Variational Quantum Simulation of Valence-Bond Solids

We introduce a hybrid quantum-classical variational algorithm to simulate ground-state phase diagrams of frustrated quantum spin models in the thermodynamic limit. The method is based on cluster-Gutzwiller ansatz where wave function cluster provided by parameterized circuit whose key ingredient two-qubit real XY gate allowing efficiently generate valence-bonds nearest-neighbor qubits. Additional tunable single-qubit Z- and ZZ-rotation gates allow description magnetically ordered paramagnetic phases while restricting optimization U(1) subspace. benchmark against J1-J2 Heisenberg model square lattice uncover its diagram, which hosts long-range Neel columnar anti-ferromagnetic phases, as well an intermediate valence-bond solid characterized periodic pattern 2x2 strongly-correlated plaquettes. Our results show that convergence guided onset order, opening promising route synthetically realize magnets their transition solids with currently developed superconducting devices.