(578c) Optimization-Based Design of Process Control Law for Implementation on Quantum Computers

Process control laws are utilized to compute the control actions that must be performed by actuators in a chemical manufacturing process to operate the process in a safe and economically viable manner. Process control is implemented today using classical computing strategies; however, as updates to computing strategies are made (e.g., as quantum computers are developed), it becomes necessary to assess whether these new computing frameworks can or should have an impact on the process control field. Quantum computers utilize the laws of quantum mechanics such as superposition, entanglement, and interference in performing computations, and therefore can act in a fundamentally different manner from classical devices [2]. Motivated by this, research focused on applications of quantum computing within the chemical manufacturing industry has received increasing attention within the process systems engineering community [3-6]. However, the manner in which quantum computers would interact with process control systems remain underexplored. It is necessary to clarify how these devices, which can produce non-deterministic results due to algorithm designs and "noise" (errors in the computations) interact with system safety when used for computing control actions.

Broadly, quantum computers may be classified as: (1) annealing quantum computers, and (2) gate-based quantum computers [7]. Quantum annealing computers perform quantum annealing which is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations (variations of energy at a point in space) [11]. Typically, quantum annealing computers have found applications in optimization. Gate-based quantum computers utilize a quantum circuit constructed using a series of quantum gates, each of which acts on a small number of qubits to manipulate the quantum state of the qubits and perform quantum algorithms. Gate-based quantum computers are more versatile than quantum annealing computers [8] and are the focus of the current work. Quantum noise within the circuits of a quantum computer impacts the accuracy of computations performed. One approach to minimize the impact of the noise within a quantum circuit may be to minimize the gate-depth (the number of quantum gates utilized to perform a computation). Motivated by this, we performed a thought experiment in [5] considering how to develop an optimization problem for locating only a few gates which form a given algorithm. However, we investigated this in the context of a single qubit, which was not capable of utilizing many of the important properties of quantum computation. Learning of algorithms for quantum devices has been previously considered (e.g., [1]); therefore, it is our goal in this work to consider how optimization and learning of algorithms of control-relevance may be undertaken.

Motivated by the results in [5], this work considers, the design of a multi-qubit quantum circuit to compute the control input for processes under control implemented on quantum computers. The quantum gates applied within a circuit may change with the number of qubits and the gate-depth of the circuit. Considering this, an algorithm that may be used to identify a sequence of gates that must be applied to compute the control action using a quantum circuit when a pre-specified and fixed gate-depth is designed. Specifically, the problem of identifying the sequence of gates for a given quantum circuit is cast as a convex optimization problem that minimizes the square of the error between the control input computed by the quantum computer and the control input computed by a classical computer with the same feedback as the quantum computer. Under the proposed optimization-based strategy of gates, a parameterized single qubit gate [9] is assumed to operate on each qubit at each gate-depth. This means that that for an n-qubit system, the tensor product of n-parameterized single qubit gates acts to manipulate the quantum state. Furthermore, the parameterized single qubit gate may be expressed as any other quantum gate by varying three different parameters over a closed interval, thereby, allowing for the formulation of an optimization problem with continuous decision variables (which are the parameters dictating the gate that is applied on each qubit at each gate depth). The optimal sequence of gates predicted for different gate depths are computed and their performance is analyzed using simulations of an illustrative process performed over a noise-free quantum simulator [10]. Finally, using simulations of the illustrative process performed over a noisy quantum simulator that utilizes the optimal control circuit to compute the control actions, the impact of gate-depth and the quantum noise on the computed control action (and on the illustrative process) is analyzed.

References:

[1] Cincio, Lukasz, Yiğit Subaşı, Andrew T. Sornborger, and Patrick J. Coles. "Learning the quantum algorithm for state overlap." New Journal of Physics 20, no. 11 (2018): 113022.

[2] Berman, G.P., “Introduction to quantum computers”, World Scientific, 1998.

[3] A., Ajagekar, and F., You, “New frontiers of quantum computing in chemical engineering”, Korean Journal of Chemical Engineering, volume 39, pp. 811–820, 2022.

[4] Nieman, K., Rangan, K. K., and Durand, H., “Control Implemented on Quantum Computers: Effects of Noise, Non-Determinism, and Entanglement”, Industrial & Engineering Chemistry Research, volume 61(28), pp. 10133-10155, 2022.

[5] Nieman, K., Durand, H., Patel, S., Koch, D. and Alsing, P.M., “Investigating an amplitude amplification-based optimization algorithm for model predictive control”, Digital Chemical Engineering, volume 10, p.100134, 2024.

[6] Rangan, K. K., Abou Halloun, J., Oyama, H., Cherney, S., Assoumani, I. A., Jairazbhoy, N., Durand, H, and Ng, S.K., “Quantum computing and resilient design perspectives for cybersecurity of

feedback systems”, Proceedings of the 13th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems, volume 55(7), pp. 703-708, Busan, Republic of Korea, 14–17 June 2022.

[7] Leprince-Ringuet, D. “ZDNet: Quantum Computing: Quantum Annealing versus Gate-Based Quantum Computers”, https://www.dwavesys.com/company/newsroom/media-coverage/zdnet-quantum-computing-quantum-annealing-versus-gate-based-quantum-computers/ , Accessed: 8^th April, 2024.

[8] Schrodinger, “Differences between quantum annealers and gate-based quantum computing”, https://quantumzeitgeist.com/differences-between-quantum-annealers-and-gate-based-quantum-computing/, Accessed: 8^th April, 2024.

[9] “Summary of Quantum Operations”, https://github.com/Qiskit/qiskit-tutorials/blob/master/tutorials/circuits/3_summary_of_quantum_operations.ipynb, Accessed: 8^th April 2024.

[10] Norlén H., “Quantum Computing in Practice with Qiskit® and IBM Quantum Experience®: Practical recipes for quantum computer coding at the gate and algorithm level with Python”, Packt Publishing Ltd, 2020.

[11] Quantum Annealing, “https://en.wikipedia.org/wiki/Quantum_annealing”, Accessed: 8^th April, 2024.