High- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>J</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:math> transmon qudits with up to 12 levels

Abstract

Qudits provide a resource-efficient alternative to qubits for quantum information processing. The multilevel nature of the transmon, with its individually resolvable transition frequencies, makes it an attractive platform for superconducting circuit-based qudits. In this work, we systematically analyze the trade-offs associated with encoding high-dimensional quantum information in fixed-frequency transmons. Designing high ${E}_{J}/{E}_{C}$ ratios of up to 325, we observe up to 12 levels ($d=12$) on a single transmon. Despite the decreased anharmonicity, we demonstrate process infidelities ${e}_{f}&lt;3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for qubitlike operations in each adjacent-level qubit subspace in the lowest ten levels. Furthermore, we achieve a ten-state readout assignment fidelity of 93.8% with the assistance of deep neural network classification of a multitone dispersive measurement. We find that the Hahn echo time ${T}_{2E}$ for the higher levels is close to the limit of ${T}_{1}$ decay, primarily limited by bosonic enhancement. We verify the recently observed Josephson harmonic model, finding that it yields better predictions for the transition frequencies and charge dispersion. Finally, we show strong $ZZ$-like coupling between the higher energy levels in a two-transmon system. Our high-fidelity control and readout methods, in combination with our comprehensive characterization of the transmon model, suggest that the high-${E}_{J}/{E}_{C}$ transmon is a powerful tool for exploring excited states in circuit quantum electrodynamics.

Topics & Concepts