Fig. 3: Energy convergence of variational quantum eigensolver (VQE) calculations with four types of ansätze.
From: Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models
Panels a, b show the energy difference between the variational and the exact ground state energy EGS as a function of a number of variational parameters Nθ. Panels c, d show the energy difference versus the number of CNOT gates Ncx. Panels a, c are for the degenerate \(({N}_{{{{{{{{\mathcal{S}}}}}}}}}=2,{N}_{{{{{{{{\mathcal{B}}}}}}}}}=2)\)eg impurity model and panels b, d correspond to the (3, 3) t2g impurity model. VQE calculations are reported with fixed Hamiltonian variational ansatz (HVA, orange dashed line) and unitary coupled cluster ansatz with single and double excitations (UCCSD, black cross) as well as with adaptive ansätze constructed from a simplified unitary coupled cluster pool with single and paired double excitation operators (sUCCSpD, black line) and a Hamiltonian commutator pool (HC, sky blue line). Here Ncx is estimated according to each multi-qubit rotation gate with a Pauli string generator P of lengthlcontributing 2(l−1) CNOT gates, which assumes a full qubit connection. The Hamiltonian parameters are ϵ = −9.8(−12.7), λ = 0.3(0.1), \({{{{{{{\mathcal{D}}}}}}}}=-0.3(-0.3)\) with the same Hubbard U = 7 for the eg (t2g) model, corresponding to the correlated bad metallic regime. The energy unit is the half-band width D of the noninteracting DOS for the multi-band lattice model (see Fig. 1).
