Algorithm 2: Boosted quantum classifier with T cycles

Input: Quantum training dataset $\left(\right|x_i\rangle ,y_i)\in X\times Y$; weak learning algorithm ${\mathcal{L}}_{qw}$; integer T of iterative cycle; form sample state vector $|\tilde{x}\rangle$ and ancilla vector $|\tilde{\phi }\rangle$ Initialize the weight of graph $w_{1,n}=D_1\left(n\right)=\frac{1}{\sqrt{2N}}$ for $n=1,\cdots ,N$, and ${\widehat{w}}_{1,n}$ for$1\le t\le T$, do 1. Construct cluster states $|{\overrightarrow{h}}^{\left(t\right)}{\rangle }_{\mathcal{C}}$ and $|{\overrightarrow{h}}_a^{\left(t\right)}{\rangle }_{\mathcal{C}}$ 2. Compute mixed state ${\rho }_{\mathcal{C}}^t$ to obtain $\overrightarrow{p^t}$ 3. Apply ${\mathcal{L}}_{qw}$ to provide $\overrightarrow{p^t}$, return $h_t:X\to [0,1]$. 4. Obtain the error ${\epsilon }_t$ of $h_t$. 5. Update weights vector ${\overrightarrow{w}}_{t+1}$ Output: the $H\left(x\right)$ of graph state $|G\rangle$.