Fast quantum control is essential to overcome decoherence in contemporary quantum platforms, yet achieving this in many-body systems remains a major challenge. We show that the time-rescaling (TR) method enables efficient acceleration of closed many-body quantum dynamics, extending its applicability beyond previously studied regimes. Applying TR to the transverse-field Ising model with a longitudinal field, we demonstrate a significant enhancement of quantum annealing performance, maintaining high ground-state fidelity at evolution times where standard adiabatic dynamics breaks down, with only weak dependence on system size. We further demonstrate high-fidelity preparation of Greenberger-Horne-Zeilinger states in many-body systems, where TR extends the accessible system sizes within fixed evolution times. We additionally show that the Mandelstam-Tamm quantum speed limit does not fundamentally limit the acceleration achievable through TR, as the reduction in evolution time is exactly compensated by increased energy fluctuations. These results establish TR as a scalable and experimentally viable approach to fast quantum control in many-body systems.
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6 pages (3 figures) + supplemental material (3 pages)
Fast quantum control is essential to overcome decoherence in contemporary quantum platforms, yet achieving this in many-body systems remains a major challenge. We show that the time-rescaling (TR) method enables efficient acceleration of closed many-body quantum dynamics, extending its applicability beyond previously studied regimes. Applying TR to the transverse-field Ising model with a longitudinal field, we demonstrate a significant enhancement of quantum annealing performance, maintaining high ground-state fidelity at evolution times where standard adiabatic dynamics breaks down, with only weak dependence on system size. We further demonstrate high-fidelity preparation of Greenberger-Horne-Zeilinger states in many-body systems, where TR extends the accessible system sizes within fixed evolution times. We additionally show that the Mandelstam-Tamm quantum speed limit does not fundamentally limit the acceleration achievable through TR, as the reduction in evolution time is exactly compensated by increased energy fluctuations. These results establish TR as a scalable and experimentally viable approach to fast quantum control in many-body systems.
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.
Abstract Time-rescaling (TR) has been recently proposed as a method to engineer fast processes, also known as shortcuts to adiabaticity (STA), which enables the coherent control of quantum systems beyond the adiabatic regime (Bernardo 2020 Phys. Rev. Res. 2 013133). In this work, we revisit the technique and show that the obtained fast dynamics are transitionless, similar to the ones designed via the famous counterdiabatic (CD) approach. However, contrary to the CD approach, the TR method has the advantage of providing the Hamiltonians that generate the fast processes without requiring information about the instantaneous eigenstates of a reference protocol, and the convenience that experimental implementations dismiss additional coupling fields when compared with the reference adiabatic protocol. Here, we also show that the time evolution of the STA found via TR relates to that of the reference adiabatic protocol by a simple reparametrization of time. To illustrate our findings, we studied the paradigmatic problem of speeding up the stimulated Raman adiabatic passage and found out that TR revealed quantum dynamics more robust to parameter variations than those provided by the CD technique. These results motivate the application of TR to the control of larger quantum systems.
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.
Quantum information processing requires fast manipulations of quantum systems in order to overcome dissipative effects. We propose a method to accelerate quantum dynamics and obtain a target state in a shorter time relative to unmodified dynamics, and apply the theory to a system consisting of two linearly coupled qubits. We extend the technique to accelerate quantum adiabatic evolution in order to rapidly generate a desired target state, thereby realizing a shortcut to adiabaticity. Further, we address experimental limitations to the rate of change of control parameters for quantum devices which often limit one's ability to generate a desired target state with high fidelity. We show that an initial state following decelerated dynamics can reach a target state while varying control parameters more slowly, enabling more experimentally feasible driving schemes.
Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial Hamiltonian into one whose ground state encodes the solution, the system traverses a complex landscape via a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Unlike gate-based quantum computing, quantum annealing is a specialised and near-term approach aimed primarily at discrete optimisation and sampling tasks. While it is not expected to provide polynomial-time solutions to NP-hard problems in the worst case, it offers a physically motivated heuristic for navigating rugged energy landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, placing them among the largest controllable quantum devices currently available. As a result, their significance extends beyond optimisation: they also function as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are difficult to access using classical simulation. In this review we present an accessible introduction to the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse how tunnelling, spectral gaps, and open-system effects shape computational performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges in benchmarking, scaling, and control. These perspectives position quantum annealing as a distinctive framework at the interface of optimisation, stochastic sampling, and programmable quantum dynamics, with a role that is complementary to both classical algorithms and gate-based quantum computing.