Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Contextuality is an indicator of nonclassicality, and a resource for various quantum procedures. In this Letter, we use contextuality to evaluate the variational quantum eigensolver (VQE), one of the most promising tools for near-term quantum simulation. We present an efficiently computable test to determine whether or not the objective function for a VQE procedure is contextual. We apply this test to evaluate the contextuality of experimental implementations of VQE, and determine that several, but not all, fail this test of quantumness.

Figure 1

Determining trees for $\pm YY$ over $\{XI,IX,ZI,IZ\}$.

Figure 2

Compatibility graphs for contextual sets of four Pauli operators.