Capacitive and resonator-mediated gates
Qubits can couple without direct electron exchange.
$$H_{ZZ}=\frac{\hbar\zeta}{4}\sigma_z^{(1)}\sigma_z^{(2)}$$
Physical intuition
Qubits can couple without direct electron exchange.
Deep dive: physical mechanism
Electric dipoles, capacitive interactions or shared resonators generate effective conditional shifts.
What is measured experimentally?
Conditional Ramsey experiments determine ZZ strength.
Assumptions, noise and limitations
Long-range coupling can amplify charge-noise exposure.
Research and simulation exercise
Simulate a controlled-phase evolution under ZZ coupling.
Connect the ideas
Explore the chapter overview, learning path, and references.