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  • Open Access

Efficient Control of a Transmon Qudit Using Effective Spin-7/2 Rotations

Elizabeth Champion*, Zihao Wang*, Rayleigh W. Parker, and Machiel S. Blok†

  • *These authors contributed equally to this work.
  • †Contact author: machielblok@rochester.edu
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Phys. Rev. X 15, 021096 – Published 18 June, 2025

DOI: https://doi.org/10.1103/vbh4-lysv

Abstract

Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems [1]. However, existing control and measurement schemes for qudit systems scale unfavorably with qudit dimension since they decompose SU(d) operations into series of qubitlike rotations and perform measurements on a small number of states [2–6]. Here, we address these challenges by employing simultaneous multifrequency drives to generate rotations and projections in an effective spin-7/2 system mapped onto the energy eigenstates of a superconducting circuit. We implement single-shot readout of the eight states using a multitone dispersive readout (Fassignment=88.3%) and exploit the strong nonlinearity in a high-EJ/EC transmon to simultaneously address each transition and realize a spin displacement operator. Combining this displacement operator with a virtual SNAP gate, we realize arbitrary single-qudit unitary operations in O(d) physical pulses and extract spin displacement gate fidelities ranging from 0.997 to 0.989 for virtual spins of size j=1 to j=7/2. We demonstrate the potential of our control scheme in three ways: the direct measurement of the spin qudit Wigner function, randomized benchmarking of a logical qubit encoded into the qudit state, and randomized benchmarking of the full qudit Clifford group. In the latter experiment, we implement the d-dimensional quantum Fourier transform with an average gate fidelity of 0.91(6) in d=8. Our multifrequency approach to qudit control and measurement can be readily extended to other physical platforms that realize a multilevel system coupled to a cavity and can become a building block for efficient qudit-based quantum computation and simulation.

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Quantum computers are usually built from qubits—two-level systems that store quantum information. However, researchers are increasingly exploring qudits, quantum systems with more than two levels, which can potentially perform computations more efficiently and make better use of current hardware. In this study, we demonstrate a superconducting quantum processor built from transmon circuits operating as qudits with up to eight energy levels. The new finding is that we can control these multilevel systems with high efficiency and fidelity by treating them as large quantum spins.

Rather than using traditional methods that apply pulses between neighboring energy levels one at a time, we use a novel technique that drives all transitions simultaneously. This creates a coherent “spin displacement” across the qudit states, achieving a control fidelity of 98.9%. We also introduce a method to interleave these displacements with phase shifts of individual tones, allowing us to achieve full universal control over the qudit. With this toolbox, we implement a key algorithm—the single-qudit quantum Fourier transform—and find that its performance rivals that of top-tier qubit-based systems.

These results demonstrate the promise of qudit-based quantum computation for near-term processors. Our control scheme is applicable to any qudit architecture with individually addressable transitions, and we expect that it will enable previously infeasible qudit experiments, particularly when combined with qudit entangling gates.

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Phys. Rev. X 15, 021096– Published 18 June, 2025
  • Received 13 May 2024
  • Revised 18 February 2025
  • Accepted 6 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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