Toward Strategies for Characterizing NISQ Device Requirements in Linear Systems Control via Stability and Profitability Analysis

Classical computing systems find utility in performing engineering computations in both design and operation of chemical manufacturing processes. During operation, computing systems may be used within process control systems (PCSs) to operate processes by computing control actions. Control engineers may eventually need to determine the utility of other computing devices such as quantum devices (QCs) within PCSs. A QC that is not fault-tolerant may introduce errors in control computations due to the noise (e.g., quantum noise) and result in the process states (e.g., temperature, concentration) deviating from desired operating limits. Deviations of process states may result in one or both of two undesirable consequences that need to be addressed: (1) unsafe situations (e.g., due to loss of containment) and (2) reduction in the profitability of the process (e.g., due to low quality product). Thus, it is currently unclear to what extent errors in noisy intermediate-scale quantum (NISQ) devices would need to be eliminated before they could have potential utility for control action computation. In the current work, we investigate how control theory might aid in guiding answers to this question. We first characterize the stability of linear processes with proportional control implemented on a QC by treating quantum noise as a bounded disturbance exogenous to the process. Then, we analyze the extent to which an optimal control formulation for processes with noise and plant/model mismatch might apply to processes with unexpected control actions from a NISQ device. We demonstrate the results using a single-input/single-output system under a control law implemented using a quantum simulator with a depolarizing error noise model affecting the control action computations.