  The hybrid tensor network approach allows us to perform calculations on
systems larger than the scale of a quantum computer. However, when calculating
transition amplitudes, there is a problem that the number of terms to be
measured increases exponentially with that of contracted operators. The problem
is caused by the fact that the contracted operators are represented as
non-Hermitian operators. In this study, we propose a method for the hybrid
tensor network calculation that contracts non-Hermitian operators without the
exponential increase of the number of terms. In the proposed method,
calculations of transition amplitudes are performed by combining the singular
value decomposition of the contracted non-Hermitian operators with the Hadamard
test. The method significantly extends the applicability of the hybrid tensor
network approach.
