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 ($\kappa\approx 2\chi_s$, $\chi_s\approx 2\pi\times 0.15 \:\mbox{MHz}$), 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 $98\%$ can be attained within a readout time of around $0.6\:\mu\mbox{s}$. 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 $99.99\%$ at a slightly later time, around $0.9\:\mu\mbox{s}$, while maintaining all other parameters at the same settings.