Encoding of Probability Distributions for Quantum Monte Carlo Using Tensor Networks
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917840643162112 |
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| author | Pereira, Antonio Villarino, Alba Cortines, Aser Mugel, Samuel Orus, Roman Beltran, Victor Leme Scursulim, J. V. S. Brito, Samurai |
| author_facet | Pereira, Antonio Villarino, Alba Cortines, Aser Mugel, Samuel Orus, Roman Beltran, Victor Leme Scursulim, J. V. S. Brito, Samurai |
| contents | The application of Tensor Networks (TN) in quantum computing has shown promise, particularly for data loading. However, the assumption that data is readily available often renders the integration of TN techniques into Quantum Monte Carlo (QMC) inefficient, as complete probability distributions would have to be calculated classically. In this paper the tensor-train cross approximation (TT-cross) algorithm is evaluated as a means to address the probability loading problem. We demonstrate the effectiveness of this method on financial distributions, showcasing the TT-cross approach's scalability and accuracy. Our results indicate that the TT-cross method significantly improves circuit depth scalability compared to traditional methods, offering a more efficient pathway for implementing QMC on near-term quantum hardware. The approach also shows high accuracy and scalability in handling high-dimensional financial data, making it a promising solution for quantum finance applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Encoding of Probability Distributions for Quantum Monte Carlo Using Tensor Networks Pereira, Antonio Villarino, Alba Cortines, Aser Mugel, Samuel Orus, Roman Beltran, Victor Leme Scursulim, J. V. S. Brito, Samurai Quantum Physics The application of Tensor Networks (TN) in quantum computing has shown promise, particularly for data loading. However, the assumption that data is readily available often renders the integration of TN techniques into Quantum Monte Carlo (QMC) inefficient, as complete probability distributions would have to be calculated classically. In this paper the tensor-train cross approximation (TT-cross) algorithm is evaluated as a means to address the probability loading problem. We demonstrate the effectiveness of this method on financial distributions, showcasing the TT-cross approach's scalability and accuracy. Our results indicate that the TT-cross method significantly improves circuit depth scalability compared to traditional methods, offering a more efficient pathway for implementing QMC on near-term quantum hardware. The approach also shows high accuracy and scalability in handling high-dimensional financial data, making it a promising solution for quantum finance applications. |
| title | Encoding of Probability Distributions for Quantum Monte Carlo Using Tensor Networks |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.11660 |