Universal algorithm for transforming Hamiltonian eigenvalues

• URL: http://arxiv.org/abs/2312.08848v4
• Date: Thu, 10 Oct 2024 06:14:36 GMT
• Title: Universal algorithm for transforming Hamiltonian eigenvalues
• Authors: Tatsuki Odake, Hlér Kristjánsson, Philip Taranto, Mio Murao,
• Abstract summary: 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 function on the eigenvalues of any unknown Hamiltonian. We present a universal algorithm to transform positive-time to negative-time dynamics without adding an auxiliary qubit.
• Score: 0.7499722271664144
• License:
• Abstract: 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 using compilation compared to a na{\"i}ve concatenation of the subroutines and outperforms similar methods based on the quantum singular value transformation. Finally, to circumvent the need for the negative-time dynamics, we present a universal algorithm to transform positive-time to negative-time dynamics without adding an auxiliary qubit, which could also be of standalone interest.

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