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The variational quantum eigensolver (VQE) stands as a prominentquantum-classical hybrid algorithm for near-term quantum computers to obtainthe ground states of molecular Hamiltonians in quantum chemistry. However, dueto the non-commutativity of the Pauli operators in the Hamiltonian, the numberof measurements required on quantum computers increases significantly as thesystem size grows, which may hinder practical applications of VQE. In thiswork, we present a protocol termed joint Bell measurement VQE (JBM-VQE) toreduce the number of measurements and speed up the VQE algorithm. Our methodemploys joint Bell measurements, enabling the simultaneous measurement of theabsolute values of all expectation values of Pauli operators present in theHamiltonian. In the course of the optimization, JBM-VQE estimates the absolutevalues of the expectation values of the Pauli operators for each iteration bythe joint Bell measurement, while the signs of them are measured lessfrequently by the conventional method to measure the expectation values. Ourapproach is based on the empirical observation that the signs do not oftenchange during optimization. We illustrate the speed-up of JBM-VQE compared toconventional VQE by numerical simulations for finding the ground states ofmolecular Hamiltonians of small molecules, and the speed-up of JBM-VQE at theearly stage of the optimization becomes increasingly pronounced in largersystems. Our approach based on the joint Bell measurement is not limited to VQEand can be utilized in various quantum algorithms whose cost functions areexpectation values of many Pauli operators.

Accelerated variational quantum eigensolver with joint Bell measurement