Fast Quantum Process Tomography via Riemannian Gradient Descent
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917652735197184 |
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| author | Volya, Daniel Nikitin, Andrey Mishra, Prabhat |
| author_facet | Volya, Daniel Nikitin, Andrey Mishra, Prabhat |
| contents | Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process tomography, in which the goal is to retrieve the underlying quantum process based on a given set of measurement data. In this paper, we introduce a modified version of stochastic gradient descent on a Riemannian manifold that integrates recent advancements in numerical methods for Riemannian optimization. This approach inherently supports the physically driven constraints of a quantum process, takes advantage of state-of-the-art large-scale stochastic objective optimization, and has superior performance to traditional approaches such as maximum likelihood estimation and projected least squares. The data-driven approach enables accurate, order-of-magnitude faster results, and works with incomplete data. We demonstrate our approach on simulations of quantum processes and in hardware by characterizing an engineered process on quantum computers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18840 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast Quantum Process Tomography via Riemannian Gradient Descent Volya, Daniel Nikitin, Andrey Mishra, Prabhat Quantum Physics Machine Learning Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process tomography, in which the goal is to retrieve the underlying quantum process based on a given set of measurement data. In this paper, we introduce a modified version of stochastic gradient descent on a Riemannian manifold that integrates recent advancements in numerical methods for Riemannian optimization. This approach inherently supports the physically driven constraints of a quantum process, takes advantage of state-of-the-art large-scale stochastic objective optimization, and has superior performance to traditional approaches such as maximum likelihood estimation and projected least squares. The data-driven approach enables accurate, order-of-magnitude faster results, and works with incomplete data. We demonstrate our approach on simulations of quantum processes and in hardware by characterizing an engineered process on quantum computers. |
| title | Fast Quantum Process Tomography via Riemannian Gradient Descent |
| topic | Quantum Physics Machine Learning |
| url | https://arxiv.org/abs/2404.18840 |