Long-Range Gates in Superconducting Dual-Rail Qubits (Part 1 - Theory)

Superconducting systems are a promising platform for quantum information processing due to their flexibility and fast processing rates. However, these systems have traditionally been limited to nearest-neighbor qubit coupling, which prevents the efficient implementation of good quantum low-density parity-check (qLDPC) codes for quantum error correction. We present a novel superconducting architecture that enables simultaneous two-qubit gates between arbitrary pairs of dual-rail transmon (DRT) qubits coupled through a one-dimensional multi-mode coupled-resonator array bus (CRAB). The ability to perform long-range two-qubit gates across the CRAB enables the efficient implementation of good qLDPC codes with high encoding rates. We achieve this by driving the DRT pairs at specific sideband frequencies of a CRAB mode, implementing an effective Mølmer-Sørensen interaction Hamiltonian. Local control of the DRT drives and careful choice of sideband frequencies helps mitigate gate crosstalk, enabling simultaneous operation. We discuss the key technical challenges of this approach, including residual cross-Kerr interactions, bus mode decay during gates, and unwanted interactions with non-computational states. We outline a calibration procedure to address these issues and provide estimates of achievable gate speeds and fidelities. The same cross-resonance interaction can also enable high-fidelity readout of the DRT qubits without leaving the computational subspace.