The Flux-Tunable Transmon
Replacing the transmon's single junction with a SQUID loop lets an applied flux tune the qubit frequency, enabling fast gates at the price of added flux sensitivity.
From Fixed to Tunable
A fixed-frequency transmon uses one Josephson junction to set a fixed effective E_J. A flux-tunable transmon replaces that junction with two junctions in a loop, forming a superconducting quantum interference device, or SQUID. The effective Josephson energy of the SQUID depends on the magnetic flux threading the loop, so an external current in a nearby flux line changes the qubit frequency in situ.
For a symmetric SQUID the effective coupling is E_J,eff = E_J,max times the absolute value of cos(pi phi_ext / phi_0). The qubit frequency, roughly the square root of 8 E_C E_J,eff minus E_C, therefore rises and falls as the flux is swept. This tunability is the resource that enables many two-qubit gate schemes.
The Cost of Tunability
Because the frequency depends on flux, any flux noise becomes qubit dephasing. The sensitivity is the slope of frequency versus flux. At the top of the band, where flux_ext is zero, the slope vanishes and the qubit is first-order insensitive to flux noise, a so-called sweet spot. Away from the sweet spot the qubit tunes quickly but dephases faster.
- At the upper sweet spot: maximum frequency, minimum flux sensitivity, longest coherence.
- Away from the sweet spot: fast tuning for gates, shorter dephasing time.
- Asymmetric SQUIDs add a second sweet spot at the band minimum.
Gate Enablement
Tunability lets two qubits, or a qubit and a coupler, be brought into and out of resonance on nanosecond timescales. Bringing two transmons near a shared avoided crossing implements controlled-phase gates; parametric modulation of the flux at a difference frequency drives iSWAP-type exchange. These mechanisms are covered in the tunable-transmon gate pages.
The engineering task is to keep the flux line quiet, well filtered, and calibrated so that the tuning is repeatable and the added dephasing stays within the error budget.