The Cross-Resonance Gate
The cross-resonance gate entangles two fixed-frequency superconducting qubits by driving one qubit at the other's frequency, needing no tunable elements.
Driving one qubit at another's frequency
Fixed-frequency transmons are quiet because they have no flux-tuning knob, but that also removes the easy way to bring two qubits into resonance. The cross-resonance (CR) gate solves this: apply a microwave drive to a control qubit at the frequency of a coupled target qubit. Through their static coupling, this drives the target in a way that depends on the control's state, generating a conditional rotation equivalent, after single-qubit corrections, to a CNOT.
The effective interaction
The leading term of the CR interaction is a ZX coupling: the target rotates about X at a rate whose sign depends on whether the control is in |0> or |1>. That state-dependent rotation is the entangling action. Unwanted terms, including direct drive of the target and classical crosstalk, must be cancelled.
Making it clean
- Echoed CR sequences that flip the control mid-gate to cancel error terms
- An active cancellation tone on the target to null direct drive
- Careful choice of the control-target frequency difference relative to the transmon anharmonicity
Trade-offs
CR needs only fixed-frequency qubits and microwave drives, so it avoids flux-noise channels and simplifies the chip. The cost is that gate speed and quality depend sensitively on the frequency detuning between the two qubits, which tightens fabrication targets and makes frequency crowding a real constraint as devices scale. Gate times are typically a few hundred nanoseconds.
The cross-resonance gate underpins several large fixed-frequency transmon processors, an alternative to the flux-activated CZ used on tunable architectures.