Universal algorithm for transforming Hamiltonian eigenvalues
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915264252084224 |
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| author | Odake, Tatsuki Kristjánsson, Hlér Taranto, Philip Murao, Mio |
| author_facet | Odake, Tatsuki Kristjánsson, Hlér Taranto, Philip Murao, Mio |
| contents | Manipulating Hamiltonians governing physical systems has found a broad range of applications, from quantum chemistry to semiconductor design. In this work, we provide a new way of manipulating Hamiltonians, by transforming their eigenvalues while keeping their eigenstates unchanged. We develop a universal algorithm that deterministically implements any desired (suitably differentiable) function on the eigenvalues of any unknown Hamiltonian, whose positive-time and negative-time dynamics are given as a black box. Our algorithm uses correlated randomness to efficiently combine two subroutines -- namely controlization and Fourier series simulation -- exemplifying a general compilation procedure that we develop. The time complexity of our algorithm is significantly reduced via said compilation technique compared to a na{ï}ve concatenation of the subroutines and outperforms similar methods based on the quantum singular value transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08848 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universal algorithm for transforming Hamiltonian eigenvalues Odake, Tatsuki Kristjánsson, Hlér Taranto, Philip Murao, Mio Quantum Physics Manipulating Hamiltonians governing physical systems has found a broad range of applications, from quantum chemistry to semiconductor design. In this work, we provide a new way of manipulating Hamiltonians, by transforming their eigenvalues while keeping their eigenstates unchanged. We develop a universal algorithm that deterministically implements any desired (suitably differentiable) function on the eigenvalues of any unknown Hamiltonian, whose positive-time and negative-time dynamics are given as a black box. Our algorithm uses correlated randomness to efficiently combine two subroutines -- namely controlization and Fourier series simulation -- exemplifying a general compilation procedure that we develop. The time complexity of our algorithm is significantly reduced via said compilation technique compared to a na{ï}ve concatenation of the subroutines and outperforms similar methods based on the quantum singular value transformation. |
| title | Universal algorithm for transforming Hamiltonian eigenvalues |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.08848 |