Geometric Quantum Machine Learning with Horizontal Quantum Gates

Understand

In the current framework of Geometric Quantum Machine Learning, the canonical method for constructing a variational ansatz that respects the symmetry of some group action is by forcing the circuit to be equivariant, i.e., to commute with the action of the group.

• This can, however, be an overzealous constraint that greatly limits the expressivity of the circuit, especially in the case of continuous symmetries.
• We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits, based on homogeneous spaces, relaxing the overly stringent requirement of equivariance.
• We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions orthogonal to those of the symmetry.