Practical Verification of Quantum Properties in Quantum Approximate Optimization Runs

TL;DR

This paper presents practical methods for verifying quantum properties such as entanglement in quantum algorithms like QAOA, using minimal measurements, and demonstrates these techniques through experiments on a 24-qubit quantum processor.

Contribution

It introduces measurement-efficient techniques and new entanglement witnesses tailored for variational quantum algorithms, enabling practical verification of quantum resources in NISQ devices.

Findings

Efficient reconstruction of single-qubit states with limited measurements

Development of Bell-type observables as entanglement witnesses

Experimental validation on a 24-qubit quantum chip

Abstract

In order to assess whether quantum resources can provide an advantage over classical computation, it is necessary to characterize and benchmark the non-classical 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 single-qubit 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 Bell-type observables for which we establish an upper bound to the expectation values in fully separable states by proving a generalization of the Cauchy-Schwarz inequality, which may serve of independent interest. We demonstrate that a subset of such observables can serve as entanglement witnesses for QAOA-MaxCut 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 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 NISQ era. We demonstrate our ideas with proof-of-concept experiments on the Rigetti Aspen-9 chip for ansatze containing up to 24 qubits.