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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.01785 |
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| _version_ | 1866915223756079104 |
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| author | Lin, Chungwei Ding, Qi Boufounos, Petros T. Ma, Yanting Wang, Yebin Sels, Dries Chien, Chih-Chun |
| author_facet | Lin, Chungwei Ding, Qi Boufounos, Petros T. Ma, Yanting Wang, Yebin Sels, Dries Chien, Chih-Chun |
| contents | Optimal control theory is applied to analyze the time-optimal solution with a single scalar control knob in a two-level quantum system without quantum decoherence. Emphasis is \change{placed} on the dependence on the maximum control strength $u_\text{max}$. General constraints on the optimal protocol are derived and used to rigorously parameterize the time-optimal solution. Two concrete problems are investigated. For generic state preparation problems, both multiple bang-bang and bang-singular-bang are legitimate and should be considered. Generally, the optimal is bang-bang for small $u_\text{max}$, and there exists a state-dependent critical amplitude above which singular control emerges. For the X-gate operation of a qubit, the optimal protocol \change{is exclusively} multiple bang-bang. The minimum gate time is about 80\% of that based on the resonant Rabi $π$-pulse over a wide range of control strength; in the $u_\text{max} \rightarrow 0$ limit this ratio is derived to be $π/4$. To develop practically feasible protocols, we present methods to smooth the abrupt changes in the bang-bang control while preserving perfect gate fidelity. \change{The presence of bang-bang segments in the time-optimal protocol} indicates that the high-frequency components and a full calculation (instead of the commonly adopted Rotating Wave Approximation) are essential for the ultimate quantum speed limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01785 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-optimal single-scalar control on a qubit of unitary dynamics Lin, Chungwei Ding, Qi Boufounos, Petros T. Ma, Yanting Wang, Yebin Sels, Dries Chien, Chih-Chun Quantum Physics Optimal control theory is applied to analyze the time-optimal solution with a single scalar control knob in a two-level quantum system without quantum decoherence. Emphasis is \change{placed} on the dependence on the maximum control strength $u_\text{max}$. General constraints on the optimal protocol are derived and used to rigorously parameterize the time-optimal solution. Two concrete problems are investigated. For generic state preparation problems, both multiple bang-bang and bang-singular-bang are legitimate and should be considered. Generally, the optimal is bang-bang for small $u_\text{max}$, and there exists a state-dependent critical amplitude above which singular control emerges. For the X-gate operation of a qubit, the optimal protocol \change{is exclusively} multiple bang-bang. The minimum gate time is about 80\% of that based on the resonant Rabi $π$-pulse over a wide range of control strength; in the $u_\text{max} \rightarrow 0$ limit this ratio is derived to be $π/4$. To develop practically feasible protocols, we present methods to smooth the abrupt changes in the bang-bang control while preserving perfect gate fidelity. \change{The presence of bang-bang segments in the time-optimal protocol} indicates that the high-frequency components and a full calculation (instead of the commonly adopted Rotating Wave Approximation) are essential for the ultimate quantum speed limit. |
| title | Time-optimal single-scalar control on a qubit of unitary dynamics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.01785 |