# A Scheme for Controlled Cyclic Asymmetric Remote State Preparation in Noisy Environment
## 2 Four-Party Controlled Cyclic Asymmetrical RSP Protocol of Sequentially Increasing Qubits States
### Experimental Realization in IBM QE
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**SPM1(A)**} & \multirow{2}{*}{**SPM1(B)**} & \multirow{2}{*}{**SPM1(C)**} & \multirow{2}{*}{**SPM2(A)**} & \multirow{2}{*}{**SPM2(B)**} & \multirow{2}{*}{**SPM2(C)**} & \multirow{2}{*}{**SPM(D)**} & \multicolumn{3}{c}{**Transformations**} \\ \cline{5-5} \cline{8-10}  & & & & & & & & **[PERSON]** & **[PERSON]** & **[PERSON]** \\ \hline \multirow{2}{*}{\(\ket{\Phi^{+}}_{g}\)} & \multirow{2}{*}{\(\ket{\Phi^{+}}_{5}\)} & \multirow{2}{*}{\(\ket{\Phi^{+}}_{1}\)} & \multirow{2}{*}{\(\ket{\Psi^{+}}_{d}\)} & \multirow{2}{*}{\(\ket{\Psi^{+}}_{b^{\prime\prime}}\)} & \multirow{2}{*}{\(\ket{\Psi^{+}}_{c^{\prime\prime\prime}}\)} & \(\ket{0}_{10}\) & \(l^{234}\) & \(l^{8}\) & \(l^{67}\) \\ \cline{5-5} \cline{8-10}  & & & & & & \(\ket{1}_{10}\) & \(\sigma_{z}^{2}\otimes\sigma_{x}^{34}\) & \(-i\sigma_{y}^{8}\) & \(i\sigma_{y}^{6}\otimes\sigma_{x}^{2}\) \\ \hline \multirow{2}{*}{\(\ket{\Phi^{+}}_{g}\)} & \multirow{2}{*}{\(\ket{\Phi^{+}}_{5}\)} & \multirow{2}{*}{\(\ket{\Phi^{+}}_{1}\)} & \multirow{2}{*}{\(\ket{\Psi^{-}}_{d}\)} & \multirow{2}{*}{\(\ket{\Psi^{-}}_{b^{\prime\prime}}\)} & \multirow{2}{*}{\(\ket{\Psi^{-}}_{c^{\prime\prime\prime}}\)} & \(\ket{0}_{10}\) & \(\sigma_{z}^{234}\) & \(\sigma_{z}^{8}\) & \(\sigma_{z}^{67}\) \\ \cline{5-5} \cline{8-10}  & & & & & & \(\ket{1}_{10}\) & \(l^{2}\otimes\sigma_{x}^{34}\) & \(-\sigma_{x}^{8}\) & \(\sigma_{z}^{67}\) \\ \hline \multirow{2}{*}{\(\ket{\Phi^{-}}_{g}\)} & \multirow{2}{*}{\(\ket{\Phi^{-}}_{5}\)} & \multirow{2}{*}{\(\ket{\Phi^{-}}_{1}\)} & \multirow{2}{*}{\(\ket{\Psi^{+}}_{d}\)} & \multirow{2}{*}{\(\ket{\Psi^{+}}_{b^{\prime\prime}}\)} & \(\ket{\Psi^{+}}_{c^{\prime\prime\prime}}\) & \(\ket{0}_{10}\) & \(-i\sigma_{y}^{2}\otimes\sigma_{x}^{34}\) & \(-i\sigma_{y}^{8}\) & \(-i\sigma_{y}^{6}\otimes\sigma_{x}^{7}\) \\ \cline{5-5} \cline{8-10}  & & & & & \(\ket{1}_{10}\) & \(\sigma_{z}^{2}\otimes l^{34}\) & \(-l^{8}\) & \(l^{67}\) \\ \hline \multirow{2}{*}{\(\ket{\Phi^{-}}_{g}\)} & \multirow{2}{*}{\(\ket{\Phi^{-}}_{5}\)} & \multirow{2}{*}{\(\ket{\Phi^{-}}_{1}\)} & \multirow{2}{*}{\(\ket{\Psi^{-}}_{d}\)} & \multirow{2}{*}{\(\ket{\Psi^{-}}_{b^{\prime\prime}}\)} & \(\ket{\Psi^{-}}_{c^{\prime\prime\prime}}\) & \(\ket{0}_{10}\) & \(\sigma_{x}^{234}\) & \(\sigma_{x}^{8}\) & \(\sigma_{z}^{67}\) \\ \cline{5-5} \cline{8-10}  & & & & & \(\ket{1}_{10}\) & \(\sigma_{x}^{2}\otimes l^{34}\) & \(\sigma_{z}^{8}\otimes l^{67}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Joint collapsed states of some cases and reconstructed unitary transformation. Figure 4: Quantum circuit illustrating four-party controlled cyclic asymmetrical RSP protocol. in the ibmq_qsam_simulator (Figure 5a). We successfully implement quantum circuit in the IBM quantum computer to realize the cyclic asymmetric RSP scheme. In Table 2, we have shown the outcome of 10 runs for the output state each run having 8192 shots. According the average value and standard deviation, we obtain the average error between the ideal results and the experimental results is 0.004. The discrepancy arises from the finite coherence time of the qubits, the implementation of the gates and the process of reading out the qubits.