Controlled-Z gates
Conditional energy shifts generate a two-qubit phase gate.
Physical intuition
Conditional energy shifts generate a two-qubit phase gate. This is the starting point for understanding how superconducting circuit parameters determine quantum energy levels and dynamics.
Deep dive: how the mechanism works
Bias or drive trajectories accumulate a conditional phase while suppressing population leakage.
How the quantum phenomenon appears
Flux-pulsed or microwave-activated CZ gates entangle neighboring transmons. 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
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
See the chapter guide and further reading.