Fig. 1: Information sharing framework.

Parallel Bayesian optimisation for physically parameterised VQE tasks. Separate BO’s \({\mathcal{B}}({{\bf{x}}}_{\alpha })\) optimise for different cost functions C_α, corresponding to different values of the physical parameters x_α, using the same parameterised ansatz circuit U(θ). Every iteration, each \({\mathcal{B}}({{\bf{x}}}_{\alpha })\) requests a new variational parameter point θ_α, at which the set of Pauli strings {P_i} are measured. These expectation values are used to compute any C_β cost functions (dashed lines) at θ_α, for all α, β. Each BO can then be updated using the measurement results obtained for several θ_α, θ_β, … parameter points each iteration (bold arrows), dramatically speeding up convergence at all x_α.