Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution
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Jianwen Xu,
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Yujia Zhang,
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Wen Zheng,
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Haoyang Cai,
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Haoyu Zhou,
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Xianke Li,
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Xudong Liao,
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Yu Zhang,
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Shaoxiong Li,
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Dong Lan,
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Xinsheng Tan,
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Yang Yu
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Abstract
Adiabatic time-optimal quantum controls are extensively used in quantum technologies to break the constraints imposed by short coherence times. However, practically it is crucial to consider the trade-off between the quantum evolution speed and instantaneous energy cost of process because of the constraints in the available control Hamiltonian. Here, we experimentally show that using a transmon qubit that, even in the presence of vanishing energy gaps, it is possible to reach a highly time-optimal adiabatic quantum driving at low energy cost in the whole evolution process. This validates the recently derived general solution of the quantum Zermelo navigation problem, paving the way for energy-efficient quantum control which is usually overlooked in conventional speed-up schemes, including the well-known counter-diabatic driving. By designing the control Hamiltonian based on the quantum speed limit bound quantified by the changing rate of phase in the interaction picture, we reveal the relationship between the quantum speed limit and instantaneous energy cost. Consequently, we demonstrate fast and high-fidelity quantum adiabatic processes by employing energy-efficient driving strengths, indicating a promising strategy for expanding the applications of time-optimal quantum controls in superconducting quantum circuits.
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Cite this article:
Jianwen Xu, Yujia Zhang, Wen Zheng, Haoyang Cai, Haoyu Zhou, Xianke Li, Xudong Liao, Yu Zhang, Shaoxiong Li, Dong Lan, Xinsheng Tan, Yang Yu. Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution[J]. Chin. Phys. Lett., 2024, 41(4): 040202. DOI: 10.1088/0256-307X/41/4/040202
Jianwen Xu, Yujia Zhang, Wen Zheng, Haoyang Cai, Haoyu Zhou, Xianke Li, Xudong Liao, Yu Zhang, Shaoxiong Li, Dong Lan, Xinsheng Tan, Yang Yu. Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution[J]. Chin. Phys. Lett., 2024, 41(4): 040202. DOI: 10.1088/0256-307X/41/4/040202
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Jianwen Xu, Yujia Zhang, Wen Zheng, Haoyang Cai, Haoyu Zhou, Xianke Li, Xudong Liao, Yu Zhang, Shaoxiong Li, Dong Lan, Xinsheng Tan, Yang Yu. Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution[J]. Chin. Phys. Lett., 2024, 41(4): 040202. DOI: 10.1088/0256-307X/41/4/040202
Jianwen Xu, Yujia Zhang, Wen Zheng, Haoyang Cai, Haoyu Zhou, Xianke Li, Xudong Liao, Yu Zhang, Shaoxiong Li, Dong Lan, Xinsheng Tan, Yang Yu. Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution[J]. Chin. Phys. Lett., 2024, 41(4): 040202. DOI: 10.1088/0256-307X/41/4/040202
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