Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912246587719680 |
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| author | Xu, Yingdan Guo, Lingzhen |
| author_facet | Xu, Yingdan Guo, Lingzhen |
| contents | We develop a systematic perturbative framework to engineer an arbitrary target Hamiltonian in the Floquet phase space of a periodically driven oscillator based on Floquet-Magnus expansion. The high-order errors in the engineered Floquet Hamiltonian are mitigated by adding high-order driving potentials perturbatively. We introduce a transformation method that allows us to obtain an analytical expression of the leading-order correction drive for engineering a target Hamiltonian with discrete rotational and chiral symmetries in phase space. We also provide a numerically efficient procedure to calculate high-order correction drives and apply it to engineer the target Hamiltonian with degenerate eigenstates of multi-component cat states that are important for fault-tolerant hardware-efficiency bosonic quantum computation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_10467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian Xu, Yingdan Guo, Lingzhen Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases Applied Physics Optics We develop a systematic perturbative framework to engineer an arbitrary target Hamiltonian in the Floquet phase space of a periodically driven oscillator based on Floquet-Magnus expansion. The high-order errors in the engineered Floquet Hamiltonian are mitigated by adding high-order driving potentials perturbatively. We introduce a transformation method that allows us to obtain an analytical expression of the leading-order correction drive for engineering a target Hamiltonian with discrete rotational and chiral symmetries in phase space. We also provide a numerically efficient procedure to calculate high-order correction drives and apply it to engineer the target Hamiltonian with degenerate eigenstates of multi-component cat states that are important for fault-tolerant hardware-efficiency bosonic quantum computation. |
| title | Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases Applied Physics Optics |
| url | https://arxiv.org/abs/2410.10467 |