qubit connectivity

Qubit connectivity describes which qubits on a chip can directly talk to each other. Two-qubit gates only work between qubits that share a physical coupling, so the chip's wiring forms a graph: each qubit is a dot, and a line is drawn wherever a direct gate is possible. In today's superconducting chips that graph is sparse — a qubit might be connected to just two, three, or four neighbors, not to everyone.

If your algorithm needs a gate between two qubits that aren't directly linked, the compiler has to move the quantum information across the chip first, hopping it through intermediate qubits with extra SWAP operations. Every SWAP is itself made of gates, so it adds time and adds error. A well-matched topology — common shapes are a square lattice or IBM's heavy-hex layout — keeps the qubits a program actually pairs up close together, so it needs fewer of these detours.

More connectivity sounds strictly better, but it isn't free. Packing more couplers around each qubit crowds the chip with control lines and pushes neighboring qubits closer in frequency, which worsens crosstalk and frequency crowding — qubits accidentally nudging or leaking into one another. So connectivity is a genuine architecture tradeoff: designers deliberately keep the graph sparse (heavy-hex is partly a choice to reduce crowding) and pay for it in SWAPs, rather than chase all-to-all wiring that no one has built at scale.