The existence theorem for replica-symmetry breaking (RSB) in the transverse
    field Sherrington-Kirkpatrick (SK) model is extended to the model with a
    general random exchange interactions. The relation between the expectation
    value of the exchange interaction energy and the Duhamel correlation function
    of spin operators can be obtained by an approximate integration by parts for
    general random interactions. In addition to the Falk-Bruch inequality, these
    explicit evaluations enable us to prove that the variance of overlap between
    two replica spin operators does not vanish under sufficiently weak transverse
    field in sufficiently low temperature. The absence of the ferromagnetic long
    range order is also shown to distinguish RSB from the $\mathbb Z_2$-symmetry

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