Deterministic Generation of Arbitrary Fock States via Resonant Subspace Engineering
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arXiv
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| Format: | Preprint |
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2026
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| author | Jin, Shan Li, Ming Cai, Weizhou Chen, Zi-Jie Xu, Yifang Zhou, Yilong Huang, Hongwei Zhu, Yunlai Hua, Ziyue Guo, Guang-Can Sun, Luyan Wang, Xiaoting Zou, Chang-Ling |
| author_facet | Jin, Shan Li, Ming Cai, Weizhou Chen, Zi-Jie Xu, Yifang Zhou, Yilong Huang, Hongwei Zhu, Yunlai Hua, Ziyue Guo, Guang-Can Sun, Luyan Wang, Xiaoting Zou, Chang-Ling |
| contents | Deterministic preparation of high-excitation Fock states is a central challenge in bosonic quantum information, with control complexity that generically explodes as the Hilbert space dimension grows. Here we introduce resonant subspace engineering (RSE), a protocol that analytically confines the infinite-dimensional bosonic dynamics to a two-dimensional invariant subspace spanned by an initial coherent state and the target state. State transfer then reduces to a geodesic rotation on a synthetic Bloch sphere, governed by resonance and phase-matching conditions we derive in closed form. For single Fock states, RSE achieves $O(n^{1/4})$ scaling in both evolution time and gate depth, showing a fundamental improvement over existing deterministic schemes. The construction generalizes to $K$-component superpositions via a $(K{+}1)$-dimensional invariant subspace with full $\mathrm{SU}(K{+}1)$ controllability, requiring only 3-5 iterations of operations for superpositions spanning photon numbers 70--100. RSE provides a scalable and analytically transparent framework for large-scale bosonic state engineering and gate synthesis across single- and multimode platforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12156 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deterministic Generation of Arbitrary Fock States via Resonant Subspace Engineering Jin, Shan Li, Ming Cai, Weizhou Chen, Zi-Jie Xu, Yifang Zhou, Yilong Huang, Hongwei Zhu, Yunlai Hua, Ziyue Guo, Guang-Can Sun, Luyan Wang, Xiaoting Zou, Chang-Ling Quantum Physics Deterministic preparation of high-excitation Fock states is a central challenge in bosonic quantum information, with control complexity that generically explodes as the Hilbert space dimension grows. Here we introduce resonant subspace engineering (RSE), a protocol that analytically confines the infinite-dimensional bosonic dynamics to a two-dimensional invariant subspace spanned by an initial coherent state and the target state. State transfer then reduces to a geodesic rotation on a synthetic Bloch sphere, governed by resonance and phase-matching conditions we derive in closed form. For single Fock states, RSE achieves $O(n^{1/4})$ scaling in both evolution time and gate depth, showing a fundamental improvement over existing deterministic schemes. The construction generalizes to $K$-component superpositions via a $(K{+}1)$-dimensional invariant subspace with full $\mathrm{SU}(K{+}1)$ controllability, requiring only 3-5 iterations of operations for superpositions spanning photon numbers 70--100. RSE provides a scalable and analytically transparent framework for large-scale bosonic state engineering and gate synthesis across single- and multimode platforms. |
| title | Deterministic Generation of Arbitrary Fock States via Resonant Subspace Engineering |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.12156 |