Fast and high-fidelity dispersive readout of a spin qubit via squeezing and resonator nonlinearity

Fast and high-fidelity qubit measurement is crucial for achieving quantum error correction, a fundamental element in the development of universal quantum computing. For electron spin qubits, fast readout stands out as a major obstacle in the pursuit of error correction. In this work, we explore the dispersive measurement of an individual spin in a semiconductor double quantum dot coupled to a nonlinear microwave resonator. By utilizing displaced squeezed vacuum states, we achieve rapid and high-fidelity readout for semiconductor spin qubits. Our findings reveal that introducing modest squeezing and mild nonlinearity can significantly improve both the signal-to-noise ratio (SNR) and the fidelity of qubit-state readout. By properly marching the phases of squeezing, the nonlinear strength, and the local oscillator, the optimal readout time can be reduced to the sub-microsecond range. With current technology parameters ($\kappa \approx 2{\chi }_s$, ${\chi }_s\approx 2\pi \times 0.15MHz$), utilizing a displaced squeezed vacuum state with $30$ photons and a modest squeezing parameter $r\approx 0.6$, along with a nonlinear microwave resonator charactered by a strength of $\lambda \approx -1.2{\chi }_s$, a readout fidelity of $98\mathrm{\%}$ can be attained within a readout time of around $0.6\mu s$. Intriguing, by using a positive nonlinear strength of $\lambda \approx 1.2{\chi }_s$, it is possible to achieve an SNR of approximately $6$ and a readout fidelity of $99.99\mathrm{\%}$ at a slightly later time, around $0.9\mu s$, while maintaining all other parameters at the same settings.