Study of Error Propagation and Generation in Harrow-Hassidim-Lloyd (HHL) Quantum Algorithm
Publication Date
1-1-2022
Document Type
Conference Proceeding
Publication Title
2022 IEEE Latin American Electron Devices Conference (LAEDC)
DOI
10.1109/LAEDC54796.2022.9908231
Abstract
In this paper, we study the error propagation and generation in the Harrow-Hassidim-Lloyd (HHL) quantum algorithm runs on IBM-Q hardware with the help of a MATLAB simulator. HHL is a quantum algorithm that can provide exponential speedup over the fastest classical algorithm (conjugate gradient method) in solving systems of linear equations (SLE). However, without error correction, it cannot give correct results even in a 2-variable system due to its complexity. In this study, an HHL quantum circuit for a 2-variable SLE is implemented in IBM-Q and the error is extracted after each stage of the circuit and compared to a MATLAB simulator. We identified three major sources of errors, namely single-qubit flipping, gate infidelity, and error propagation. We also found that at the ancillary bit rotation stage, the error becomes large but the encoded solution still has high fidelity. However, the solution is mostly lost after the inverse quantum phase estimation which is necessary to extract the solution efficiently. Therefore, it is suggested that error correction resources, if limited, should be added to the second half of the circuit.
Funding Number
2046220
Funding Sponsor
National Science Foundation
Keywords
Error, HHL, Quantum Algorithm, Quantum Computing, Qubit Flipping
Department
Electrical Engineering
Recommended Citation
Anika Zaman and Hiu Yung Wong. "Study of Error Propagation and Generation in Harrow-Hassidim-Lloyd (HHL) Quantum Algorithm" 2022 IEEE Latin American Electron Devices Conference (LAEDC) (2022). https://doi.org/10.1109/LAEDC54796.2022.9908231
