Building Spatial Symmetries into Parameterized Quantum Circuits for Faster Training

Practical success of quantum learning models hinges on having a suitablestructure for the parameterized quantum circuit. Such structure is defined bothby the types of gates employed and by the correlations of their parameters.While much research has been devoted to devising adequate gate-sets, typicallyrespecting some symmetries of the problem, very little is known about how theirparameters should be structured. In this work, we show that an ideal parameterstructure naturally emerges when carefully considering spatial symmetries(i.e., the symmetries that are permutations of parts of the system understudy). Namely, we consider the automorphism group of the problem Hamiltonian,leading us to develop a circuit construction that is equivariant under thissymmetry group. The benefits of our novel circuit structure, called ORB, arenumerically probed in several ground-state problems. We find a consistentimprovement (in terms of circuit depth, number of parameters required, andgradient magnitudes) compared to literature circuit constructions.