(156g) Effects of Noise When Implementing Linear Control Laws on Quantum Computers

Quantum computation is receiving greater interest in process systems engineering. For example, it has been used for optimization ^[1] and fault detection ^[2]. From a controls perspective, however, quantum computing remains relatively unexplored within the process systems engineering field. One of the reasons for this is that it is not currently clear whether there exists a quantum computing algorithm that can provide speedups for control design to provide a benefit from quantum computing. However, it is our hypothesis that a more detailed understanding of how control design and theory interact with quantum computing algorithms could help to suggest modifications to the logic of the quantum computing algorithms to achieve control objectives, which may also aid in revealing beneficial algorithms from a computational perspective. This work thus takes a control-theoretic perspective on quantum computing for control, rather than an algorithmic efficiency perspective, with the hope of spurring future work in algorithm development.

In this talk, we will describe our work at the interface of control and quantum computing,^[3] focusing first on the impacts of noise in quantum hardware on the stabilization of the state of a single-input/single-output process under a control law that can be computed using an addition circuit based on the Quantum Fourier Transform (QFT).^[4] This system was simulated using a quantum simulator available from IBM's Quantum Experience. This allows addition of a custom noise model to simulate errors in the computations due to the hardware that would be seen on an actual device. The custom noise model used was based on the depolarizing error. The state and input trajectories for the process when the control law is the same but control actions are computed by a classical computer or the quantum simulator in the absence of noise are compared with the case that the inputs are computed by the quantum simulator with noise. This is performed for different initial conditions and numbers of runs of the quantum simulator. In all cases, the closed-loop state was eventually driven to the origin. This motivates further study of the manner in which different tuning variables for the system impact the result. For example, different error parameters were also tested, and both an estimate of the percentage of the inputs that would drive the closed-loop state toward the origin from a given state as well as the different frequencies with which these inputs were computed for different implementations of the control law at the addition algorithm implementation level were examined.

The fact that undesired inputs were still able to drive the closed-loop state toward the origin with time under the control policy with different error parameters in the noise model for the quantum device raises the question of what this result implies for cybersecurity of control systems. Our group has developed control-theoretic studies regarding cybersecurity of process control systems (e.g., ^[5,6]) in which we develop conditions under which we can guarantee that attacks are detected when the process is controlled by an advanced control law, and/or when we can guarantee safety until the time of detection in the sense that the closed-loop state is maintained in a bounded region of state-space. Cyberattacks on a control system can be thought of as an undesired input policy; we therefore compare the results under the quantum computing and cyberattack scenarios to better understand relationships between these cases and what the relationships indicate about techniques for handling both methods. Finally, we conclude with a discussion of techniques for examining quantum noise in the context of other control laws besides that applied for the single input-single output control law.

References:

[1] Ajagekar, A., & You, F. (2019). Quantum computing for energy systems optimization: Challenges and opportunities. Energy, 179, 76-89.

[2] Ajagekar, A., & You, F. (2020). Quantum computing assisted deep learning for fault detection and diagnosis in industrial process systems. Computers & Chemical Engineering, 143, 107119.

[3] Nieman, K., Rangan, K. K., & Durand, H. Control Implemented on Quantum Computers: Effects of Noise, Non-Determinism, and Entanglement. Industrial & Engineering Chemistry Research (in press).

[4] Ruiz-Perez, L., & Garcia-Escartin, J. C. (2017). Quantum arithmetic with the quantum Fourier transform. Quantum Information Processing, 16(6), 1-14.

[5] Rangan, K. K., Oyama, H., & Durand, H. Integrated Cyberattack Detection and Handling for Nonlinear Systems with Evolving Process Dynamics under Lyapunov-based Economic Model Predictive Control. Chemical Engineering Research and Design (2021).

[6] Oyama, H., Rangan, K. K., & Durand, H. Lyapunov-Based Economic Model Predictive Control for Detecting and Handling Actuator and Simultaneous Sensor/Actuator Cyberattacks on Process Control Systems. Frontiers in Chemical Engineering, 11.