Advanced Quantum Poisson Solver in the NISQ era

Robson, Walter; Saha, Kamal K.; Howington, Connor; Suh, In-Saeng; Nabrzyski, Jarosław

doi:10.1109/qce53715.2022.00103

Cited by 2 publications

(4 citation statements)

References 9 publications

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“…1 [1,23]. As the figure shows, the algorithm consists of three stages: phase estimation, controlled rotation, and uncomputation.…”

Section: Quantum Algorithm and Circuit Designmentioning

confidence: 99%

“…As a result, the accumulated errors of the CNOT -gates result in the washing out of the experimental accuracy, which contributes to the artifact of a nonzero contribution for the |00 state (see the figure in Ref. [1]). In general, experimenting with the circuit on different IBM hardware would end up with similar results, as the best CNOT accuracy on any system is less than 0.99.…”

Section: Effects Of Cnot Error On the Experiments Of 3 × 3 Problem On...mentioning

confidence: 99%

“…Our previous work [1] serves as an initial outline of our research on the quantum Poisson equation solver. It presents a proof-of-concept demonstration of our quantum Poisson solver algorithm and validates preliminary results for a simple case of 3 × 3 problem.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, by solving different sizes of problems, this paper demonstrates the advancement of our algorithm for solving the Poisson equation in several aspects: (1) Improve the precision of phase estimation by increasing the accuracy of the eigenvalues. Unlike the previous approach [23] where only the integer part of the eigenvalues was encoded, we implement non-truncated eigenvalues through eigenvalue amplification.…”

Section: Introductionmentioning

confidence: 99%

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Enhancing scalability and accuracy of quantum poisson solver

Saha,

Robson,

Howington

et al. 2024

Quantum Inf Process

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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 $$3\times 3$$ 3 × 3 problem. In this work, we delve into comprehensive research details, presenting the results on up to $$15\times 15$$ 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 $$2^8$$ 2 8 , 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.

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“…1 [1,23]. As the figure shows, the algorithm consists of three stages: phase estimation, controlled rotation, and uncomputation.…”

Section: Quantum Algorithm and Circuit Designmentioning

confidence: 99%

Section: Effects Of Cnot Error On the Experiments Of 3 × 3 Problem On...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Enhancing scalability and accuracy of quantum poisson solver

Saha,

Robson,

Howington

et al. 2024

Quantum Inf Process

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Quantum algorithms for scientific computing

Au-Yeung,

Camino,

Rathore

et al. 2024

Rep. Prog. Phys.

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Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in real world applications. Areas that are likely to have the greatest impact on high performance computing (HPC) include simulation of quantum systems, optimization, and machine learning. We draw our examples from electronic structure calculations and computational fluid dynamics which account for a large fraction of current scientific and engineering use of HPC. Potential challenges include encoding and decoding classical data for quantum devices, and mismatched clock speeds between classical and quantum processors. Even a modest quantum enhancement to current classical techniques would have far-reaching impacts in areas such as weather forecasting, engineering, aerospace, drug design, and the design of ``green'' materials for sustainable development. This requires significant effort from the computational science, engineering and quantum computing communities working together.

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Advanced Quantum Poisson Solver in the NISQ era

Cited by 2 publications

References 9 publications

Enhancing scalability and accuracy of quantum poisson solver

Enhancing scalability and accuracy of quantum poisson solver

Quantum algorithms for scientific computing

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