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

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

Automated summary

The proposed VQE circuit fabrics have advantageous properties for simulating strongly correlated ground and excited states of molecules and materials. These entangler circuits are expressive even at low depth and parameter count, and may become universal when parameters are sufficiently large and properly initialized, without having to cross regions of vanishing gradient. Optimal four-term parameter shift rules are derived and numerical demonstrations are performed on highly correlated molecules up to 20 qubits.