Theoretical analysis on the composite qubit approach to superconducting quantum computing

Encoded qubit scheme [1] for superconducting qubit architecture could be a useful alternative to the conventional approach for simpler control of qubits. The composite qubit (CQB) defined in a two-dimensional subspace of a system of two physical transmon qubits can be manipulated using only base band control of each transmon qubit frequencies, allowing for microwave-free single- and two-qubit quantum gates. We present theoretical analysis of the optimal operating point (sweet spot) and the gate operations in a real device in the presence of various sources of noise and errors. The CQB computational subspace consists of excited states of the system and relaxation to the physical ground state is one of the main sources of error. We discuss the randomized benchmarking (RB) protocol in the presence of this leakage error.

[1] Yun-Pil Shim and Charles Tahan, Nat. Commun. 7, 11059 (2016).