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  • Open Access

Universal Pulses for Superconducting Qudit Ladder Gates

Boxi Li1,2,*, F.A. Cárdenas-López1, Adrian Lupascu3, and Felix Motzoi1,2,†

  • *Contact author: b.li@fz-juelich.de
  • †Contact author: f.motzoi@fz-juelich.de
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PRX Quantum 6, 030357 – Published 19 September, 2025

DOI: https://doi.org/10.1103/9dxw-4c7y

Abstract

Qudits, generalizations of qubits to multilevel quantum systems, offer enhanced computational efficiency by encoding more information per lattice cell, avoiding costly swap operations and providing even exponential speedup in some cases. Utilizing the d-level manifold, however, requires high-speed gate operations because of the stronger decoherence at higher levels. While analytical control methods have proven effective for qubits in achieving fast gates with minimal control errors, their extension to qudits is nontrivial due to the increased complexity of the energy-level structure arising from additional ancillary states. In this work, we present a universal pulse construction for generating rapid, high-fidelity unitary rotations between adjacent qudit levels, thereby providing a prescription for any gate in SU(d). Control errors in these operations are effectively analyzed within a four-level subspace, including two leakage levels with approximately opposite detuning. By identifying the optimal degrees of freedom, we derive concise analytical pulse schemes that suppress multiple control errors and outperform existing methods. Remarkably, our approach achieves consistent coherent error scaling across all levels, approaching the quantum speed limit independently of parameter variations between levels. Numerical validation on transmon circuits demonstrates significant improvements in gate fidelity for various qudit sizes aiming for 10−4 error. This method provides a scalable solution for improving qudit control and can be broadly applied to other quantum systems with ladder structures or operations involving multiple ancillary levels.

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Popular Summary

Quantum computers use qubits as their building blocks. However, the nature of quantum systems is intrinsically multilevel, enabling access to qudits, which can store more information and perform computations more efficiently. Despite these advantages, controlling qudits is more challenging than controlling qubits. As the number of accessible energy levels increases, so does the risk of triggering unwanted transitions. This work addresses a key challenge in qudit-based quantum computation: how to perform fast, accurate operations between selected levels without disturbing the rest of the system.

Our focus is on transmon circuits, which are naturally suited to hosting qudits, but our method also applies to any quantum system with a ladderlike level structure and uneven energy-level spacing. This spacing allows selective control of neighboring levels but also increases the chance of unintentionally exciting nearby states leading to errors. By analyzing system dynamics, we identified the main sources of such errors and reduced the control problem to an effective four-level model. We developed a class of compact, analytical control pulses that suppress unwanted transitions and are independent of the specific qudit level or transmon parameters. These universal pulses enable fast, high-fidelity operations that approach theoretical speed limits while remaining easy to calibrate experimentally.

Our method advances the ability to fully exploit all available energy levels in quantum systems, improving both the efficiency and scalability of quantum computing.

Article Text

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PRX Quantum 6, 030357– Published 19 September, 2025
  • Received 17 January 2025
  • Revised 7 July 2025
  • Accepted 19 August 2025
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