Local, expressive, quantum-number-preserving VQE ansätze for fermionic systems

Abstract We propose VQE circuit fabrics with advantageous properties for the simulation of strongly correlated ground and excited states molecules materials under Jordan–Wigner mapping that can be implemented linearly locally preserve all relevant quantum numbers: number spin up ( ? ) down ? electrons total squared. demonstrate our entangler circuits are expressive already at low depth parameter count, appear to become universal, may trainable without having cross regions vanishing gradient, when parameters becomes sufficiently large these suitably initialized. One particularly appealing construction achieves this just orbital rotations pair exchange gates. derive optimal four-term shift rules provide explicit decompositions preserving gates perform numerical demonstrations on highly 20 qubits.