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

IEEE Symposium Series on Computational Intelligence (SSCI)

Design of a Linear Quantum Projection Filter

Peng Zhang, Qing Zhong Gao, Jinhu Lv, Daoyi Dong

Published Dec 1, 2020• 2 citations
Publisher

Abstract

In order to reduce the computational cost for online calculation of the quantum filter, in this paper, a linear quantum projection filtering scheme is developed by projecting the time evolution trajectory of quantum system state onto a lower-dimensional linear submanifold spanned by a set of basis matrices. The lower-dimensional submanifold is obtained through an extended singular value decomposition algorithm. Compared with the existing works on quantum projection filtering, the proposed approach requires no prior knowledge on the structure of the submanifold, and thus can be used to deal with general open quantum systems. Simulation results demonstrate that the proposed linear projection filter is able to approximate the high-dimensional quantum filter within acceptable accuracy.

DOI
10.1109/ssci47803.2020.9308176

Related papers

Quantum projection filtering

ZT Wu, Qing Zhong Gao, GF Zhang

A quantum filter extracts the optimal estimate of quantum system states from the past history of weak continuous measurements on a quantum system by using the quantum Bayesian theory. However, the online computation burden of a quantum filter increases quadratically along with the increase of the quantum system dimension. We propose a quantum projection filtering method, aiming to reduce the online computation burden of the quantum filter. By using a differential geometric approach, the trajectory of the resulting quantum filter is constrained to be evolving within a finite-dimensional differentiable submanifold. In other words, the quantum state can be calculated through online calculation of the coordinate system of this submanifold. Simulation results from a two-level quantum system demonstrate the effectiveness of the proposed method.

•Jan 1, 2017•3 citations

Design of a Quantum Projection Filter

Qing Zhong Gao, Daoyi Dong, Ian R. Petersen +1 more

This article develops a quantum projection filtering approach to approximating the quantum filter equation based on It$\hat{\rm o}$ stochastic Taylor expansions and quantum information geometric techniques. The proposed approximation scheme is designed so that the truncated Taylor expansion of the difference between the true quantum trajectory, and its approximation on a lower dimensional differential submanifold is minimized, through an orthogonal projection operation in the quantum Fisher metric. In addition, a convenient design for a special class of open quantum systems is formulated. Simulation results from a numerical example demonstrate the approximation capability of the proposed quantum projection filter.

IEEE Transactions on Automatic Control•Nov 14, 2019•15 citations

Quantum projection filtering for open quantum systems

Qing Zhong Gao, Guofeng Zhang

This paper presents an approximation quantum projection filtering strategy, aiming to reduce the computational cost in calculating the standard quantum filter equation in time. By using a differential geometric approach, the trajectory of the resulting quantum projection filter is constrained to evolve in a finite-dimensional differentiable manifold consisting of an exponential family of quantum density operators. A convenient design of the differentiable manifold is then developed through reduction of the local approximation errors, which allows simplification of the quantum projection filter equations. Finally, simulation results from a two-level quantum system example illustrate the approximation performance of the proposed filtering scheme. The proposed approach is expected to be of practical use in developing more efficient quantum control methods.

IEEE Conference on Decision and Control (CDC)•Dec 1, 2017•0 citations

Quantum Projection Filtering for State Estimation and Feedback Stabilization in Open Quantum Systems

Ibrahim Ramadan, Nina H. Amini, Paolo Mason

In this paper, we examine an open quantum system that is subject to indirect and imperfect measurements. Specifically, for quantum non-demolition (QND) measurements, we show that the evolution of the system is confined to a properly selected manifold. This allows us to express the exact solution of the quantum filter equation in terms of a lower-dimensional stochastic differential equation, significantly reducing the computational complexity. Motivated by a quantum state reduction result for the predicted dynamics under QND measurement, we propose, in the case when the Hamiltonian and the coupling operator do not commute, a projection filter approach for the quantum state estimation. The efficiency of the proposed quantum projection filter is verified by numerical simulations. The latter suggest that, even when paired with a stabilizing feedback control mechanism that depends on the projected state, the filter maintains its robustness. More generally, our numerical results suggest the effectiveness of the adopted quantum projection filter approach as a method for state estimation and feedback stabilization of open quantum systems.

IEEE Conference on Decision and Control (CDC)•Dec 9, 2025•0 citations

Quantum tensor singular value decomposition*

Xiaoqiang Wang, Lejia Gu, Heung-wing Lee +1 more

Abstract Tensors are increasingly ubiquitous in various areas of applied mathematics and computing, and tensor decompositions are of practical significance and benefit many applications in data completion, image processing, computer vision, collaborative filtering, etc. Recently, Kilmer and Martin propose a new tensor factorization strategy, tensor singular value decomposition (t-svd), which extends the matrix singular value decomposition to tensors. However, computing t-svd for high dimensional tensors costs much computation and thus cannot efficiently handle large scale datasets. Motivated by advantage of quantum computation, in this paper, we present a quantum algorithm of t-svd for third-order tensors and then extend it to order-p tensors. We prove that our quantum t-svd algorithm for a third-order N dimensional tensor runs in time  N polylog ( N ) if we do not recover classical information from the quantum output state. Moreover, we apply our quantum t-svd algorithm to context-aware multidimensional recommendation systems, where we just need to extract partial classical information from the quantum output state, thus achieving low time complexity.

Journal of Physics Communications•Jun 22, 2021•4 citations

Exact Solution and Projection Filters for Open Quantum Systems Subject to Imperfect Measurements

Ibrahim Ramadan, Nina H. Amini, Paolo Mason

In this letter, we consider an open quantum system undergoing imperfect and indirect measurement. For quantum non-demolition (QND) measurement, we show that the system evolves on an appropriately chosen manifold and we express the exact solution of the quantum filter equation in terms of the solution of a lower dimensional stochastic differential equation. In order to further reduce the dimension of the system under study, we consider the projection on the lower dimensional manifold originally introduced in Gao et al. (2019) for the case of perfect measurements. An error analysis is performed to evaluate the precision of this approximate quantum filter, focusing on the case of QND measurement. Simulations suggest the efficiency of the proposed quantum projection filter, even in presence of a stabilizing feedback control which depends on the projection filter.

arXiv:2303.09667•IEEE Control Systems Letters•Dec 14, 2022•7 citations
In order to reduce the computational cost for online calculation of the quantum filter, in this paper, a linear quantum projection filtering scheme is developed by projecting the time evolution trajectory of quantum system state onto a lower-dimensional linear submanifold spanned by a set of basis matrices. The lower-dimensional submanifold is obtained through an extended singular value decomposition algorithm. Compared with the existing works on quantum projection filtering, the proposed approach requires no prior knowledge on the structure of the submanifold, and thus can be used to deal with general open quantum systems. Simulation results demonstrate that the proposed linear projection filter is able to approximate the high-dimensional quantum filter within acceptable accuracy.
A quantum filter extracts the optimal estimate of quantum system states from the past history of weak continuous measurements on a quantum system by using the quantum Bayesian theory. However, the online computation burden of a quantum filter increases quadratically along with the increase of the quantum system dimension. We propose a quantum projection filtering method, aiming to reduce the online computation burden of the quantum filter. By using a differential geometric approach, the trajectory of the resulting quantum filter is constrained to be evolving within a finite-dimensional differentiable submanifold. In other words, the quantum state can be calculated through online calculation of the coordinate system of this submanifold. Simulation results from a two-level quantum system demonstrate the effectiveness of the proposed method.
This article develops a quantum projection filtering approach to approximating the quantum filter equation based on Ito^\hat{\rm o}o^ stochastic Taylor expansions and quantum information geometric techniques. The proposed approximation scheme is designed so that the truncated Taylor expansion of the difference between the true quantum trajectory, and its approximation on a lower dimensional differential submanifold is minimized, through an orthogonal projection operation in the quantum Fisher metric. In addition, a convenient design for a special class of open quantum systems is formulated. Simulation results from a numerical example demonstrate the approximation capability of the proposed quantum projection filter.
This paper presents an approximation quantum projection filtering strategy, aiming to reduce the computational cost in calculating the standard quantum filter equation in time. By using a differential geometric approach, the trajectory of the resulting quantum projection filter is constrained to evolve in a finite-dimensional differentiable manifold consisting of an exponential family of quantum density operators. A convenient design of the differentiable manifold is then developed through reduction of the local approximation errors, which allows simplification of the quantum projection filter equations. Finally, simulation results from a two-level quantum system example illustrate the approximation performance of the proposed filtering scheme. The proposed approach is expected to be of practical use in developing more efficient quantum control methods.
In this paper, we examine an open quantum system that is subject to indirect and imperfect measurements. Specifically, for quantum non-demolition (QND) measurements, we show that the evolution of the system is confined to a properly selected manifold. This allows us to express the exact solution of the quantum filter equation in terms of a lower-dimensional stochastic differential equation, significantly reducing the computational complexity. Motivated by a quantum state reduction result for the predicted dynamics under QND measurement, we propose, in the case when the Hamiltonian and the coupling operator do not commute, a projection filter approach for the quantum state estimation. The efficiency of the proposed quantum projection filter is verified by numerical simulations. The latter suggest that, even when paired with a stabilizing feedback control mechanism that depends on the projected state, the filter maintains its robustness. More generally, our numerical results suggest the effectiveness of the adopted quantum projection filter approach as a method for state estimation and feedback stabilization of open quantum systems.
Abstract Tensors are increasingly ubiquitous in various areas of applied mathematics and computing, and tensor decompositions are of practical significance and benefit many applications in data completion, image processing, computer vision, collaborative filtering, etc. Recently, Kilmer and Martin propose a new tensor factorization strategy, tensor singular value decomposition (t-svd), which extends the matrix singular value decomposition to tensors. However, computing t-svd for high dimensional tensors costs much computation and thus cannot efficiently handle large scale datasets. Motivated by advantage of quantum computation, in this paper, we present a quantum algorithm of t-svd for third-order tensors and then extend it to order-p tensors. We prove that our quantum t-svd algorithm for a third-order N dimensional tensor runs in time  N polylog ( N ) if we do not recover classical information from the quantum output state. Moreover, we apply our quantum t-svd algorithm to context-aware multidimensional recommendation systems, where we just need to extract partial classical information from the quantum output state, thus achieving low time complexity.
In this letter, we consider an open quantum system undergoing imperfect and indirect measurement. For quantum non-demolition (QND) measurement, we show that the system evolves on an appropriately chosen manifold and we express the exact solution of the quantum filter equation in terms of the solution of a lower dimensional stochastic differential equation. In order to further reduce the dimension of the system under study, we consider the projection on the lower dimensional manifold originally introduced in Gao et al. (2019) for the case of perfect measurements. An error analysis is performed to evaluate the precision of this approximate quantum filter, focusing on the case of QND measurement. Simulations suggest the efficiency of the proposed quantum projection filter, even in presence of a stabilizing feedback control which depends on the projection filter.