Practical Verification of Quantum Properties in Quantum Approximate Optimization Runs
Abstract
In order to assess whether quantum resources can provide an advantage over classical computation, it is necessary to characterize and benchmark the nonclassical properties of quantum algorithms in a practical manner. In this paper, we show that using measurements in no more than 3 out of the possible $3^N$ bases, one can not only reconstruct the singlequbit reduced density matrices and measure the ability to create coherent superpositions, but also possibly verify entanglement across all $N$ qubits participating in the algorithm. We introduce a family of generalized Belltype observables for which we establish an upper bound to the expectation values in fully separable states by proving a generalization of the CauchySchwarz inequality, which may serve of independent interest. We demonstrate that a subset of such observables can serve as entanglement witnesses for QAOAMaxCut states, and further argue that they are especially well tailored for this purpose by defining and computing an entanglement potency metric on witnesses. A subset of these observables also certify, in a weaker sense, the entanglement in GHZ states, which share the $\mathbb{Z}_2$ symmetry of QAOAMaxCut. The construction of such witnesses follows directly from the cost Hamiltonian to be optimized, and not through the standard technique of using the projector of the state being certified. It may thus provide insights to construct similar witnesses for other variational algorithms prevalent in the NISQ era. We demonstrate our ideas with proofofconcept experiments on the Rigetti Aspen9 chip for ansatze containing up to 24 qubits.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.01639
 Bibcode:
 2021arXiv210501639S
 Keywords:

 Quantum Physics