Universal Qudit Gate Synthesis for Transmons

• Published in: PRX quantum 2023-08, Vol.4 (3), p.030327, Article 030327
• Main Authors: Fischer, Laurin E., Chiesa, Alessandro, Tacchino, Francesco, Egger, Daniel J., Carretta, Stefano, Tavernelli, Ivano
• Format: Article
• Language: English
• ISSN: 2691-3399; 2691-3399
• DOI: 10.1103/PRXQuantum.4.030327

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 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.