  Tensor networks and quantum computation are two of the most powerful tools
for the simulation of quantum many-body systems. Rather than viewing them as
competing approaches, here we consider how these two methods can work in
tandem. We introduce a novel algorithm that combines tensor networks and
quantum computation to produce results that are more accurate than what could
be achieved by either method used in isolation. Our algorithm is based on
multiproduct formulas (MPF) - a technique that linearly combines Trotter
product formulas to reduce algorithmic error. Our algorithm uses a quantum
computer to calculate the expectation values and tensor networks to calculate
the coefficients used in the linear combination. We present a detailed error
analysis of the algorithm and demonstrate the full workflow on a
one-dimensional quantum simulation problem on $50$ qubits using two IBM quantum
computers: $ibm\_torino$ and $ibm\_kyiv$.
