CS), the quantum state estimation task can be formulated as a convex optimization problem subject to positive semi-definite and unit-trace Hermitian constraints. This paper proposes an improved Alternating Direction Multiplier Method (AD-MM) for high-dimensional quantum state reconstruction. The proposed method not only greatly reduces the computational complexity and speeds up the convergence, but also has a strong robustness to the noise. For the density matrix reconstruction of 11-qubit quantum system, the proposed algorithm achieves 4.54e-2 reconstruction error using 0.6% of total measurement data and 99.26 seconds.

Asian Control Conference (ASCC)•Dec 1, 2017•2 citations

On-Line State Estimation of 2-qubit Quantum Systems

Yaru Tang, Shuang Cong

In this paper, the online estimation of 2-qubit states is studied based on the quantum continuous weak measurement and compressed sensing (CS) theory. The stochastic master equation is used to describe the dynamic evolution of the system. The weak measurement operator acting on the system and the dynamic equation of the measurement operator over time are derived. The number of measurements is reduced based on the CS theory. The non-negative LS algorithm is used to reconstruct the quantum system state in free evolution. At last, the numerical simulations of the on-line state estimation of 2-qubit quantum systems are carried out in MATLAB environment, and the influences of the parameters on the estimation results are analyzed by the performance comparisons.

Mediterranean Conference on Control and Automation (MED)•Jul 1, 2019•0 citations

An improved quantum state estimation algorithm via compressive sensing

Shuang Cong, H. Zhang, K. Li

The dimension of the density matrix of a quantum system increases with the qubits of the quantum system, which makes the quantum state estimation time consuming and requires huge computation. In order to reduce the computational time in quantum state estimation, the problem of quantum state estimation based on compressive sensing is changed to the optimization problem with error constraint. In this paper, an improved Alternating Direction Method of Multipliers (ADMM) algorithm is proposed to design the optimization scheme of solving the pure state of quantum state estimation in the cases of with and without external noise. The experiments are implemented in the MATLAB. The comparison results between adaptive and fixed weight value indicate that the improved algorithm has better performances in both aspects of estimation accuracy and robustness to external disturbances. We also extend the quantum state estimation to the qubits of six and seven.

IEEE International Conference on Robotics and Biomimetics (ROBIO)•Dec 1, 2014•1 citation
In this paper, we propose an online optimization algorithm for estimating state density in free evolution quantum systems from noisy continuous weak measurements. The problem is formulated via sparsity-promoting semidefinite programming, and an online quantum state estimation algorithm is developed based on online proximal gradient and alternating direction multiplier method. The proposed algorithm is computationally efficient and further features high robustness to measurement noise. The merits of the approach are illustrated by numerical experiments in 1-, 2-, 3-, and 4-qubit systems.
In this paper, the convergence rates of two algorithms for the online quantum states reconstruction with Gaussian measurement noise in continuous weak measurement are studied, one is the online proximal gradient-based alternating direction method of multipliers (OPG-ADMM) algorithm, and another is Kalman fitering-based quantum state estimation (KF-QSE) algorithm. For the OPG-ADMM algorithm, by defining the loss function of the optimization function and the constraint condition in the times T tracking process, the convergence rate theorem of the two loss functions is obtained and proved. Then, the convergence order of the normalized distance of the density matrix under the OPG-ADMM algorithm is derived from the conclusion of the theorem. For the KF-QSE algorithm, after defining the loss function of the optimization function, the theorem of the convergence order of the loss function is investigated. Then, the convergence order of the normalized distance of the KF-QSE algorithm is deduced from the conclusion of the theorem. Finally, in the numerical simulation experiments, we use the normalized distance of density matrix as the indicator and use two algorithms for online reconstruction of the 4-bit quantum system. The derived performance of algorithm convergence rates are verified by the comparison and analysis of the results.
In this paper, we propose an online state tomography method for [Formula: see text]-qubit quantum system based on the continuous weak measurement and compressed sensing (CS). The quantum system is described by stochastic master equation. The continuous weak measurement operators for the [Formula: see text]-qubit quantum system, which are indirectly acted on the quantum system, are derived according to the measurement operator results of two-level quantum system. The online time-varying measurement operators are obtained by means of the dynamic evolution equation of the system. The quantum state is online estimated by solving the optimization problem of minimizing the two-norm with the positive definite constraints of density matrix, and we use the nonnegative least squares algorithm to solve the optimization problem. CS theory is used to reduce the number of the measurements in the process of online state estimation. In the numerical experiments, we study the effects of external control field, measurement rate and the different numbers of qubits on the performance in the proposed method. The minimum required numbers of measurements for 2, 3, 4 and 5 qubits are found. The normalized distance and fidelity of our proposed method can achieve satisfying accuracy with small number of measurements.
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that determines how much weight is given to the new measurement results obtained in each step. We show convergence of the running state estimate in probability to the true state for both noiseless and noisy measurements. We find that in the latter case the learning rate has to be chosen adaptively and decreasing to guarantee convergence beyond the noise threshold. As a practical alternative we then propose to use running averages of the measurement statistics and a constant learning rate to overcome the noise problem. The proposed algorithm is numerically compared with batch maximum-likelihood and least-squares estimators. The results show a superior performance of the new algorithm in terms of accuracy and runtime complexity.
Based on the theoretical lower bounds of the number of measurements given by Compressive Sensing (CS), the quantum state estimation task can be formulated as a convex optimization problem subject to positive semi-definite and unit-trace Hermitian constraints. This paper proposes an improved Alternating Direction Multiplier Method (AD-MM) for high-dimensional quantum state reconstruction. The proposed method not only greatly reduces the computational complexity and speeds up the convergence, but also has a strong robustness to the noise. For the density matrix reconstruction of 11-qubit quantum system, the proposed algorithm achieves 4.54e-2 reconstruction error using 0.6% of total measurement data and 99.26 seconds.
In this paper, the online estimation of 2-qubit states is studied based on the quantum continuous weak measurement and compressed sensing (CS) theory. The stochastic master equation is used to describe the dynamic evolution of the system. The weak measurement operator acting on the system and the dynamic equation of the measurement operator over time are derived. The number of measurements is reduced based on the CS theory. The non-negative LS algorithm is used to reconstruct the quantum system state in free evolution. At last, the numerical simulations of the on-line state estimation of 2-qubit quantum systems are carried out in MATLAB environment, and the influences of the parameters on the estimation results are analyzed by the performance comparisons.
The dimension of the density matrix of a quantum system increases with the qubits of the quantum system, which makes the quantum state estimation time consuming and requires huge computation. In order to reduce the computational time in quantum state estimation, the problem of quantum state estimation based on compressive sensing is changed to the optimization problem with error constraint. In this paper, an improved Alternating Direction Method of Multipliers (ADMM) algorithm is proposed to design the optimization scheme of solving the pure state of quantum state estimation in the cases of with and without external noise. The experiments are implemented in the MATLAB. The comparison results between adaptive and fixed weight value indicate that the improved algorithm has better performances in both aspects of estimation accuracy and robustness to external disturbances. We also extend the quantum state estimation to the qubits of six and seven.