Browsing by Subject "ic-povm"

The variational quantum eigensolver (VQE) is one of the most promising proposals for a hybrid quantum-classical algorithm made to take advantage of near-term quantum computers. With the VQE it is possible to find ground state properties of various of molecules, a task which many classical algorithms have been developed for, but either become too inaccurate or too resource-intensive especially for so called strongly correlated problems. The advantage of the VQE comes in the ability of a quantum computer to represent a complex system with fewer so-called qubits than a classical computer would with bits, thus making the simulation of large molecules possible. One of the major bottlenecks for the VQE to become viable for simulating large molecules however, is the scaling of the number of measurements necessary to estimate expectation values of operators. Numerous solutions have been proposed including the use of adaptive informationally complete positive operator-valued measures (IC-POVMs) by García-Pérez et al. (2021). Adaptive IC-POVMs have shown to improve the precision of estimations of expectation values on quantum computers with better scaling in the number of measurements compared to existing methods. The use of these adaptive IC-POVMs in a VQE allows for more precise energy estimations and additional expectation value estimations of separate operators without any further overhead on the quantum computer. We show that this approach improves upon existing measurement schemes and adds a layer of flexibility, as IC-POVMs represent a form of generalized measurements. In addition to a naive implementation of using IC-POVMs as part of the energy estimations in the VQE, we propose techniques to reduce the number of measurements by adapting the number of measurements necessary for a given energy estimation or through the estimation of the operator variance for a Hamiltonian. We present results for simulations using the former technique, showing that we are able to reduce the number of measurements while retaining the improvement in the measurement precision obtained from IC-POVMs.