Two-mode qubit design inspired by the GKP Hamiltonian

Protected qubits are promising candidates for quantum computation, for example with the fluxonium qubit showing greatly improved coherence times relative to the transmon [1]. It was also proposed that a two-mode qubit, the $0-pi$ qubit, could offer optimal protection against both charge and flux noise [2,3]. This qubit was experimentally realized, albeit in a regime where the protection is not complete [4]. Additionally, there has been a recent proposal to implement a GKP qubit with the help of a gyrator and two fluxonium circuits [5]. The logical subspace of a GKP qubit would be equally strongly decoupled from its environment. In this talk, we derive an effective two-mode circuit that shares a similar eigenspectrum at low energies and is based on a recently proposed charge-phase interaction [6]. We provide analytical expressions for the low-energy spectrum, eigenstates and qubit operators which show strong agreement with numerical diagonalisation. We analyze the robustness of this qubit to both noise and disorder, and compare this qubit with both the GKP qubit and the $0-pi$ qubit. We also present a longitudinal readout scheme and single-qubit gates protocols.

[1] Long B. Nguyen, et al., Phys. Rev. X 9, 041041, (2019).

[2] Peter Groszkowski, et al., New J. Phys. 20 043053, (2018).

[3] András Gyenis, et al., PRX Quantum 2, 030101, (2021).

[4] András Gyenis, et al., PRX Quantum 2, 010339, (2021).

[5] Martin Rymarz, et al., Phys. Rev. X 11, 011032, (2021).

[6] Catherine Leroux, et al., arXiv:2209.06194, (2022).