Local, Expressive, Quantum-Number-Preserving VQE Ansatze for Fermionic Systems

TL;DR

This paper introduces quantum variational ansatze for fermionic systems that preserve key quantum numbers, are highly expressive at low depth, and are demonstrated on complex molecules, advancing quantum simulation capabilities.

Contribution

It presents new quantum circuit ansatze that preserve quantum numbers and are efficient, expressive, and trainable for simulating strongly correlated fermionic systems.

Findings

Ansatz circuits are expressive at low depth and parameter count.

Circuits can become universal and trainable without vanishing gradients.

Numerical demonstrations on molecules up to 20 qubits show effectiveness.

Abstract

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.