Efficient Quantum State Preparation with Walsh Series

Understand

A new approximate Quantum State Preparation (QSP) method is introduced, called the Walsh Series Loader (WSL).

• The WSL approximates quantum states defined by real-valued functions of single real variables with a depth independent of the number $n$ of qubits.
• Two approaches are presented: the first one approximates the target quantum state by a Walsh Series truncated at order $O(1/\sqrt{\epsilon})$, where $\epsilon$ is the precision of the approximation in terms of infidelity.
• The circuit depth is also $O(1/\sqrt{\epsilon})$, the size is $O(n+1/\sqrt{\epsilon})$ and only one ancilla qubit is needed.