Control and Engineering of Open Quantum Systems

Dear Colleagues,

In response to the growing intersection of quantum theory, stochastic processes, and applied mathematics, the field of Quantum Stochastic Differential Equations (QSDEs) has emerged as a fundamental framework for modeling and analyzing open quantum systems, quantum noise, and complex quantum-dynamical phenomena. Recent advances in quantum technologies, quantum information processing, and quantum engineering have further driven significant theoretical and practical developments in this area. The study of QSDEs not only deepens our understanding of quantum stochastic calculus and non-commutative dynamics but also enables powerful applications in quantum control, quantum filtering, quantum finance, and quantum algorithm design. This Special Issue, titled “Control and Engineering of Open Quantum Systems,” aims to present cutting-edge research that bridges mathematical rigor with interdisciplinary applicability.

We invite contributions that address recent progress, novel methodologies, and innovative applications related to QSDEs. Topics of interest include, but are not limited to, the following:

• Mathematical foundations and recent theoretical developments in QSDEs;
• Numerical methods and computational techniques for solving QSDEs;
• Applications in quantum open systems, decoherence, and dissipation;
• Quantum stochastic control and filtering theory;
• Connections between QSDEs and quantum probability, operator algebras, and quantum walks;
• Role of QSDEs in quantum measurement, trajectory theory, and continuous quantum monitoring;
• Applications in quantum finance, risk modeling, and quantum stochastic modeling in economics;
• Interplay with quantum machine learning and quantum neural networks;
• Implementations and simulations in quantum software platforms and quantum hardware;
• Cross-disciplinary perspectives linking QSDEs to statistical physics, engineering, and biological modeling.

We welcome original research articles and comprehensive reviews that explore these and related themes, fostering dialog and collaboration across mathematics, physics, finance, engineering, and quantum computation. Join us in advancing this vibrant field and contributing to the next generation of stochastic methods for the quantum era.

We look forward to your submissions.

Dr. Zhiyuan Dong
Guest Editor

Manuscript Submission Information

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• quantum stochastic analysis
• open quantum systems
• quantum filtering and control
• non-commutative stochastic processes
• quantum financial mathematics