Achieving fast high-fidelity optimal control of many-body dynamics

We apply recent state-of-the-art optimal control techniques to a challenging many-body problem: driving the superfluid-Mott insulator transition in an optical lattice. At system sizes well beyond the reach of exact diagonalization approaches, and thus requiring a matrix product state ansatz, we obtain fidelities in the range 0.99-0.9999 and beyond with associated quantum speed limit estimates. Whereas previous efforts yielded lower fidelity solutions with smooth, monotonic controls, we efficiently identify a rich hierarchy of bang-bang-like solutions. These facilitate the non-adiabatic quantum interference pathways using sequential tunneling and phase-imprinting dynamics necessary for high fidelity. Mapping out the optimal solutions at various process durations, we observe a characteristic, exponential dependence for the fidelity across several orders of magnitude. Overall, we achieve these results by utilizing the counter-intuitive fact that appropriate dynamical approximations lead to a more precise and significantly cheaper implementation of optimal control than a full dynamical solution. In discussing the technique's generality, this demonstration may pave the way for fulfilling the comprehensive demands for efficient high-fidelity control in very high-dimensional systems which has hitherto not been feasible.We apply recent state-of-the-art optimal control techniques to a challenging many-body problem: driving the superfluid-Mott insulator transition in an optical lattice. At system sizes well beyond the reach of exact diagonalization approaches, and thus requiring a matrix product state ansatz, we obtain fidelities in the range 0.99-0.9999 and beyond with associated quantum speed limit estimates. Whereas previous efforts yielded lower fidelity solutions with smooth, monotonic controls, we efficiently identify a rich hierarchy of bang-bang-like solutions. These facilitate the non-adiabatic quantum interference pathways using sequential tunneling and phase-imprinting dynamics necessary for high fidelity. Mapping out the optimal solutions at various process durations, we observe a characteristic, exponential dependence for the fidelity across several orders of magnitude. Overall, we achieve these results by utilizing the counter-intuitive fact that appropriate dynamical approximations lead to a more precise and significantly cheaper implementation of optimal control than a full dynamical solution. In discussing the technique's generality, this demonstration may pave the way for fulfilling the comprehensive demands for efficient high-fidelity control in very high-dimensional systems which has hitherto not been feasible.

Aug 13, 20201 citation

Achieving fast high-fidelity optimal control of many-body quantum dynamics

Jesper Hasseriis Mohr Jensen, Frederik Møller, Jens Jakob Sørensen +1 more

We demonstrate the efficiency of a recent exact-gradient optimal control methodology by applying it to a challenging many-body problem, crossing the superfluid to Mott-insulator phase transition in the Bose-Hubbard model. The system size necessitates a matrix product state representation and this seamlessly integrates with the requirements of the algorithm. We observe fidelities in the range 0.99--0.9999 with associated minimal process duration estimates displaying an exponential fidelity-duration trade-off across several orders of magnitude. The corresponding optimal solutions are characterized in terms of a predominantly linear sweep across the critical point followed by bang-bang-like structure. This is quite different from the smooth and monotonic solutions identified by earlier gradient-free optimizations which are hampered in locating the higher complexity protocols in the regime of high fidelities at low process durations. Overall, the comparison suggests significant methodological improvements also for many-body systems in the ideal open-loop setting. Acknowledging that idealized open-loop control may deteriorate in actual experiments, we discuss the merits of using such an approach in combination with closed-loop control---in particular, high-fidelity physical insights extracted with the former can be used to formulate practical, low-dimensional search spaces for the latter.We demonstrate the efficiency of a recent exact-gradient optimal control methodology by applying it to a challenging many-body problem, crossing the superfluid to Mott-insulator phase transition in the Bose-Hubbard model. The system size necessitates a matrix product state representation and this seamlessly integrates with the requirements of the algorithm. We observe fidelities in the range 0.99--0.9999 with associated minimal process duration estimates displaying an exponential fidelity-duration trade-off across several orders of magnitude. The corresponding optimal solutions are characterized in terms of a predominantly linear sweep across the critical point followed by bang-bang-like structure. This is quite different from the smooth and monotonic solutions identified by earlier gradient-free optimizations which are hampered in locating the higher complexity protocols in the regime of high fidelities at low process durations. Overall, the comparison suggests significant methodological improvements also for many-body systems in the ideal open-loop setting. Acknowledging that idealized open-loop control may deteriorate in actual experiments, we discuss the merits of using such an approach in combination with closed-loop control---in particular, high-fidelity physical insights extracted with the former can be used to formulate practical, low-dimensional search spaces for the latter.

arXiv:2008.06076Physical Review ANov 16, 202115 citations

Optimal Control Technique for Many-Body Quantum Dynamics

Patrick Doria, Tommaso Calarco, Simone Montangero

We present an efficient strategy for controlling a vast range of nonintegrable quantum many-body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods such as the density matrix renormalization group. To demonstrate its potential, we employ it to solve a major issue in current optical-lattice physics with ultracold atoms: we show how to reduce by about 2 orders of magnitude the time needed to bring a superfluid gas into a Mott insulator state, while suppressing defects by more than 1 order of magnitude as compared to current experiments [T. Stöferle et al., Phys. Rev. Lett. 92, 130403 (2004)]. Finally, we show that the optimal pulse is robust against atom number fluctuations.We present an efficient strategy for controlling a vast range of nonintegrable quantum many-body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods such as the density matrix renormalization group. To demonstrate its potential, we employ it to solve a major issue in current optical-lattice physics with ultracold atoms: we show how to reduce by about 2 orders of magnitude the time needed to bring a superfluid gas into a Mott insulator state, while suppressing defects by more than 1 order of magnitude as compared to current experiments [T. Stöferle et al., Phys. Rev. Lett. 92, 130403 (2004)]. Finally, we show that the optimal pulse is robust against atom number fluctuations.

arXiv:1003.3750Physical Review LettersMay 11, 2011422 citations

State preparation in a Jaynes-Cummings lattice with quantum optimal control

Prabin Parajuli, Anuvetha Govindarajan, Lin Tian

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.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.

arXiv:2306.11968Scientific ReportsNov 14, 20235 citations

Time-optimal quantum gates with bang-bang control in multilevel systems

Valentín Reparaz, Santiago Ferreyra, María José Sánchez +2 more

We determine the optimal quantum manipulation protocols for implementing high-fidelity, fast single-qubit gates. We demonstrate that the time-optimal pulse sequence is a ``bang-bang'' sequence: discrete pulses of either positive or negative maximum amplitude or zero. The non-adiabatic bang-bang pulse sequence minimizes gate duration providing a speedup for low-frequency architectures. We first derive the protocol for a transversally driven two-level system, extracting exact analytic expressions for minimum gate times. We then extend this framework to general multilevel architectures, identifying conditions that enable the coherent suppression of leakage errors. Using the fluxonium circuit as a representative case study, we optimize $X/2$ and $Y/2$ gates through a combination of discrete bang sequences and continuous waveform smoothing. This approach preserves near-optimal execution speeds while mitigating transitions outside the computational subspace. Open-system simulations demonstrate that these sequences outperform commensurate and resonant pulse schemes across different fluxonium regimes, achieving low-error manipulation significantly faster than standard resonant control, even in the presence of $1/f$ flux noise and dissipation.We determine the optimal quantum manipulation protocols for implementing high-fidelity, fast single-qubit gates. We demonstrate that the time-optimal pulse sequence is a ``bang-bang'' sequence: discrete pulses of either positive or negative maximum amplitude or zero. The non-adiabatic bang-bang pulse sequence minimizes gate duration providing a speedup for low-frequency architectures. We first derive the protocol for a transversally driven two-level system, extracting exact analytic expressions for minimum gate times. We then extend this framework to general multilevel architectures, identifying conditions that enable the coherent suppression of leakage errors. Using the fluxonium circuit as a representative case study, we optimize $X/2$ and $Y/2$ gates through a combination of discrete bang sequences and continuous waveform smoothing. This approach preserves near-optimal execution speeds while mitigating transitions outside the computational subspace. Open-system simulations demonstrate that these sequences outperform commensurate and resonant pulse schemes across different fluxonium regimes, achieving low-error manipulation significantly faster than standard resonant control, even in the presence of $1/f$ flux noise and dissipation.

quant-pharXiv:2608.16702Aug 18, 20260 citations

Invariant-based control of quantum many-body systems across critical points

Hilario Espinós, Loris Maria Cangemi, Amikam Levy +2 more

Quantum many-body systems are emerging as key elements in the quest for quantum-based technologies and in the study of fundamental physics. In this study, we address the challenge of achieving fast and high-fidelity evolutions across quantum phase transitions, a crucial requirement for practical applications. We introduce a control technique based on dynamical invariants tailored to ensure adiabatic-like evolution within the lowest-energy subspace of the many-body systems described by the transverse-field Ising and long-range Kitaev models. By tuning the controllable parameter according to analytical control results, we achieve high-fidelity evolutions operating close to the speed limit. Remarkably, our approach leads to the breakdown of Kibble-Zurek scaling laws, offering tunable and significantly improved time scaling behavior. We provide detailed numerical simulations to illustrate our findings, demonstrating scalability with the system size and robustness against noisy controls and disorder, as well as its applicability to a non-integrable system.Quantum many-body systems are emerging as key elements in the quest for quantum-based technologies and in the study of fundamental physics. In this study, we address the challenge of achieving fast and high-fidelity evolutions across quantum phase transitions, a crucial requirement for practical applications. We introduce a control technique based on dynamical invariants tailored to ensure adiabatic-like evolution within the lowest-energy subspace of the many-body systems described by the transverse-field Ising and long-range Kitaev models. By tuning the controllable parameter according to analytical control results, we achieve high-fidelity evolutions operating close to the speed limit. Remarkably, our approach leads to the breakdown of Kibble-Zurek scaling laws, offering tunable and significantly improved time scaling behavior. We provide detailed numerical simulations to illustrate our findings, demonstrating scalability with the system size and robustness against noisy controls and disorder, as well as its applicability to a non-integrable system.

arXiv:2309.05469Sep 11, 20230 citations

X/2

and

Y/2

gates through a combination of discrete bang sequences and continuous waveform smoothing. This approach preserves near-optimal execution speeds while mitigating transitions outside the computational subspace. Open-system simulations demonstrate that these sequences outperform commensurate and resonant pulse schemes across different fluxonium regimes, achieving low-error manipulation significantly faster than standard resonant control, even in the presence of

1/f

flux noise and dissipation.