How a Quantum Computer Could Solve a Microkinetic Model

Abstract

A CO oxidation microkinetic model is set up for a quantum circuit. The CO oxidation microkinetic model, and microkinetic models in general, exhibit an advantage of not requiring an encoding step because of being a subclass of systems of equations. The microkinetic model is cast as a nonlinear set of equations at first. Then, a linearizing approximation is made, and the resulting linear set of equations may be iterated to converge to the solution to the nonlinear set of equations. In this CO oxidation, the linearized set of equations is realized to chemical accuracy with one iteration. Current limitations in executing the quantum circuit to obtain the solution are discussed. v 1 1 CO 1 CO (3a)

How a quantum computer could accurately solve a hydrogen-air combustion model

“…There currently exist a number of quantum algorithms for solving linear systems of equations, 10 the most prominent of which is Harrow, Hassidim and Lloyd (HHL). 11 Linear systems are fundamental in chemical kinetics, 12 partial differential equations, 13 back-propagation in neural networks, 14 and graph theory analytics. [15][16][17] So, the importance of a quantum speedup for solving linear systems cannot be understated.…”

How a Quantum Computer Could Quantify Uncertainty in Microkinetic Models

“…5−7 The microkinetic model is linearized in preparation for input to a quantum circuit. 8 The algorithm employed is the Harrow, Hassidim, and Lloyd 9 (HHL) algorithm for linear systems. 4,10 Three variations of the CO oxidation microkinetic model are created to illustrate uncertainty quantification (UQ) on this model.…”

“…An advantageous consideration is that once enough qubits are added to the compute register 8 to obtain the necessary precision, no more qubits need to be added to this register despite growth in the number of UQ samples. The qubit registers of the quantum circuit have been previously established, 8 but the reason is that the register which holds the eigenvalues is separate from the register holding the solution vector x. That is, when the number of samples grows, and with it the matrix dimension, qubits are added to the memory register only.…”

“…Although the quantum circuit for a microkinetic model has been previously elaborated, 8 it is necessary to provide further analysis of the quantum circuit in the context of microkinetic models. The reason is UQ will provide variations to the quantum circuit input, and it is necessary to know how this will impact the solution and the computational burden.…”

“…In this Letter, carbon monoxide (CO) oxidation reaction via a Rh(111) catalyst is evaluated for its uncertainty. The free-energy path is calculated with density functional theory (DFT), and the results parametrize a mean-field microkinetic model. − The microkinetic model is linearized in preparation for input to a quantum circuit . The algorithm employed is the Harrow, Hassidim, and Lloyd (HHL) algorithm for linear systems. , Three variations of the CO oxidation microkinetic model are created to illustrate uncertainty quantification (UQ) on this model.…”