Secondly, because the various decoherence phenomena occurring the NISQ devices that limit the number of quantum operations, one thus desires circuits that can be easily executed on a quantum computer, with a well-behaved and rapidly convergent optimization of variational parameters. The circuit depth, which depends on the number of quantum gates (thus the number of operators/parameters), has become the decisive factor to determine whether a quantum algorithm can run in real quantum computers or not. Thirdly, as we discussed above, once the Hamiltonian sampling method and precision are specific, N T determines the total number of measurements and thus the computational time. Therefore N T is the indicator to evaluate the time cost of an algorithm in practice.