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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2502.11239 |
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| _version_ | 1866915156954447872 |
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| author | Tu, Yue Dubynskyi, Mark Mohammadisiahroudi, Mohammadhossein Riashchentceva, Ekaterina Cheng, Jinglei Ryashchentsev, Dmitry Terlaky, Tamás Liu, Junyu |
| author_facet | Tu, Yue Dubynskyi, Mark Mohammadisiahroudi, Mohammadhossein Riashchentceva, Ekaterina Cheng, Jinglei Ryashchentsev, Dmitry Terlaky, Tamás Liu, Junyu |
| contents | Quantum computing, a prominent non-Von Neumann paradigm beyond Moore's law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum noise complicates resource estimations and classical comparisons. We provide a detailed estimation of space, time, and energy resources for fault-tolerant superconducting devices running the Harrow-Hassidim-Lloyd (HHL) algorithm, a quantum linear system solver relevant to linear algebra and machine learning. Excluding memory and data transfer, possible quantum advantages over the classical conjugate gradient method could emerge at $N \approx 2^{33} \sim 2^{48}$ or even lower, requiring ${O}(10^5)$ physical qubits, ${O}(10^{12}\sim10^{13})$ Joules, and ${O}(10^6)$ seconds under surface code fault-tolerance with three types of magic state distillation (15-1, 116-12, 225-1). Key parameters include condition number, sparsity, and precision $κ, s\approx{O}(10\sim100)$, $ε\sim0.01$, and physical error $10^{-5}$. Our resource estimator adjusts $N, κ, s, ε$, providing a map of quantum-classical boundaries and revealing where a practical quantum advantage may arise. Our work quantitatively determine how advanced a fault-tolerant quantum computer should be to achieve possible, significant benefits on problems related to real-world. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards identifying possible fault-tolerant advantage of quantum linear system algorithms in terms of space, time and energy Tu, Yue Dubynskyi, Mark Mohammadisiahroudi, Mohammadhossein Riashchentceva, Ekaterina Cheng, Jinglei Ryashchentsev, Dmitry Terlaky, Tamás Liu, Junyu Quantum Physics Artificial Intelligence Machine Learning Optimization and Control Quantum computing, a prominent non-Von Neumann paradigm beyond Moore's law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum noise complicates resource estimations and classical comparisons. We provide a detailed estimation of space, time, and energy resources for fault-tolerant superconducting devices running the Harrow-Hassidim-Lloyd (HHL) algorithm, a quantum linear system solver relevant to linear algebra and machine learning. Excluding memory and data transfer, possible quantum advantages over the classical conjugate gradient method could emerge at $N \approx 2^{33} \sim 2^{48}$ or even lower, requiring ${O}(10^5)$ physical qubits, ${O}(10^{12}\sim10^{13})$ Joules, and ${O}(10^6)$ seconds under surface code fault-tolerance with three types of magic state distillation (15-1, 116-12, 225-1). Key parameters include condition number, sparsity, and precision $κ, s\approx{O}(10\sim100)$, $ε\sim0.01$, and physical error $10^{-5}$. Our resource estimator adjusts $N, κ, s, ε$, providing a map of quantum-classical boundaries and revealing where a practical quantum advantage may arise. Our work quantitatively determine how advanced a fault-tolerant quantum computer should be to achieve possible, significant benefits on problems related to real-world. |
| title | Towards identifying possible fault-tolerant advantage of quantum linear system algorithms in terms of space, time and energy |
| topic | Quantum Physics Artificial Intelligence Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2502.11239 |