Fig. 6: Ansätze and gates tested with the VQE.
From: First-order phase transition of the Schwinger model with a quantum computer
Decomposition of a generic SO(4) gate depending on the six parameters θ1, …, θ6 (a) the \({R}_{XX+YY}(\theta )={R}_{{Z}_{0}}\exp (-i\theta (XX+YY)/2){R}_{{Z}_{0}}^{\dagger }\) (b), into CNOT and Pauli rotation gates. The \({R}_{{Z}_{0}}\) rotations in the definition of RXX+YY(θ) restrict the state to the real subspace. Boxes acting on a single qubit correspond to Pauli rotation gates, \({R}_{P}(\alpha )=\exp -i\alpha P/2\) with P ∈ {X, Y, Z}. Single-qubit gates where the argument is omitted refer to rotations around an angle π/2, RP(π/2). The light blue boxes represent the parameterized gates which are R(α, β, γ) = RX(γ)RZ(β)RX(α) in (a) and RY(θ) in (b). Panel (c) and (d) illustrate one layer of the brick and ladder ansatz, respectively, both following a non-parametric part for preparing the initial state \(\vert {\psi }_{in}\rangle\) (yellow box). The first layer in the brick ansatz has a CNOT-depth of 4 whereas in ladder it is 2n − 2, where n is the number of qubits, and in both cases it increases by 4 with each layer.
