Fast QND Readout of Spin Qubits via Hybrid Longitudinal-Transverse Coupling: A Numerical Study

Abstract

Spin qubits have attracted significant attention in quantum computing due to their long coherence times and compatibility with semiconductor fabrication processes. However, quantum non-demolition (QND) readout of spin qubits faces the challenge of balancing speed and fidelity. While traditional longitudinal coupling maintains high fidelity, it suffers from limited readout speed. Conversely, transverse coupling can enhance speed but compromises the QND conditions. This study proposes and systematically investigates a hybrid longitudinal-transverse coupling mechanism to achieve fast and high-fidelity spin qubit readout.

We establish a theoretical model with a hybrid coupling Hamiltonian containing longitudinal terms $\sigma_Z (a+a^\dagger)$, transverse terms $\sigma_X (a+a^\dagger)$, and microwave driving terms $\varepsilon(a+a^\dagger)$, where the ratio of longitudinal to transverse coupling strength is controlled by modulation angle $\theta$. Numerical simulations are performed using Monte Carlo wavefunction methods based on the Lindblad master equation. Quantum state evolution dynamics are analyzed through Wigner function phase-space trajectories, and a comprehensive performance evaluation system, including readout speed, QND fidelity, and state distinguishability, is established.

Numerical results demonstrate that: (1) longitudinal coupling exhibits QND fidelity >99.9\% with readout time ~30$\mu s$, independent of coupling strength; (2) transverse coupling shows decreasing readout time (from 28.7$\mu s$ to 21.0$\mu s$) with increasing coupling strength, while QND fidelity degrades slightly (<0.2\%); (3) hybrid coupling achieves optimal balance between speed and QND properties within parameter range $A \leq 6$ MHz, $\varepsilon=1.0$ MHz, with readout time ~21.5$\mu s$; (4) hybrid coupling show the best state separability among the three coupling models, when $A=5\mathrm{MHz}$, $\varepsilon=0.9\mathrm{MHz}$, it is 200\% higher than longitudinal coupling and 45\% higher than transverse coupling. Fourier analysis of square wave driving reveals that theoretical predictions require a $(4/\pi)^2$ correction factor, showing excellent agreement between numerical results and corrected theoretical formulas.

This study systematically demonstrates for the first time the advantages of hybrid longitudinal-transverse coupling mechanisms in spin qubit QND readout, providing an effective solution to address the traditional speed-fidelity trade-off problem in QND readout, and establishing theoretical foundations for designing high-performance quantum readout schemes in practical quantum computing systems.