Figure 7

Total gate count (total), CNOT gate count (cx) and T gate count (t) of the quantum circuit preparing the state of a sparse vector \({\textbf{b}}\). In our system, the number of qubits is fixed at \({n_b}=12\) while W, the number of nonzero entries in \({\textbf{b}}\) corresponding to randomly-generated injection/extraction sites, increases from 1 to 25. For each value of W, gate counts from 5 random state samples are shown with \(+\) symbols, along with their average and bars extending from smallest to largest value. Theoretically, the state preparation method’s total gate count scales as \(O(W {n_b})\), further broken down as \(O(W n_b)\) CNOT gates and \(O(W\log W + n_b)\) single-qubit gates.