(204g) Design of Short-Time Approximate Quantum Algorithms for Process Control

The recent years have seen rapid development in the field of quantum computing [1]. This advancement of the field has motivated a multi-disciplinary investigation into the applicability of quantum computers within various scientific fields (e.g., [2], [3]). Within the theory and practice of control engineering, the applicability of quantum computers for computing control inputs to be implemented on manufacturing processes may need to be determined by control engineers.

The current generation of quantum computers are subject to hardware-intrinsic quantum noise that manifests as error prone computations which may impact the stability of the process. In prior work by our group, the stability of a process with control implemented on a noisy computer was analyzed [4]. The results indicated when process control may be implemented on a quantum computer. Furthermore, the results indicated that for practical implementation, the impact of quantum noise on the control input computations may need to be minimized. The impact of quantum noise on the computations performed by a quantum computer increases with the quantum circuit depth which specifies the number of gates (operations performed by the quantum computer on its internal states to perform computations). In another work [5], several path finding studies were presented that analyzed how quantum circuit design may be utilized to minimize the impact of quantum noise on a process with control implemented on a quantum computer, including a method utilizing the CHSH method to identify short-cut approximations for control laws that can be implemented over short circuit depths.

The CHSH strategy describes the sequence of moves two players may make to win against a referee who communicates a value of x or y (which can each be 0 or 1) to each of the players [6]. To win the game, the players must each communicate values a and b (each of which can take values 0 or 1) to the referee such that (a+b) mod 2 = x*y. During the game the players cannot communicate with each other. However, before the game begins, they decide on a strategy that relies on them sharing one half of an entangled state. Under the CHSH strategy, the players can win against the referee with a probability of 85%. The results presented in [6] demonstrated that for a given entangled state pair and a fixed set of state measurements, there exist viable control law approximations for policies that may be implemented over a short-depth circuit with a prespecified depth. However, a single control law approximation that was valid over all scenarios considered was not found.

In this work, the optimization problem in [6] is solved to identify control law approximations that are valid over a range of entangled state pair and state measurements with a certain probability specified by a probability constraint within the optimization problem. Enforcing the probability constraints influences the errors in control inputs computed using the control law approximations. This may mean that a tradeoff between performance and control law approximations may exist. The bound on the error may be influenced by the probability constraints and the circuit depths. Therefore, the magnitude of error from control law approximations over a range of probability constraints and the circuit depths are analyzed to study how the various factors influence control law approximations. The studies serve as analyses considering how CHSH game may be leveraged to aid in the implementation of process control on a quantum computer.

References:

[1] Gill, S. S., et al., "Quantum computing: A taxonomy, systematic review and future directions.", Software: Practice and Experience, vol. 52, no.1, pp. 66-114, 2022.

[2] Flöther, F. F., "The state of quantum computing applications in health and medicine.", Research Directions: Quantum Technologies, vol. 1, p. e10, 2023.

[3] Fauseweh, B., "Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges.”, Nature Communications, vol. 15, no.1, p. 2123, 2024.

[4] Narasimhan, S., et al., “Toward strategies for characterizing NISQ device requirements in linear systems control via stability and profitability analysis,” in Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE24), vol. 01, Montréal, Québec, Canada, pp. 1203–1213, 31 Aug- 5 Sep 2024.

[5] S. Narasimhan, et al., “Tools to Design Algorithms for Implementing Control Over Quantum

Computers”, In Press, 2025.

[6] J. F., Clauser, et al., "Proposed experiment to test local hidden-variable theories.", Physical review letters, vol. 23, no.15, p. 880, 1969.