(149ab) Considerations of Closed-Loop Control on Quantum Computers Using a Modified Grover’s Algorithm for Simulation of a Chemical Process

Quantum computing is becoming of greater interest for a variety of reasons. These include that some quantum computing algorithms, such as Grover’s and Shor’s algorithms, have been shown to offer a speedup over their classical computing analogues [1]. Quantum computing has been receiving recent attention in the process systems engineering field for applications in modeling, optimization, and machine learning tasks [2,3]. It is not yet clear how quantum algorithms could impact process control. The use of quantum computing algorithms in control can introduce phenomena that need to be accounted for such as nondeterminism, "noise" (unexpected/erroneous results from computations), and rounding effects, among other considerations [2, 3]. In our previous work [4], we sought to understand some of the effects of nondeterminism in control law selection due to a quantum algorithm on control-theoretic safety guarantees. The control law used a lookup table of state measurement/control input relationships that was "searched" using a quantum circuit based on the database-searching algorithm known as Grover's algorithm [4]. The search procedure in [4] used a series of controlled Grover blocks to obtain the control input corresponding to a measurement from the table with a certain probability. Initial results considering how this would integrate with the control-theoretic guarantees of an advanced control framework known as Lyapunov-based economic model predictive control (LEMPC) [5,6] were described.

Our prior work in [4] was a proof-of-concept and addressed theory considerations, but did not showcase through example how the algorithm could be designed for a chemical process or how a process system might act when controlled by such an algorithm. In this talk, we discuss how the modified Grover's algorithm framework from [4] could be applied to a simulation of control of a chemical process. We will discuss the creation of a lookup table of control actions for state measurements for a process operating under LEMPC, which is a requirement of implementing the quantum computing algorithm. Due to an assumption of limited qubit availability, measured process states and inputs must be rounded before incorporation into the table. The effects of different total numbers of qubits on the results will be explored in simulation, and the relationship of the results to the theory from [4] will be discussed. Following this, we will also discuss a modification of this algorithm, where additional gates are added to the algorithm to prevent the selection of certain unwanted control actions. This is a concern because the nondeterminism involved in the algorithm means that there is a probability of measuring one of many different quantum states, and it is possible that one of the control inputs returned through this process could be problematic for safety. We will discuss ways of creating these gates, including by solving an optimization problem where, for a given process state measurement, the qubit amplitude of an undesired control action is constrained to zero. Finally, we will discuss methods of dealing with the nondeterminism in the control actions, such as specifying regions where a stabilizing classical control action is activated to ensure an equilibrium remains stable.

[1]. Yanofsky, Noson S., and Mirco A. Mannucci. Quantum computing for computer scientists. Cambridge University Press, 2008.

[2]. Andersson, Martin P., et al. "Quantum computing for chemical and biomolecular product design." Current Opinion in Chemical Engineering 36 (2022): 100754.

[3]. Ajagekar, Akshay, and Fengqi You. "New frontiers of quantum computing in chemical engineering." Korean Journal of Chemical Engineering 39.4 (2022): 811-820.

[4]. Nieman, Kip, Keshav Kasturi Rangan, and Helen Durand. "Control Implemented on Quantum Computers: Effects of Noise, Nondeterminism, and Entanglement." Industrial & Engineering Chemistry Research 61.28 (2022): 10133-10155.

[5]. Heidarinejad, Mohsen, Jinfeng Liu, and Panagiotis D. Christofides. "Economic model predictive control of nonlinear process systems using Lyapunov techniques." AIChE Journal 58.3 (2012): 855-870.

[6]. Ellis, Matthew, Helen Durand, and Panagiotis D. Christofides. "A tutorial review of economic model predictive control methods." Journal of Process Control 24.8 (2014): 1156-1178.