Report
Universal algorithm for transforming Hamiltonian eigenvalues
| Title: | Universal algorithm for transforming Hamiltonian eigenvalues |
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| Authors: | Odake, Tatsuki, Kristjánsson, Hlér, Taranto, Philip, Murao, Mio |
| Source: | Phys. Rev. Research 7, 013331 (2025) |
| Publication Year: | 2023 |
| Collection: | Quantum Physics |
| Subject Terms: | Quantum Physics |
| Description: | 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{\"i}ve concatenation of the subroutines and outperforms similar methods based on the quantum singular value transformation. Comment: 12+23 pages, 14 figures, close to published version. Note that a previous version of this article [v4] contains an algorithm to implement negative-time Hamiltonian dynamics without any auxilliary systems |
| Document Type: | Working Paper |
| DOI: | 10.48550/arXiv.2312.08848 |
| Access URL: | http://arxiv.org/abs/2312.08848 |
| Accession Number: | edsarx.2312.08848 |
| Database: | arXiv |
| DOI: | 10.48550/arXiv.2312.08848 |
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