Practical Verification of Quantum Properties in QuantumApproximateOptimization 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 three 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 states of the quantumapproximateoptimization algorithm for the MaxCut problem (QAOA MaxCut), 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 certifies, in a weaker sense, the entanglement in GHZ states, which share the Z_{2} symmetry of QAOA MaxCut. 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 noisy intermediatescale quantum era. We demonstrate our ideas with proofofconcept experiments on the Rigetti Aspen9 chip for ansatz containing up to 24 qubits.
 Publication:

Physical Review Applied
 Pub Date:
 February 2022
 DOI:
 10.1103/PhysRevApplied.17.024026
 arXiv:
 arXiv:2105.01639
 Bibcode:
 2022PhRvP..17b4026A
 Keywords:

 Quantum Physics
 EPrint:
 Phys. Rev. Applied 17, 024026, 9 February 2022