SRBB-Based Quantum State Preparation

In this work, a scalable algorithm for the approximate quantum state preparation problem is proposed, approaching the optimal theoretical depth bounds present in the literature. The desired quantum state is approximated by a scalable quantum neural network, whose CNOT-optimized variational circuit is designed on the diagonal subalgebra of the Standard Recursive Block Basis (SRBB). The results highlight the potential of SRBB in close connection with the geometry of unitary groups, achieving high accuracy up to 4 qubits in simulation, but also its current limitations with an increasing number of qubits. The SRBB-based state preparation algorithm has also been tested on real quantum devices.