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arXiv · 2212.04496

Universal qudit gate synthesis for transmons

Laurin E. Fischer·Alessandro Chiesa·Francesco Tacchino·Daniel J. Egger·Stefano Carretta·Ivano Tavernelli
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Abstract

Gate-based quantum computers typically encode and process information in two-dimensional units called qubits. Using $d$-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored encodings and embedded error correction. In this work, we design a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels. We propose a universal gate set featuring a two-qudit cross-resonance entangling gate, for which we predict fidelities beyond $99\%$ in the $d=4$ case of ququarts with realistic experimental parameters. Furthermore, we present a decomposition routine that compiles general qudit unitaries into these elementary gates, requiring fewer entangling gates than qubit alternatives. As proof-of-concept applications, we numerically demonstrate the synthesis of ${\rm SU}(16)$ gates for noisy quantum hardware and an embedded error correction sequence that encodes a qubit memory in a transmon ququart to protect against pure dephasing noise. We conclude that universal qudit control -- a valuable extension to the operational toolbox of superconducting quantum information processing -- is within reach of current transmon-based architectures and has applications to near-term and long-term hardware.

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Laurin E. Fischer, Alessandro Chiesa, Francesco Tacchino, Daniel J. Egger, Stefano Carretta, Ivano Tavernelli. 2022-12-08. Universal qudit gate synthesis for transmons. https://doi.org/10.1103/prxquantum.4.030327

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