  The hybrid tensor network (HTN) method is a general framework allowing for
the construction of an effective wavefunction with the combination of classical
tensors and quantum tensors, i.e., amplitudes of quantum states. In particular,
hybrid tree tensor networks (HTTNs) are very useful for simulating larger
systems beyond the available size of the quantum hardware. However, while the
realistic quantum states in NISQ hardware are highly likely to be noisy, this
framework is formulated for pure states. In this work, as well as discussing
the relevant methods, i.e., Deep VQE and entanglement forging under the
framework of HTTNs, we investigate the noisy HTN states by introducing the
expansion operator for providing the description of the expansion of the size
of simulated quantum systems and the noise propagation. This framework enables
the general tree HTN states to be explicitly represented and their physicality
to be discussed. We also show that the expectation value of a measured
observable exponentially vanishes with the number of contracted quantum
tensors. Our work will lead to providing the noise-resilient construction of
HTN states.
