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arXiv:2409.03084 · EPJ Quantum Technology

Quantum geometric protocols for fast high-fidelity adiabatic state transfer

Christian Ventura Meinersen, Stefano Bosco, Maximilian Rimbach-Russ

Published Oct 31, 2025• 6 citations

Abstract

Efficient adiabatic control schemes, where one steers a quantum system along an adiabatic path ensuring minimal excitations while achieving a desired final state, that enable fast, high-fidelity operations are essential for any practical quantum computation. However, current optimization protocols are not universally tractable due to stringent requirements imposed by the microscopic systems encoding the qubit, including complex energy level structures and unwanted transitions, and generally require a trade-off between speed and fidelity of the operation. Here, we address these challenges by developing a general framework for optimal control based on the quantum metric tensor. This framework allows for fast and high-fidelity adiabatic pulses, even for a dense energy spectrum, based solely on the Hamiltonian of the system instead of the time evolution propagator and independent of the size of the underlying Hilbert space. Furthermore, our framework suppresses diabatic transitions and state-dependent crosstalk effects without the need for additional control fields. As an example, we study the adiabatic charge transfer in a double quantum dot to find optimal control pulses with improved performance. We show that for the geometric protocol, the transfer fidelities are lower bounded $\mathcal{F}>99\%$ for ultrafast $20~\mbox{ns}$ pulses, regardless of the size of the anti-crossing, while being robust against miscalibration errors and quasistatic noise.

DOI: 10.1140/epjqt/s40507-025-00426-2

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\mathcal{F}>99\%

for ultrafast

20~\mbox{ns}

pulses, regardless of the size of the anti-crossing, while being robust against miscalibration errors and quasistatic noise.

We introduce a geometric framework for efficient few-parameter pulse optimization in multi-level quantum systems, enabling high-fidelity state transfer beyond the adiabatic limit. Our method interpolates smoothly between adiabatic and diabatic dynamics to minimize unwanted excitations and maximize desired transitions even within a multi-level structure. Crucially, for single-parameter pulse control, the optimization reduces to solving a first-order ordinary differential equation. We showcase the flexibility of our diabatic-adiabatic protocols through two examples in spin-based quantum information processing: state initialization and qubit state transfer.

Topological pumping has attracted great attention in topological physics and is highly valuable in the realization of robust quantum state transfer (QST). However, speeding up the topological QST under the requirement of adiabatic evolutions remains challenging. In this work, we propose a geometric adiabatic criterion with an effective quantum metric that characterizes non-adiabatic transitions during evolutions via the quantum metric, minimal energy gap and cycle time. Using two generalized Su–Schrieffer–Heeger models, we systematically validate our adiabatic criterion in optimizing topological pumping paths for transferring single-site states and two-site entangled states, respectively. With numerical simulations, we show that by designing pumping paths for minimizing the effective quantum metric, the fidelity and speed of the QST can be significantly improved. Our works provides a general framework for high-fidelity topological QST via quantum metric optimization.

We introduce a geometric framework for efficient few-parameter pulse optimization in multi-levelquantum systems, enabling high-fidelity state transfer beyond the adiabatic limit. Our methodinterpolates smoothly between adiabatic and diabatic dynamics to minimize unwanted excitationsand maximize desired transitions even within a multi-level structure. Crucially, for single-parameterpulse control, the optimization reduces to solving a first-order ordinary differential equation. Weshowcase the flexibility of our diabatic-adiabatic protocols through two examples in spin-basedquantum information processing: state initialization and qubit state transfer.

We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary sufficiently slow protocols using adiabatic perturbation theory, and show that the bound is saturated by geodesic protocols, which keep the energy variance constant along the trajectory. Our conjecture implies that any optimal unit-fidelity protocol, even those which drive the system far from equilibrium, are fundamentally constrained by the quantum geometry of adiabatic evolution. When the control space includes all possible couplings, spanning the full Hilbert space, we recover the well-known Mandelstam-Tamm bound. However, using only accessible local controls to anneal in complex models such as glasses, or target individual excited states in quantum chaotic systems, the geometric bound for the QSL can be exponentially large in the system size due to a diverging geodesic length. We validate our conjecture both analytically by constructing counter-diabatic and fast-forward protocols for a three-level system, and numerically in non-integrable spin chains using optimal control.

Adiabatic quantum operations are ubiquitous in fields such as quantum information processing, quantum control, and magnetic resonance, where their high fidelity and general robustness renders them an essential tool for various applications. This inherent robustness due to adiabaticity can, however, be impaired in cases where the experimental conditions strictly require very fast evolution times. In this thesis, we provide a gradient-based numerical optimization protocol for efficiently engineering adiabatic operations, allowing for the systematic inclusion of robustness criteria against various experimental non-idealities, including inhomogeneities and uncertainties in system parameters, as well as perturbations in the Hamiltonian such as spin-spin interactions. \nThe protocol is implemented in the context of adiabatic passages for magnetic resonance, and \nit is shown that in addition to conventional adiabatic pulses, it can also generate exceptionally fast operations that although slightly deviate from adiabaticity in limited instances, still lead to a high fidelity. \nThe effectiveness of our method for addressing perturbations is also demonstrated by designing a fast adiabatic passage for dipolar-coupled electrons, and numerically comparing its performance with a pulse without such considerations.

We develop protocols for high-fidelity single-qubit gates that exploit and extend theoretical ideas for accelerated adiabatic evolution. Our protocols are compatible with qubit architectures where direct transitions between logical states are either vanishingly small or nonexistent; in such systems traditional approaches cannot be implemented. Prime examples are superconducting fluxonium qubits, which have highly localized states, and AMO systems, where there are no dipole allowed transitions between the ground states encoding the logical states. By using an accelerated adiabatic protocol we can enforce the desired adiabatic evolution while having gate times that are comparable to the inverse adiabatic energy gap (a scale that is ultimately set by the amount of power used in the control pulses). By modeling the effects of decoherence, we explore the trade-off between speed and robustness that is inherent to shortcuts-to-adiabaticity approaches.