The singlet-triplet and exchange-only flopping-mode qubit

Spin qubits embedded into a superconducting microwave

cavity constitute a fast-progressing and promising platform

for realizing fast and fault-tolerant qubit control with long-range two-qubit coupling.

The flopping-mode spin

qubit consists of a single electron in a double quantum dot combining a charge qubit with a spin qubit. With its strong and tunable cavity coupling, the flopping-mode qubit is proven to be well-suited for low-power qubit control and

cavity-mediated long-range quantum gates.

We combine the flopping-mode concept with the singlet-triplet (ST) and exchange-only (EO) qubits and propose two new

flopping-mode qubits that

consist of three (four) quantum dots,

occupied by two (three) electrons near the

(1,0,1) ↔ (0,1,1)

[ (1,0,1,1) ↔ (0,1,1,1) ]

charge transition. The two-electron system augments the ST spin qubit with a charge qubit

that interacts transversally and longitudinally with a cavity.

Both couplings are highly tunable, and the longitudinal coupling

distinguishes the flopping-mode ST qubit from the regular flopping-mode qubit.

The longitudinal coupling allows for non-dissipative universal

control similar to superconducting transmon qubits.

The EO flopping-mode qubit comprises four dots

occupied by three electrons and opens a new possibility to perform two-qubit gates for EO qubits that are challenging to perform directly with the exchange coupling.

We use input-output theory to provide means of extracting the coupling strengths

from cavity transmission data.