This study investigates the quantum effects in transverse-field Ising spin glass models with rotationally invariant random interactions. The primary aim is to evaluate the validity of a quasistatic approach that captures the imaginary-time dependence of the order parameters beyond the conventional static approximation. Using the replica method combined with the Suzuki–Trotter decomposition, we established a stability condition for the replica symmetric solution, which is analogous to the de Almeida–Thouless criterion. Numerical analysis of the Sherrington–Kirkpatrick model estimates a value of the critical transverse field, ${\mathrm{\Gamma }}_{\mathrm{c}}$, which is consistent with previous Monte Carlo-based estimations. For the Hopfield model, it provides an estimate of ${\mathrm{\Gamma }}_{\mathrm{c}}$, which has not been previously evaluated. For the random orthogonal model, our analysis suggests that quantum effects alter the random first-order transition scenario in the low-temperature limit. This study supports a quasistatic treatment for analyzing quantum spin glasses and may offer useful insights into the analysis of quantum optimization algorithms.

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• Optimization problems
• Quantum phase transitions
• Quantum statistical mechanics
• Disordered systems
• Spin glasses