Concept 31 of 42 · Control and Entangling Gates

Parametric iSWAP interactions

Modulating circuit parameters can resonantly exchange qubit excitations.

01 / Mathematical framework

$$H_{\mathrm{ex}}/\hbar=g_{\mathrm{eff}}(\sigma_+^{(1)}\sigma_-^{(2)}+\mathrm{h.c.})$$

Physical intuition

Modulating circuit parameters can resonantly exchange qubit excitations. This is the starting point for understanding how superconducting circuit parameters determine quantum energy levels and dynamics.

Deep dive: how the mechanism works

A flux modulation activates otherwise detuned exchange interactions through sidebands.

How the quantum phenomenon appears

Tunable couplers implement iSWAP-family entangling gates. To establish the predicted quantum behavior, connect the circuit Hamiltonian to a measured transition, coherence experiment, gate benchmark or calibrated readout signal.

Assumptions and limitations

Spurious sidebands and coupler-induced loss limit performance.

Research and simulation exercise

Identify the tunable parameters, predict the observable from the stated model, and sweep one parameter while holding the others fixed. Compare against a simpler reference model, quantify loss and uncertainty, and state which observations would falsify the hypothesis.

Connect the ideas

Cross-resonance gates Readout resonator and measurement chain

See the chapter guide and further reading.

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ΦParametric iSWAP interactions