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IEEE International Conference on Quantum Computing and Engineering (QCE)

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

Shilpa Narasimhan, Keshav Kasturi Rangan, Helen Durand

Published Sep 15, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.1109/qce60285.2024.00142

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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.
Processing and storage demands of industrial processes are causing fields such as optimization, scheduling, and control to assess the effectiveness of quantum devices in their applications. A key objective of control systems is to ensure process safety. This paper focuses on the potential of quantum devices to compute control inputs that maintain system safety despite sources of nondeterminism inherent to currently available quantum devices (quantum noise). In our previous work, we employed a quantum simulator to assess whether a quantum implementation of a proportional (P) control law could stabilize a single-input/single-output system under quantum noise approximated from a real quantum device. While one algorithm achieved this objective, another performed poorly, raising questions about the underlying reasons for their differing performance. This study explores how conventional control engineering techniques for handling nondeterminism (e.g., modifying sampling period lengths or applying only stabilizing control actions based on steady-state tracking) could enhance system response in the presence of noise. Utilizing IBM’s Qiskit, a quantum simulator was used to evaluate algorithmic and heuristic control strategies to improve the steady-state tracking performance of a P-control law under quantum noise. The objective here is to provide insight into the feasibility of near-term quantum devices to execute control actions with safety considerations.
A major challenge to determining the applicability (and potential outperformance over classical computers) of a quantum computer (QC) within chemical manufacturing processes is quantum noise. Computations by a QC are error-prone due to the influence of quantum noise inherent to the hardware. Errors in control inputs may destabilize a chemical process and lead to unsafe conditions for manufacturing personnel and the environment. The response of a process with control implemented on a QC to errors due to noise must be investigated thoroughly. In this work, the impacts of control input errors due to quantum noise on a process are modeled as bounded additive exogenous signals. Process and control element dynamics dictate the response of the process due to perturbations from exogenous signals. A theoretical analysis of the influence of process and control element dynamics on the response of a process to errors in control implemented on a QC is presented. Using simulations of a process example, a demonstration of the interplay between process response to noise, process dynamics, and control valve dynamics is illustrated. The results evaluate, for a specific process, aspects of how process and control element dynamics may mitigate the impact of noise.
A major challenge to determining the applicability (and potential outperformance over classical computers) of a quantum computer (QC) within chemical manufacturing processes is quantum noise. Computations by a QC are error-prone due to the influence of quantum noise inherent to the hardware. Errors in control inputs may destabilize a chemical process and lead to unsafe conditions for manufacturing personnel and the environment. The response of a process with control implemented on a QC to errors due to noise must be investigated thoroughly. In this work, the impacts of control input errors due to quantum noise on a process are modeled as bounded additive exogenous signals. Process and control element dynamics dictate the response of the process due to perturbations from exogenous signals. A theoretical analysis of the influence of process and control element dynamics on the response of a process to errors in control implemented on a QC is presented. Using simulations of a process example, a demonstration of the interplay between process response to noise, process dynamics, and control valve dynamics is illustrated. The results evaluate, for a specific process, aspects of how process and control element dynamics may mitigate the impact of noise.
Quantum computing has advanced in recent years to the point that there are now some quantum computers and quantum simulators available to the public for use. In addition, quantum computing is beginning to receive attention within the process systems engineering community for directions such as machine learning and optimization. A logical next step for its evaluation within process systems engineering is for control, specifically for computing control actions to be applied to process systems. In this work, we provide some initial studies regarding the implementation of control on quantum computers, including the implementation of a single-input/single-output proportional control law on a quantum simulator with noise, evaluation of potential impacts of nondeterminism on theory for advanced control laws, and discussion of consequences of the way that entanglement works for next-generation manufacturing communication objectives.
Noisy intermediate-scale quantum (NISQ) devices are valuable platforms for testing the tenets of quantum computing, but these devices are susceptible to errors arising from de-coherence, leakage, cross-talk, and other sources of noise. This raises concerns regarding the stability of results when using NISQ devices since strategies for mitigating errors generally require well-characterized and stationary error models. Here, we quantify the reliability of NISQ devices by assessing the necessary conditions for generating stable results within a given tolerance. We use similarity metrics derived from device characterization data to derive and validate bounds on the stability of a 5-qubit implementation of the Bernstein-Vazirani algorithm. Simulation experiments conducted with noise data from IBM washington, spanning January 2022 to April 2023, revealed that the reliability metric fluctuated between 41% and 92%. This variation significantly surpasses the maximum allowable threshold of 2.2% needed for stable outcomes. Consequently, the device proved unreliable for consistently reproducing the statistical mean in the context of the Bernstein-Vazirani circuit.
Quantum devices in the noisy intermediate-scale quantum (NISQ) era are highly susceptible to different types of quantum noise, which directly impact the reliability of experimental results. This work provides a characterization of error behavior arising from quantum noises on IBM's superconducting quantum processor, offering practical insights for algorithm design, benchmarking, and error-mitigation strategies on a real superconducting quantum processor in the NISQ era. The study begins with the measurement of the basis state, without applying any gate, to quantify state-preparation and measurement (SPAM) errors. Additionally, the errors are further quantified due to the application of single-qubit Pauli-X, two-qubit CNOT gate and other multi-qubit Controlled-X gates. Each circuit was executed with 1024 shots, and the percentage error between the expected and observed outputs was computed. The results show that the single-qubit Pauli-X gate exhibits relatively low errors in comparison with the two-qubit CNOT gate, whereas other multi-qubit Controlled-X gates lead to significantly higher deviations. This work also analyzes the noise effect of a fourqubit Controlled-X gate being implemented using a three-qubit Controlled-X gate with an extra auxiliary qubit, and the result shows a significant reduction in the error rate.