Optimal Dispersive Readout of a Spin Qubit with a Microwave Cavity

Benjamin D'Anjou, Guido Burkard

Published 2019-05-23Version 1

Strong coupling of semiconductor spin qubits to superconducting microwave cavities was recently demonstrated. These breakthroughs pave the way for quantum information processing that combines the long coherence times of solid-state spin qubits with the long-distance connectivity, fast control, and fast high-fidelity quantum-non-demolition readout of existing superconducting qubit implementations. Here, we theoretically analyze and optimize the dispersive readout of a single spin in a semiconductor double quantum dot (DQD) coupled to a microwave cavity via its electric dipole moment. The strong spin-photon coupling arises from the motion of the electron spin in a local magnetic field gradient. We calculate the signal-to-noise ratio (SNR) of the readout accounting for both Purcell spin relaxation and spin relaxation arising from intrinsic electric noise within the semiconductor. We express the maximum achievable SNR in terms of the cooperativity associated with these two dissipation processes. We find that while the cooperativity increases with the strength of the dipole coupling between the DQD and the cavity, it does not depend on the strength of the magnetic field gradient. We then optimize the SNR as a function of experimentally tunable DQD parameters. We identify wide regions of parameter space where the unwanted backaction of the cavity photons on the qubit is small. Moreover, we find that the coupling of the cavity to other DQD transitions can enhance the SNR by at least a factor of two, a `straddling' effect that occurs only at non-zero energy detuning of the DQD potential well. We estimate that with current technology, single-shot readout fidelities in the range 82%-95% can be achieved within a few $\mu\textrm{s}$ of readout time without requiring the use of Purcell filters.