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arXiv:2606.29854

Nonperturbative Leakage Elimination Operator-Based Quantum Control Pulse Design Beyond the High Frequency Driving Regime

Hang Yu, Kai-Yu Yuan, Feng-Hua Ren, Zhao-Ming Wang

quant-phSubmitted Jun 29, 2026• Announced Jun 30, 2026• 0 citations
v1 · Jun 29, 2026v2 · Oct 18, 2026
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Abstract

Precise quantum pulse design is central to achieving high precision quantum control, while level leakage induced by system environment coupling is the bottleneck limiting control precision. The leakage elimination operator (LEO) approach is highly effective at suppressing leakage from target subspace to other leakage spaces. The analytical control conditions under the high frequency driving limit have been derived via the Feshbach PQ partitioning technique. However, low frequency driving is experimentally more feasible, and the driving strength is subject to a fundamental physical bound. In this work, we overcome the high frequency driving limit in the pulse design by recasting the LEO protocol within the nonperturbative Floquet-Magnus framework. Applying the Magnus expansion to Floquet dynamical localization, we establish a generalized optimal control formalism that is applicable to the low frequency regime. We prove that the analytical control conditions derived via the Feshbach PQ partitioning technique are equivalent to the zero order Magnus expansion, and that higher order Magnus terms must be taken into account in the low frequency driving regime. We validate our nonperturbative framework using two examples: near perfect quantum state transfer in a one dimensional spin chain and adiabatic speedup in a two level system, corresponding to time independent and time dependent system Hamiltonians, respectively. Our results provide an effective route for designing control pulses in the low frequency regime, which is promising for practical quantum information processing tasks across diverse experimental platforms, including superconducting qubits and ion traps.

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Precise quantum pulse design is central to achieving high precision quantum control, while level leakage induced by system environment coupling is the bottleneck limiting control precision. The leakage elimination operator (LEO) approach is highly effective at suppressing leakage from target subspace to other leakage spaces. The analytical control conditions under the high frequency driving limit have been derived via the Feshbach PQ partitioning technique. However, low frequency driving is experimentally more feasible, and the driving strength is subject to a fundamental physical bound. In this work, we overcome the high frequency driving limit in the pulse design by recasting the LEO protocol within the nonperturbative Floquet-Magnus framework. Applying the Magnus expansion to Floquet dynamical localization, we establish a generalized optimal control formalism that is applicable to the low frequency regime. We prove that the analytical control conditions derived via the Feshbach PQ partitioning technique are equivalent to the zero order Magnus expansion, and that higher order Magnus terms must be taken into account in the low frequency driving regime. We validate our nonperturbative framework using two examples: near perfect quantum state transfer in a one dimensional spin chain and adiabatic speedup in a two level system, corresponding to time independent and time dependent system Hamiltonians, respectively. Our results provide an effective route for designing control pulses in the low frequency regime, which is promising for practical quantum information processing tasks across diverse experimental platforms, including superconducting qubits and ion traps.
Adiabatic evolution is used in a variety of quantum information processing tasks. However, the elimination of errors is not as well developed as it is for circuit model processing. Here, we present a strategy to improve the performance of a quantum adiabatic process by adding leakage elimination operators (LEOs) to the evolution. These are a sequence of pulse controls acting in an adiabatic subspace to eliminate errors by suppressing unwanted transitions. Using the Feshbach PQPQPQ partitioning technique, we obtain an analytical solution for a set of pulse controls. The effectiveness of the LEO is independent of the specific form of the pulse but depends on the average frequency of the control function. By observing that the evolution of the target eigenstate is governed by a periodic function appearing in the integral of the control function, we show that control parameters can be chosen in such a way that the instantaneous eigenstates of the system are unchanged, yet a speedup can be achieved by suppressing transitions. Furthermore, we give the exact expression of the control function for a counter unitary transformation to be used in experiments which provides a clear physical meaning for the LEO, aiding in the implementation.
Decoherence-induced leakage errors can potentially damage physical or logical qubits embedded in a subspace of the entire Hilbert space by coupling them to other system levels. Here we report the first experimental implementation of Leakage Elimination Operators (LEOs) that aims to reduce this undermining. LEOs are a type of dynamical decoupling control that have been previously introduced to counteract leakage from a chosen subspace into the rest of a Hilbert space, and have been widely explored theoretically. Different from other error correction strategies, LEOs are compatible with any gate sequence in a code space, and thus, compatible with universal quantum computation. Using IBM's cloud quantum computer (QC), we design three potentially applicable examples of subspaces in two- and three-qubit Hilbert spaces and derive the explicit forms of the corresponding LEOs for these subspaces. For the first time, we experimentally demonstrate that these LEOs significantly suppress leakage. The results also show that the LEO time-scale condition can be satisfied with noise in the IBM's cloud QC and pave a way for quantum setups to get rid of leakage trouble.
High-fidelity quantum operations require the system dynamics to be strictly confined to the computational subspace. In practice, however, control fields inevitably couple to leakage levels, giving rise to quantum state leakage that significantly reduces the fidelity of the operation. To address this challenge, we propose a general strategy for actively suppressing leakage errors by applying small, static offsets to tunable system parameters. This approach systematically mitigates leakage's detrimental impact on quantum control, without modifying the original control framework or incurring additional time overhead. By avoiding the need for extra suppression pulses or complex optimization procedures altogether, it offers a streamlined solution for leakage compensation while remaining fully compatible with subsequent optimal control techniques. Numerical validation conducted on superconducting quantum circuits demonstrates effective leakage suppression, enabling high-fidelity single-qubit gates, precise control of two-qubit interactions, and perfect state transfer in multi-level systems. Moreover, when integrated with optimal control techniques, our approach also allows for the cooperative suppression of both leakage errors and residual crosstalk. Therefore, this work provides a feasible technical pathway toward the low error thresholds required for fault-tolerant quantum computation.
Dynamical decoupling operations have been shown to reduce errors in quantum information processing. Leakage from an encoded subspace to the rest of the system space is a particularly serious problem for which leakage elimination operators (LEOs) were introduced. Here we provide an analysis of nonideal pulses, rather than the well-understood idealization or bang-bang controls. Under realistic conditions, we show that these controls will provide the same protection from errors as idealized controls. Our work indicates that the effectiveness of LEOs depends on the integral of the pulse sequence in the time domain, which has been missing because of the idealization of pulse sequences. Our results are applied to a three-level system for the nitrogen-vacancy centers under an external magnetic field and are illustrated by the fidelity dynamics of LEO sequences, ranging from regular rectangular pulses, random pulses, and even disordered (noisy) pulses.
Quantum communication through spin chains has been extensively investigated. In this scenario, state transfer through linearly arranged spins connected by uniform nearest-neighbor couplings qualifies as a natural choice, with minimal control requirements. However, quantum states usually cannot be perfectly transferred through a uniformly coupled chain due to the dispersion of the chain. Here, we propose an effective quantum control technique to realize almost exact state transfer (AEST) in a quantum spin chain. The strategy is to add a leakage elimination operator Hamiltonian to the evolution, which implements a sequence of pulse control acting on a perfect state transfer subspace. By using the one-component Feshbach PQ partitioning technique, we obtain the conditions over the required pulses. AEST through a spin chain can then be obtained under a suitable pulse intensity and duration.
The slow evolution required for adiabaticity in adiabatic quantum computation renders the system vulnerable to environmental noise. Leakage elimination operator (LEO) control provides an effective strategy to realize adiabatic speedup over a short timescale, thus mitigating the noise impact. Despite extensive theoretical investigations, the realization of LEO-based adiabatic speedup on realistic superconducting quantum processors remains absent. In this work, we present such a realization on IBM superconducting quantum processors. We first characterize the trade-off between adiabaticity and noise accumulation by varying the total evolution time on both the Qiskit simulator and the ibm_marrakesh processor, employing a comprehensive noise model that closely reproduces the experimental results. We then implement ideal LEO pulse derived for a closed system and achieve a significant enhancement of adiabatic fidelity within a short evolution time. To further improve the adiabatic fidelity, we refine the ideal LEO pulse via Bayesian optimization based on the comprehensive noise model. The optimized pulse yields a modest fidelity gain in simulation, yet on hardware it falls short of the ideal pulse under the present experimental conditions. Our work validates the feasibility of LEO-based adiabatic speedup on a superconducting quantum processor and highlights the potential of LEO for noise-aware adiabatic dynamics.