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arXiv:2607.14175 · New Journal of Physics

Transducer leakage error suppression using invariant-based shortcut

Shi-Qiang Qiao, Zheng Shan, Xue-Ke Song, Shi-Lei Su, Liu Ye, Dong Wang

quant-phSubmitted Jul 15, 2026• Announced Jul 16, 2026• 0 citations
v1 · Jul 15, 2026v2 · Aug 3, 2026
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Abstract

We present a method for suppressing transducer leakage errors in spin-superconducting hybrid quantum systems with the theory of optimal invariant-based shortcut. By mediated virtual photons as a transducer to exchange the energy between the spin qubit and a transmon qubit, the fidelity of the population of the final state features a broad range above 99\% under the influence of leakage error. The leakage probability from computational subspace to non-computational subspace can be effectively suppressed at a lowest value with $0.01$. Based on the optimized pulse control designed by the invariant-based inverse engineering, the high-fidelity quantum iSWAP gate operations and entanglement state preparation within the computational subspace are achieved. {Compared to the traditional $π$ pulse, derivative removal by adiabatic gate, counter-diabatic shortcut schemes, and limited-memory Broyden-Fletcher-Goldfarb-Shanno gradient ascent pulse engineering, the optimized shortcut scheme can still achieve a high fidelity with 99\% in the presence of decoherence and control error.} When taking into account the possibility of leakage errors in actual situations, our solution can still largely resist the influence of control errors. The results provides a feasible path for precisely manipulating the quantum state of hybrid quantum systems.

Journal reference
2026 New J. Phys. 28 074515
DOI
10.1088/1367-2630/ae8c7c

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We present a method for suppressing transducer leakage errors in spin-superconducting hybrid quantum systems with the theory of optimal invariant-based shortcut. By mediated virtual photons as a transducer to exchange the energy between the spin qubit and a transmon qubit, the fidelity of the population of the final state features a broad range
above 99% under the influence of leakage error. The leakage probability from computational subspace to non-computational subspace can be effectively suppressed at a lowest value with 0.010.010.01.
Based on the optimized pulse control designed by the invariant-based inverse engineering, the high-fidelity quantum iSWAP gate operations and entanglement state preparation within the computational subspace are achieved. {Compared to the traditional πππ pulse, derivative removal by adiabatic gate, counter-diabatic shortcut schemes, and limited-memory Broyden-Fletcher-Goldfarb-Shanno gradient ascent pulse engineering, the optimized shortcut scheme can still achieve a high fidelity with 99% in the presence of decoherence and control error.} When taking into account the possibility of leakage errors in actual situations, our solution can still largely resist the influence of control errors. The results provides a feasible path for precisely manipulating the quantum state of hybrid quantum systems.
Hybrid quantum systems consisting of quantum dot spins and superconducting circuits have emerged as a promising platform for quantum information processing. However, the development of scalable architectures requires the ability to entangle different quantum systems over long distances, which remains an outstanding challenge for hybrid systems with complex interactions and multiple energy levels. Here, we devise methods to implement entangling gates by using engineered virtual photons as a transducer to couple spin-superconducting systems. We propose to tailor such transducers by tuning the driving pulse using shortcuts to adiabaticity. We demonstrate the realization of high-fidelity entangling gates of 99% in short timescales of a few tens of nanoseconds, and we show the robustness of this approach to control parameters. Furthermore, our method enables state transfer and remote entanglement between different modules of the hybrid system with fidelity exceeding the fault-tolerance threshold, thus demonstrating the scalability of this approach. These results pave the way for fast, high-fidelity quantum information processing on leading hybrid platforms.
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.
Superconducting qubits are often based on the first two energy levels of a physical anharmonic LC oscillator. Since the anharmonicity of such systems is usually much lower than the involved energy gaps, population can easily leak to higher energy states. This is what characterizes leakage errors, and it can have multiple sources: from coherent error induced by the control platform to incoherent thermal dissipation. In this work, we adapt an optimal control method based on sub-Riemannian geodesic search in the unitary group for a system consisting of two superconducting qubits with leakage levels. We use the Rx(π/2)R_x(π/2)Rx​(π/2) rotation for single-qubit operation analysis, and the iiiSWAP operation for two-qubit analysis. For the former, we find considerable performance improvement in average gate fidelity as well as in the reduction of leakage errors when comparing the obtained optimal pulses with Gaussian and DRAG pulses, especially for short duration pulses. For the iiiSWAP gate, although leakage error remains roughly the same, we manage to obtain considerably higher fidelities with the cost of requiring a slightly longer time evolution.
Improving the speed and fidelity of quantum logic gates is essential to reach quantum advantage with future quantum computers. However, fast logic gates lead to increased leakage errors in superconducting quantum processors based on qubits with low anharmonicity, such as transmons. To reduce leakage errors, we propose and experimentally demonstrate two new analytical methods, Fourier ansatz spectrum tuning derivative removal by adiabatic gate (FAST DRAG) and higher-derivative (HD) DRAG, both of which enable shaping single-qubit control pulses in the frequency domain to achieve stronger suppression of leakage transitions compared to previously demonstrated pulse shapes. Using the new methods to suppress the e f transition of a transmon qubit with an anharmonicity of − 212 MHz, we implement R X ( π / 2 ) gates achieving a leakage error below 3.0 × 10 − 5 down to a gate duration of 6.25 ns without the need for iterative closed-loop optimization. The obtained leakage error represents a 20-fold reduction in leakage compared to a conventional cosine DRAG pulse. Employing the FAST DRAG method, we further achieve an error per gate of ( 1.56 ± 0.07 ) × 10 − 4 at a 7.9-ns gate duration, outperforming conventional pulse shapes both in terms of error and gate speed. Furthermore, we study error-amplifying measurements for the characterization of temporal microwave control-pulse distortions, and demonstrate that non-Markovian coherent errors caused by such distortions may be a significant source of error for sub-10-ns single-qubit gates unless corrected using predistortion. Published by the American Physical Society 2024
One of the main enablers in quantum computing is having qubit control that is precise and fast. However, qubits typically have multilevel structures making them prone to unwanted transitions from fast gates. This leakage out of the computational subspace is especially detrimental to algorithms as it has been observed to cause long-lived errors, such as in quantum error correction. This forces a choice between either achieving fast gates or having low leakage. Previous works focus on suppressing leakage by mitigating the first to second excited state transition, overlooking multi-photon transitions, and achieving faster gates with further reductions in leakage has remained elusive. Here, we demonstrate single qubit gates with a total leakage error consistently below 2.0×10−52.0\times10^{-5}2.0×10−5, and obtain fidelities above 99.98%99.98\%99.98% for pulse durations down to 6.8 ns for both XXX and X/2X/2X/2 gates. This is achieved by removing direct transitions beyond nearest-neighbor levels using a double recursive implementation of the Derivative Removal by Adiabatic Gate (DRAG) method, which we name the R2D method. Moreover, we find that at such short gate durations and strong driving strengths the main error source is from these higher order transitions. This is all shown in the widely-used superconducting transmon qubit, which has a weakly anharmonic level structure and suffers from higher order transitions significantly. We also introduce an approach for amplifying leakage error that can precisely quantify leakage rates below 10−610^{-6}10−6. The presented approach can be readily applied to other qubit types as well.
Abstract Reaching high-speed, high-fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. We directly optimize the amplitude and phase of each sample point of the digitized control pulse. We thereby fully exploit the capabilities of the pulse generation electronics and create a 4.16 ns single-qubit pulse with 99.76 % fidelity and 0.044 % leakage. This is a sevenfold reduction of the leakage rate and a threefold reduction in standard errors of the best DRAG pulse we have calibrated at such short durations on the same system.