A modular superconducting quantum processor includes a first superconducting chip including a first plurality of qubits each having substantially a first resonance frequency and a second plurality of qubits each having substantially a second resonance frequency, the first resonance frequency being different from the second resonance frequency, and a second superconducting chip including a third plurality of qubits each having substantially the first resonance frequency and a fourth plurality of qubits each having substantially the second resonance frequency. The quantum processor further includes an interposer chip connected to the first superconducting chip and to the second superconducting chip. The interposer chip has interposer coupler elements configured to couple the second plurality of qubits to the fourth plurality of qubits.