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.