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arXiv:2506.00354 · Science China Physics Mechanics and Astronomy

A geometric quantum speed limit: Theoretical insights and photonic implementation

Qianyi Wang, Ben Wang, Jun Wang, Lijian Zhang

Published Jun 30, 2025• 0 citations
arXivHTMLPDF
DOI
10.1007/s11433-025-2691-9

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We present a geometric optimization method for implementing quantum gates by optimally controlling the Hamiltonian parameters, with the goal of approaching the Mandelstam-Tamm quantum speed limit (MT-QSL). Achieving this bound requires satisfying precise geometric conditions that govern the evolution of quantum states. We extend this geometric framework to quantum unitary operators in arbitrary dimensions and analyze the conditions necessary for saturation of the bound. Additionally, we show that the quantum brachistochrone, when generalized to operators, does not, in general, saturate the MT-QSL bound. Finally, we propose a systematic optimal control strategy based on geometric principles to approach the quantum speed limit for unitary driving. We illustrate this optimization method on a set of four well-known two-qubit quantum gates. Our procedure significantly reduces the deviation from the optimal quantum speed limit while preserving high quantum fidelity.
We derive a family of quantum speed limit results in time independent systems with pure states and a finite dimensional state space, by using a geometric method based on right invariant action functionals on SU(N). The method relates speed limits for implementing quantum gates to bounds on orthogonality times. We reproduce the known result of the Margolus-Levitin theorem, and a known generalisation of the Margolis-Levitin theorem, as special cases of our method, which produces a rich family of other similar speed limit formulas corresponding to positive homogeneous functions on su(n). We discuss the general relationship between speed limits for controlling a quantum state and a system's time evolution operator.