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arXiv:2605.24781

Time optimal quantum state engineering

Sam Edmunds, Obinna Abah

quant-phSubmitted May 23, 2026• Announced May 26, 2026• 0 citations
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Abstract

The efficient generation of highly nonclassical quantum states is essential for emerging quantum technologies, yet it remains challenging due to decoherence and the long preparation times associated with conventional adiabatic protocols. Here, we employ time-optimal control methods based on the quantum brachistochrone formalism to engineer nonclassical states in light--matter systems described by the time-dependent Jaynes--Cummings and quantum Rabi models. We demonstrate the deterministic generation of Fock states and highly entangled Schrödinger cat states at unit fidelity, and characterize their nonclassical properties through joint Wigner phase-space distributions. We further show that the wind control generates these non-classical states at speed limit which leads to a reduced energetic cost and robustness against dissipation, relaxation, and dephasing across a broad range of environmental conditions. Our results establish time-optimal control as an efficient and experimentally feasible approach for fast and nonclassical state engineering in hybrid quantum platforms.

Comments
10 pages, 8 figures

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The efficient generation of highly nonclassical quantum states is essential for emerging quantum technologies, yet it remains challenging due to decoherence and the long preparation times associated with conventional adiabatic protocols. Here, we employ time-optimal control methods based on the quantum brachistochrone formalism to engineer nonclassical states in light--matter systems described by the time-dependent Jaynes--Cummings and quantum Rabi models. We demonstrate the deterministic generation of Fock states and highly entangled Schrödinger cat states at unit fidelity, and characterize their nonclassical properties through joint Wigner phase-space distributions. We further show that the wind control generates these non-classical states at speed limit which leads to a reduced energetic cost and robustness against dissipation, relaxation, and dephasing across a broad range of environmental conditions. Our results establish time-optimal control as an efficient and experimentally feasible approach for fast and nonclassical state engineering in hybrid quantum platforms.
High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation.
Abstract Time-optimal control holds promise across the full spectrum of quantum technologies, where the rapid generation of unitary gates and state transformations is crucial to mitigate decoherence effects. In practical scenarios, quantum systems are always immersed in an external time-dependent field or potential, either owing to the inevitable influence of the environment or as a sought-after effect for enhanced coherence. The challenge then lies in finding the time-optimal approach to navigate quantum systems amidst dynamical ambient Hamiltonians, a pursuit that has proven elusive thus far. We showcase the implementation of arbitrary quantum state transformations and a universal set of single-qubit gates under a background Landau-Zener Hamiltonian. Leveraging the favorable coherence properties of timedomain Rabi oscillations, we achieve velocities surpassing the Mandelstam-Tamm quantum speed limit and significantly lower energy costs than those incurred by conventional quantum control techniques. These findings highlight a promising pathway to expedite and economize high-fidelity quantum operations.
Time-efficient control schemes for manipulating quantum systems are of great importance in quantum technologies, where environmental forces rapidly degrade the quality of pure states over time. In this Letter, we formulate an approach to time-optimal control that circumvents the boundary-value problem that plagues the quantum brachistochrone equation at the expense of relaxing the form of the control Hamiltonian. In this setting, a coupled system of equations, one for the control Hamiltonian and another one for the duration of the protocol, realizes an ansatz-free approach to quantum control theory. We show how driven systems, in the form of a Landau-Zener type Hamiltonian, can be efficiently maneuvered to speed up a given state transformation in a highly adiabatic manner and with a low energy cost.
Abstract One of the key questions in quantum information is the preparation of desired multipartite quantum states with high fidelity. Adiabatic evolution has been widely explored to achieve state preparation in quantum many-body systems. However, in noisy quantum systems, the adiabatic approach faces a dilemma: either extending the evolution timescales to reduce diabatic transitions or shortening the timescales to mitigate decoherence effects. Various quantum control approaches have been studied to resolve this dilemma. In a few recent works, we utilized Jaynes-Cummings (JC) lattices as a platform to investigate the potential of several quantum control techniques in preparing quantum many-body states, including the optimized adiabatic evolution approach, the quantum optimal control technique, and quantum shortcuts to adiabaticity. Here we first give an overview of our previous results on utilizing quantum optimal control in JC lattices with unit filling and utilizing local counterdiabatic driving in JC lattices with a single excitation. Then we present our results on the energy costs and energy fluctuations in these approaches. Our studies give insights into the implementation of different approaches in practical quantum devices and the connection between the energy costs and the quantum speed limit in preparing desired quantum many-body states for quantum simulation and quantum computation.
We propose a method for the fast generation of nonclassical ground states of the Rabi model in the ultrastrong and deep-strong coupling regimes via the shortcuts-to-adiabatic (STA) dynamics. The time-dependent quantum Rabi model is simulated by applying parametric amplification to the Jaynes-Cummings model. Using experimentally feasible parametric drive, this STA protocol can generate large-size Schrödinger cat states, through a process that is ∼10 times faster compared to adiabatic protocols. Such fast evolution increases the robustness of our protocol against dissipation. Our method enables one to freely design the parametric drive, so that the target state can be generated in the lab frame. A largely detuned light-matter coupling makes the protocol robust against imperfections of the operation times in experiments.