  Variational quantum eigensolver (VQE), which combines quantum systems with
classical computational power, has been arisen as a promising candidate for
near-term quantum computing applications. However, the experimental resources
such as the number of measurements to implement VQE rapidly increases as the
Hamiltonian problem size grows. Applying entanglement measurements to reduce
the number of measurement setups has been proposed to address this issue,
however, entanglement measurements themselves can introduce additional resource
demands. Here, we apply entanglement measurements to the photonic VQE utilizing
polarization and path degrees of freedom of a single-photon. In our photonic
VQE, entanglement measurements can be deterministically implemented using
linear optics, so it takes full advantage of introducing entanglement
measurements without additional experimental demands. Moreover, we show that
such a setup can mitigate errors in measurement apparatus for a certain
Hamiltonian.
