Advanced Quantum Poisson Solver in the NISQ era

Walter Robson; Kamal K. Saha; Connor Howington; In Saeng Suh; Jaroslaw Nabrzyski

doi:10.1109/QCE53715.2022.00103

Advanced Quantum Poisson Solver in the NISQ era

Walter Robson, Kamal K. Saha, Connor Howington, In Saeng Suh, Jaroslaw Nabrzyski

Technology Integration

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental results, and discuss the sources of errors. Finally, we conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.

Original language	English
Title of host publication	Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	741-744
Number of pages	4
ISBN (Electronic)	9781665491136
DOIs	https://doi.org/10.1109/QCE53715.2022.00103
State	Published - 2022
Event	3rd IEEE International Conference on Quantum Computing and Engineering, QCE 2022 - Broomfield, United States Duration: Sep 18 2022 → Sep 23 2022

Publication series

Name	Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022

Conference

Conference	3rd IEEE International Conference on Quantum Computing and Engineering, QCE 2022
Country/Territory	United States
City	Broomfield
Period	09/18/22 → 09/23/22

Funding

This research was supported in part by the Notre Dame Center for Research Computing through the HPC resources. This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid up, irrevocable, world-wide license to publish or reproduce the published form of the manuscript, or allow others to do so, for United States Government purposes This research was supported in part by the Notre Dame Center for Research Computing through the HPC resources. This manuscript has been authored by UT-Battelle,LLC under Contract No. DE-AC05-00OR22725with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid up, irrevocable, world-wide license to publish or reproduce the published form of the manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

Keywords

HHL Algorithm
Poisson Equation
Quantum Algorithm
Quantum Circuit

Access to Document

10.1109/QCE53715.2022.00103

Cite this

Robson, W., Saha, K. K., Howington, C., Suh, I. S., & Nabrzyski, J. (2022). Advanced Quantum Poisson Solver in the NISQ era. In Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022 (pp. 741-744). (Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/QCE53715.2022.00103

Robson, Walter ; Saha, Kamal K. ; Howington, Connor et al. / Advanced Quantum Poisson Solver in the NISQ era. Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022. Institute of Electrical and Electronics Engineers Inc., 2022. pp. 741-744 (Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022).

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title = "Advanced Quantum Poisson Solver in the NISQ era",

abstract = "The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental results, and discuss the sources of errors. Finally, we conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.",

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Robson, W, Saha, KK, Howington, C, Suh, IS & Nabrzyski, J 2022, Advanced Quantum Poisson Solver in the NISQ era. in Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022. Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022, Institute of Electrical and Electronics Engineers Inc., pp. 741-744, 3rd IEEE International Conference on Quantum Computing and Engineering, QCE 2022, Broomfield, United States, 09/18/22. https://doi.org/10.1109/QCE53715.2022.00103

Advanced Quantum Poisson Solver in the NISQ era. / Robson, Walter; Saha, Kamal K.; Howington, Connor et al.
Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022. Institute of Electrical and Electronics Engineers Inc., 2022. p. 741-744 (Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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PY - 2022

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N2 - The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental results, and discuss the sources of errors. Finally, we conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.

AB - The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental results, and discuss the sources of errors. Finally, we conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.

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Robson W, Saha KK, Howington C, Suh IS, Nabrzyski J. Advanced Quantum Poisson Solver in the NISQ era. In Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022. Institute of Electrical and Electronics Engineers Inc. 2022. p. 741-744. (Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022). doi: 10.1109/QCE53715.2022.00103

Advanced Quantum Poisson Solver in the NISQ era

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