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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2412.17289 |
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| _version_ | 1866916972536528896 |
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| author | Byrne, Adam Kirby, William Soodhalter, Kirk M. Zhuk, Sergiy |
| author_facet | Byrne, Adam Kirby, William Soodhalter, Kirk M. Zhuk, Sergiy |
| contents | The problem of estimating the ground-state energy of a quantum system is ubiquitous in chemistry and condensed matter physics. Krylov quantum diagonalization (KQD) has emerged as a promising approach for this task. However, many KQD methods rely on subroutines, particularly the Hadamard test, that are challenging to implement on near-term quantum computers. We present a novel KQD method that uses only real-time evolutions and recovery probabilities, making it well adapted for existing quantum hardware. The method entails numerical differentiation in post-processing, and so we present a novel derivative estimation algorithm that is robust to noisy data. Under assumptions on the spectrum of the Hamiltonian, we prove that our algorithm converges exponentially quickly to the ground-state energy and present a numerical demonstration using tensor network simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The quantum super-Krylov method Byrne, Adam Kirby, William Soodhalter, Kirk M. Zhuk, Sergiy Quantum Physics The problem of estimating the ground-state energy of a quantum system is ubiquitous in chemistry and condensed matter physics. Krylov quantum diagonalization (KQD) has emerged as a promising approach for this task. However, many KQD methods rely on subroutines, particularly the Hadamard test, that are challenging to implement on near-term quantum computers. We present a novel KQD method that uses only real-time evolutions and recovery probabilities, making it well adapted for existing quantum hardware. The method entails numerical differentiation in post-processing, and so we present a novel derivative estimation algorithm that is robust to noisy data. Under assumptions on the spectrum of the Hamiltonian, we prove that our algorithm converges exponentially quickly to the ground-state energy and present a numerical demonstration using tensor network simulations. |
| title | The quantum super-Krylov method |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.17289 |