  The variational quantum eigensolver (VQE) combines classical and quantum
resources in order simulate classically intractable quantum states. Amongst
other variables, successful VQE depends on the choice of variational ansatz for
a problem Hamiltonian. We give a detailed description of a quantum circuit
version of the 2D isometric tensor network (isoTNS) ansatz which we call
qisoTNS. We benchmark the performance of qisoTNS on two different 2D spin 1/2
Hamiltonians. We find that the ansatz has several advantages. It is qubit
efficient with the number of qubits allowing for access to some exponentially
large bond-dimension tensors at polynomial quantum cost. In addition, the
ansatz is robust to the barren plateau problem due emergent layerwise training.
We further explore the effect of noise on the efficacy of the ansatz. Overall,
we find that qisoTNS is a suitable variational ansatz for 2D Hamiltonians with
local interactions.
