# Hybrid Quantum Neural Network for Drug Response Prediction

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Machine Learning for Drug Response Prediction

## 3. Results

#### 3.1. Description of Dataset

#### 3.2. Hybrid Quantum Neural Network Architecture

#### 3.2.1. Cell Line Representation

#### 3.2.2. Drug Representation

#### 3.2.3. Quantum Neural Network

#### 3.3. Training and Results

`lightning.qubit`device, which implements a high-performance C++ backend. To obtain the gradients of the loss function with respect to each of the parameters, for the classical part of our HQNN, the standard back propagation algorithm [57] was used and for the quantum part, the

`adjoint`method [58,59] was used. The results of the simulations are shown in Figure 3. We observe that the MSE loss function of the HQNN decreases monotonically during training, while the classical model exhibits a volatile behavior. This indicates that the HQNN is more stable and efficient in minimizing the loss function.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GAN | Generative adversarial network |

HQNN | Hybrid quantum neural network |

FC | Fully connected |

GDSC | Genomics of Drug Sensitivity in Cancer |

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**Figure 1.**In each case, the drug response is calculated for a pair of chemical formulas of the medication/cell line. The drug response is evaluated using the ${\mathrm{IC}}_{50}$ value. The machine learning algorithm is a powerful drug predicting tool as it saves effort and time that could have been spent on tests in the laboratory and waiting for the results of experimental therapy courses to check whether there are improvements in the patient’s condition.

**Figure 2.**HQNN architecture. The cell line is fed to the network as a vector with 735 elements to a one-dimensional convolutional network. In parallel, the chemical composition of the drug is passed to a graph convolutional neural network. Each of these two is then processed in parallel according to the graphic above, to reach an FC layer of 128 neurons. Then, they are combined into a single layer of 256 (2 × 128) neurons. Classical information from every 8 classical neurons of 256 neurons is passed to the Quantum Depth-Infused Neural Network Layer. The information is encoded into rotation angles ${\left\{{\varphi}_{j}\right\}}_{j=1}^{256}$ around the Z-axis into each of the 8 qubits of the 32 quantum circuits forming a quantum layer. The total number of variational parameters ${\left\{{\theta}_{k}^{h}\right\}}_{k=1}^{8}$ is 1320. The measurement result of the first qubit predicts the ${\mathrm{IC}}_{50}$ value.

**Figure 3.**Dependence of the MSE loss on the number of epochs. The HQNN outperforms the classical counterpart by 15%.

**Figure 4.**Dependence of the difference between MSE losses of the classical and hybrid model on training sizes. The fewer training data, the greater the difference in loss, and the better the quantum model is compared to the classical one.

Action | Elements Name | Elements Description | Matrix Representation | Elements Notation |
---|---|---|---|---|

1 | Rotation operator X | $X\left(\theta \right)=exp\left(-i{\sigma}_{x}\theta /2\right)$ | $\left[\begin{array}{cc}cos(\theta /2)& -isin(\theta /2)\\ -isin(\theta /2)& cos(\theta /2)\end{array}\right]$ | |

2 | Rotation operator Y | $Y\left(\theta \right)=exp\left(-i{\sigma}_{y}\theta /2\right)$ | $\left[\begin{array}{cc}cos(\theta /2)& -sin(\theta /2)\\ sin(\theta /2)& cos(\theta /2)\end{array}\right]$ | |

3 | Rotation operator Z | $Z\left(\theta \right)=exp\left(-i{\sigma}_{z}\theta /2\right)$ | $\left[\begin{array}{cc}exp(-i\theta /2)& 0\\ 0& exp(i\theta /2)\end{array}\right]$ | |

4 | Controlled NOT gate | CNOT $=exp\left(i\frac{\pi}{4}\left(I-{\sigma}_{{z}_{1}}\right)\left(I-{\sigma}_{{x}_{2}}\right)\right)$ | $\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 1& 0\end{array}\right]$ |

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## Share and Cite

**MDPI and ACS Style**

Sagingalieva, A.; Kordzanganeh, M.; Kenbayev, N.; Kosichkina, D.; Tomashuk, T.; Melnikov, A.
Hybrid Quantum Neural Network for Drug Response Prediction. *Cancers* **2023**, *15*, 2705.
https://doi.org/10.3390/cancers15102705

**AMA Style**

Sagingalieva A, Kordzanganeh M, Kenbayev N, Kosichkina D, Tomashuk T, Melnikov A.
Hybrid Quantum Neural Network for Drug Response Prediction. *Cancers*. 2023; 15(10):2705.
https://doi.org/10.3390/cancers15102705

**Chicago/Turabian Style**

Sagingalieva, Asel, Mohammad Kordzanganeh, Nurbolat Kenbayev, Daria Kosichkina, Tatiana Tomashuk, and Alexey Melnikov.
2023. "Hybrid Quantum Neural Network for Drug Response Prediction" *Cancers* 15, no. 10: 2705.
https://doi.org/10.3390/cancers15102705