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Recovery of a generic local Hamiltonian from a degenerate steady state | | Jing Zhou
; D. L. Zhou
; | | Date: |
1 Sep 2023 | | Abstract: | As an important tomography technique in quantum computing, Hamiltonian
Learning (HL) provides a significant method for verifying the accuracy of a
quantum system. Often, learning a certain Hamiltonian requires the measurements
from its steady states. However, not all the Hamiltonian can be uniquely
determined from the steady state. It has been revealed that the success of HL
depends on the Hamiltonian model and the rank of the state. Here, we analyze
the HL with respect to a specific type of steady state that is decomposed by
eigenstates with degeneracy, making the Hamiltonian’s eigenstate unknown. To
overcome this challenge, we extract information from the orthogonality
relationship between the eigenstate space and its complement space,
constructing the orthogonal space equation (OSE). The equation number of OSE
can be utilized to determine whether a Hamiltonian can be recovered from a
certain steady state. Finally, we investigate how symmetries in the Hamiltonian
affect the feasibility of the HL method. | | Source: | arXiv, 2309.00334 | | Services: | Forum | Review | PDF | Favorites | |
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