Dense outputs from quantum simulations
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916294598590464 |
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| author | Liu, Jin-Peng Lin, Lin |
| author_facet | Liu, Jin-Peng Lin, Lin |
| contents | The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time $T$ and error tolerance $ε$. Our results demonstrate that the linearization approach can nearly achieve optimal complexity $\mathcal{O}(T/ε)$ for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14441 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dense outputs from quantum simulations Liu, Jin-Peng Lin, Lin Quantum Physics Numerical Analysis The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time $T$ and error tolerance $ε$. Our results demonstrate that the linearization approach can nearly achieve optimal complexity $\mathcal{O}(T/ε)$ for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning. |
| title | Dense outputs from quantum simulations |
| topic | Quantum Physics Numerical Analysis |
| url | https://arxiv.org/abs/2307.14441 |