Open Access

ARTICLE

Near Term Hybrid Quantum Computing Solution to the Matrix Riccati Equations

Augusto González Bonorino^1,*, Malick Ndiaye², Casimer DeCusatis²

1 Claremont Graduate University, Claremont, 91711, USA
2 Marist College, Poughkeepsie, 12601, USA

* Corresponding Author: Augusto González Bonorino. Email:

Journal of Quantum Computing 2022, 4(3), 135-146. https://doi.org/10.32604/jqc.2022.036706

Received 10 October 2022; Accepted 07 April 2023; Issue published 03 July 2023

Abstract

The well-known Riccati differential equations play a key role in many fields, including problems in protein folding, control and stabilization, stochastic control, and cybersecurity (risk analysis and malware propagation). Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical algorithms. While systems with many qubits are still under development, there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and limitations. In this paper, we propose a hybrid quantum-classical algorithm, the Matrix Riccati Solver (MRS). This approach uses a transformation of variables to turn a set of nonlinear differential equation into a set of approximate linear differential equations (i.e., second order non-constant coefficients) which can in turn be solved using a version of the Harrow-Hassidim-Lloyd (HHL) quantum algorithm for the case of Hermitian matrices. We implement this approach using the Qiskit language and compute near-term results using a 4 qubit IBM Q System quantum computer. Comparisons with classical results and areas for future research are discussed.

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Keywords

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