Using a quantum dot spin bus to implement CNOT gates between remote qubits

A spin bus is a chain of individual spins with strong, always-on, static interactions (e.g., a linear array of single-electron quantum dots).~ Here, we consider a spin bus coupled to multiple external qubits via the Heisenberg exchange interaction.~ Using both theoretical and numerical methods, we show that a continuous range of two-qubit gates can be constructed.~ In particular, we show that SWAP and square-root-SWAP gates can be achieved with high accuracy, when the couplings between the qubits and the bus are weak.~ In combination with single-qubit operations, we can then realize controlled-NOT gates between remote qubits, as mediated by the bus.~ The spin bus therefore shows considerable potential for implementing universal quantum gates.