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.
Existing schemes for semiconductor spin qubit readout involve either spin-to-charge conversion or electric dipole coupling to a superconducting resonator. The former requires destructive readout while the latter suffers from enhanced qubit dephasing, limiting the potential performance of quantum measurement: an open challenge in semiconductor quantum computing. Here we propose a coupling to a superconducting resonator based on qubit energy curvature versus gate voltage, which enables quantum nondemolition (QND) readout while the qubit resides in its full sweet spot and with zero dipole coupling (offering resilience to charge noise). Readout strengths of tens to hundred megahertz (MHz) can be reached, at least ten times larger than in the previously proposed schemes. We show how this curvature interaction generates two strictly QND readout approaches: (i) via a ``dispersive-like'' (quantum capacitance) spin-dependent resonator energy shift, similar in implementation to circuit-QED dispersive readout, but avoiding the Purcell effect; and (ii) with the addition of qubit gate voltage modulation, a longitudinal readout which can be selectively switched on, for a chosen n-qubit subsystem. Neither scheme requires the qubit and resonator to be close in frequency.