Noncontextuality as classicality in variational quantum eigensolvers

In this talk we show how to use contextuality, an indicator of non-classicality in quantum systems, to evaluate the variational quantum eigensolver (VQE), a promising tool for near-term quantum simulation. We present an efficiently computable test to determine whether or not the Hamiltonian in a VQE procedure is contextual. We then show that we may construct a simple, global unitary mapping that diagonalizes a noncontextual Hamiltonian. The diagonal Hamiltonian resulting from this mapping is efficiently classically calculable, which proves that the noncontextual Hamiltonian problem is NP-complete. We also give a quasi-quantized model for variational quantum eigensolvers whose Hamiltonians are noncontextual. This provides a second sense in which noncontextual Hamiltonians are essentially classical. These results support the notion of noncontextuality as classicality in quantum systems.