Implementation of an Optimally Bounded Algorithm for Quantum State Preparation

Quantum state preparation is a fundamental subroutine for many quantum algorithms, including linear system solvers, algorithms for Hamiltonian simulation, and quantum machine learning. Quantum state preparation consists in preparing an n-qubit quantum state through the definition of a unitary matrix that acts on the quantum register, conventionally initialized with all qubits in the zero state. Despite the transversal relevance, the characterization of its circuit depth complexity remained an open problem until the work by Sun et al., which discovered the asymptotically optimal space-time trade-off bounds when m ancillary qubits are available. Additionally, their algorithm resolves the depth complexity for circuits without ancillary qubits. In this work, a first implementation of the optimally bounded algorithm by Sun et al. is presented, framed in the parametric range m=2n and using the PennyLane library. A novel strategy for handling the complete set of parameters of the general complex case is presented from a theoretical point of view and tested to establish its effectiveness. To assess the scalability of the implemented algorithm, several quantum states have been prepared in simulation up to 8 qubits, both dense and sparse, including states of specific interest such as Bell or GHZ states.