Asymmetric SQUID Transmons
Making the two junctions of a SQUID unequal reduces the tuning range but adds a lower sweet spot and limits the qubit's exposure to flux noise.
Junction Asymmetry
A symmetric SQUID has two identical junctions and its effective Josephson energy can in principle be tuned to zero, giving a full-band tunable transmon that reaches very low frequencies at half flux. In practice the extreme sensitivity near the band bottom is unusable. An asymmetric SQUID deliberately makes the two junctions unequal, characterized by an asymmetry parameter d equal to the difference of the critical currents divided by their sum.
With asymmetry the effective Josephson energy becomes E_J,eff = E_J,sum times the square root of cos^2(pi phi) plus d^2 sin^2(pi phi). The important consequence is that E_J,eff never reaches zero; it bottoms out at a finite value proportional to the asymmetry. This creates a second sweet spot at half flux where the qubit is again first-order insensitive to flux.
Why Designers Choose It
- Two sweet spots, at the band top and band bottom, both flux-insensitive to first order.
- A reduced tuning range, which limits the frequency excursion caused by flux noise.
- A more predictable operating window for parking qubits away from spectators and defects.
The Design Trade
Reducing the tuning range is a deliberate sacrifice. A narrow band means less room to move a qubit into resonance for a gate or to steer it away from a two-level-system defect. Designers pick the asymmetry to balance the coherence benefit of a smaller band against the flexibility a wide band provides. Typical choices give tuning ranges of a few hundred megahertz up to one or two gigahertz.
The lower sweet spot is especially useful for parking idle qubits at a quiet, well-separated frequency, which reduces always-on crosstalk and frequency crowding in dense processors. This makes asymmetric SQUIDs common in architectures that combine fixed-frequency computational qubits with tunable elements used only for gates.
As with any tunable element, the benefit is only realized if the flux bias is stable and the flux line is properly filtered.