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. In this regard, our previous work (Robson in 2022 IEEE International Conference on Quantum Computing and Engineering (QCE), 2022) showed a proof-of-concept demonstration in advancing quantum Poisson solver algorithm and validated preliminary results for a simple case of 3×3 problem. In this work, we delve into comprehensive research details, presenting the results on up to 15×15 problems that include step-by-step improvements in Poisson equation solutions, scaling performance, and experimental exploration. In particular, we demonstrate the implementation of eigenvalue amplification by a factor of up to 28, achieving a significant improvement in the accuracy of our quantum Poisson solver and comparing that to the exact solution. Additionally, we present success probability results, highlighting the reliability of our quantum Poisson solver. Moreover, we explore the scaling performance of our algorithm against the circuit depth and width, demonstrating how our approach scales with larger problem sizes and thus further solidifies the practicality of easy adaptation of this algorithm in real-world applications. We also discuss a multilevel strategy for how this algorithm might be further improved to explore much larger problems with greater performance. Finally, through our experiments on the IBM quantum hardware, we conclude that though overall results on the existing NISQ hardware are dominated by the error in the CNOT gates, this work opens a path to realizing a multidimensional Poisson solver on near-term quantum hardware.
| Original language | English |
|---|---|
| Article number | 209 |
| Journal | Quantum Information Processing |
| Volume | 23 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 2024 |
Funding
This research was supported in part by the Notre Dame Center for Research Computing through Notre Dame Research. The authors admire Scott Hampton\u2019s comments on the manuscript. The authors also appreciate access to IBM Quantum Hardware through IBM Quantum Network. This work was supported in part by the Department of Energy, Office of Science, Advanced Scientific Computing Research program. This research used resources from the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US Department of Energy under Contract No. DE-AC05-00OR22725. Notice: This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the US Department of Energy. The publisher, by accepting the article for publication, acknowledges that the US 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 US Government purposes. The DOE will provide public access to these results in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ).
Keywords
- Poisson equation
- Poisson solver algorithm
- Quantum algorithm
- Quantum circuit
- Quantum error mitigation