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Universal algorithm for transforming Hamiltonian eigenvalues
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DOI：10.1103/PhysRevResearch.7.013331.png)
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Abstract
En 中文
Manipulating Hamiltonians governing physical systems has found a broad range of applications, from quantum chemistry to semiconductor design. In this work, we provide a 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 & iuml;ve concatenation of the subroutines and outperforms similar methods based on the quantum singular value transformation.
Keywords:
MANY-BODY THEORIES
QUANTUM
SCIENCE