Fig. 5: Variational quantum eigensolver.
From: Quantum logic with spin qubits crossing the surface code threshold
a, Lowest two molecular orbitals of a H2 molecule, formed by the 1s orbitals of two hydrogen atoms. b, The quantum circuit to implement the VQE algorithm for a H2 molecule. The orange block prepares the HF initial state by flipping Q2. The circuit in green blocks creates the parameterized ansatz state. \(-{{\rm{X}}}_{{{\rm{Q}}}_{i}}\) and \(-{{\rm{Y}}}_{{{\rm{Q}}}_{j}}\) include virtual Z gates. CNOT gates are compiled as \([-{{\rm{Y}}}_{{{\rm{Q}}}_{2}},{\rm{C}}{\rm{Z}},{{\rm{Y}}}_{{{\rm{Q}}}_{2}}]\). To make use of the high-fidelity CZ gate, such compilation is preferred instead of using a single controlled-phase gate with incremental length for creating the parameterized ansatz state. c, Expectation values of the operators in the two-qubit Hamiltonian under BK transformation as a function of θ. Black solid lines show the predicted values. The coloured solid lines are sinusoidal fits to the data (and a constant fit for the case of ZZ). d, Potential energy of the H2 molecule at varying R. The VQE data are normalized to the theoretical energy at large R to directly compare the dissociation energy with the theoretical value. The inset shows the error in the normalized experimental data.
