Today’s quantum computers are small and noisy. Hybrid quantum-classical algorithms aim to make use of these limited devices by pairing them with classical computing and assigning specialized tasks to the quantum hardware (e.g. measuring the energy expectation value of a wavefunction ansatz for a molecule). These approaches are still demanding of quantum hardware, especially since we will often want to solve multiple related instances of a problem, for example to find the electronic ground state of a molecule at a range of different nuclear separations.
In this work we introduce a hybrid algorithm whose goal is to efficiently obtain multi-dimensional energy surfaces of physical systems with many degrees of freedom. Our method treats multiple configurations in parallel by exploiting the global nature of Bayesian optimisation and sharing information between the different configurations. We experimentally demonstrate the effectiveness of our approach on IBM Quantum hardware. Considering the problem of finding the two-dimensional ground state energies of a linear chain of three hydrogen atoms we show a 100-fold improvement in efficiency compared to other approaches.