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Near Term Hybrid Quantum Computing Solution to the Matrix Riccati Equations

Augusto González Bonorino1,*, Malick Ndiaye2, Casimer DeCusatis2

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

* Corresponding Author: Augusto González Bonorino. Email: email

Journal of Quantum Computing 2022, 4(3), 135-146.


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.


Cite This Article

A. G. Bonorino, M. Ndiaye and C. DeCusatis, "Near term hybrid quantum computing solution to the matrix riccati equations," Journal of Quantum Computing, vol. 4, no.3, pp. 135–146, 2022.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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