  Geometric phase is an indispensable element for achieving robust and
high-fidelity quantum gates due to its built-in noise-resilience feature.
However, due to the complexity of manipulation and the intrinsic leakage of the
encoded quantum information to non-logical-qubit basis, the experimental
realization of universal nonadiabatic holonomic quantum computation is very
difficult. Here, we propose to implement scalable nonadiabatic holonomic
quantum computation with decoherence-free subspace encoding on a
two-dimensional square superconducting transmon-qubit lattice, where only the
two-body interaction of neighboring qubits, from the simplest capacitive
coupling, is needed. Meanwhile, we introduce qubit-frequency driving to achieve
tunable resonant coupling for the neighboring transmon qubits, and thus
avoiding the leakage problem. In addition, our presented numerical simulation
shows that high-fidelity quantum gates can be obtained, verifying the
advantages of the robustness and scalability of our scheme. Therefore, our
scheme provides a promising way towards the physical implementation of robust
and scalable quantum computation.

Quantum Physics