Entangling gates between qubits are a crucial component for performing algorithms in quantum computers. However, any quantum algorithm must ultimately operate on error-protected logical qubits encoded in high-dimensional systems. Typically, logical qubits are encoded in multiple two-level systems, but entangling gates operating on such qubits are highly complex and have not yet been demonstrated. Here, we realize a controlled NOT (CNOT) gate between two multiphoton qubits in two microwave cavities. In this approach, we encode a qubit in the high-dimensional space of a single cavity mode, rather than in multiple two-level systems. We couple two such encoded qubits together through a transmon, which is driven by an RF pump to apply the gate within 190 ns. This is two orders of magnitude shorter than the decoherence time of the transmon, enabling a high-fidelity gate operation. These results are an important step towards universal algorithms on error-corrected logical qubits.
@article{arxiv.1709.05425,
title = {A CNOT gate between multiphoton qubits encoded in two cavities},
author = {Serge Rosenblum and Yvonne Y. Gao and Philip Reinhold and Chen Wang and Christopher J. Axline and Luigi Frunzio and Steven M. Girvin and Liang Jiang and Mazyar Mirrahimi and Michel H. Devoret and Robert J. Schoelkopf},
journal= {arXiv preprint arXiv:1709.05425},
year = {2018}
}