A Scalable Quantum Neural Network for Approximate Unitary Synthesis
G. Belli, Marco Mordacci, Michele Amoretti · 2024
In this work, scalable quantum neural networks are introduced to approximate unitary evolutions through the Standard Recursive Block Basis (SRBB) and, subsequently, redesigned with a reduced number of CNOTs. This algebraic approach to the problem of unitary synthesis exploits Lie algebras and their topological features to obtain a continuous parameterization of unitary operators. First, we implemented the recursive construction of the SRBB to provide a starting tool for quickly verifying the mathematical properties needed to guarantee the original scalability scheme, already known to the literature only from a theoretical point of view. Unexpectedly, 2-qubit systems emerge as a special case outside this scheme. Furthermore, we present a method to reduce the number of CNOT gates, thus deriving a new implementable scaling scheme, which requires only one single layer and whose performance has been tested with a variety of different unitary matrices via the PennyLane library.