We propose entangling operations based on the energy curvature couplings of encoded spin qubits to a superconducting cavity, exploring the nonlinear qubit response to a gate voltage variation. For a two-qubit (
n-qubit) entangling gate we explore acquired geometric phases via a time-modulated longitudinal ${\ensuremath{\sigma}}_{z}$ coupling, offering gate times of tens of nanoseconds even when the qubits and the cavity are far detuned. No dipole moment is necessary: the qubit transverse ${\ensuremath{\sigma}}_{x}$ coupling to the resonator is zero at the full sweet spot of the encoded spin qubit of interest (a triple quantum dot three-electron exchange-only qubit or a double quantum dot singlet-triplet qubit). This approach allows always-on, exchange-only qubits, for example, to stay on their ``sweet spots'' during gate operations, minimizing the charge noise and eliminating an always-on static longitudinal qubit-qubit coupling. We calculate the main gate errors due to the (1) diffusion (Johnson) noise and (2) damping of the resonator, the (3)
1/f-charge noise qubit gate dephasing and
1/f noise on the longitudinal coupling, (4) qubit dephasing and AC-Stark frequency shifts via photon fluctuations in the resonator, and (5) spin-dependent resonator frequency shifts (via a ``dispersivelike'' static curvature coupling), most of them associated with the nonzero qubit energy curvature (quantum capacitance). Using spin-echo-like error suppression at optimal regimes, gate infidelities of ${10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}3}$ can be achieved with experimentally existing parameters. The proposed schemes seem suitable for remote spin-to-spin entanglement of two spin qubits or a cluster of spin qubits: an important resource of quantum computing.
Semiconductor-based 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; it combines 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. The singlet-triplet (ST) and exchange-only (EO) qubits are multielectron realizations that go without broadband control and are protected from some types of noise, but are challenging to couple to each other and to microwave cavities. We combine the flopping-mode concept with the ST and 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 0 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 nondissipative 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.
Implementing two-qubit gates via strong coupling between quantum-dot qubits and a superconducting microwave cavity requires achieving coupling rates that are much faster than decoherence rates. Typically, this involves tuning the qubit either to a sweet spot, where it is relatively insensitive to charge noise, or to a point where it is resonant with the microwave cavity. Unfortunately, such operating points seldom coincide. Here we theoretically investigate protocols, based on transverse or longitudinal sideband driving, for implementing two-qubit gates between quantum-dot hybrid qubits, mediated by a microwave cavity. The rich physics in these qubits gives rise to two types of sweet spots, which can occur at operating points with strong charge dipole moments. Such strong interactions provide new opportunities for off-resonant gating, thereby removing one of the main obstacles for long-distance two-qubit gates. We find that the transverse driving scheme yields faster gates, while longitudinal driving yields gates that are more resilient to photon decay. Our results suggest that the numerous tuning knobs of quantum-dot hybrid qubits make them good candidates for strong coupling. In particular, we show that off-resonant red-sideband-mediated two-qubit gates can exhibit fidelities greater than
95 for realistic operating parameters, and we describe improvements that could potentially yield gate fidelities greater than
99.