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Hybrid quantum neural network for drug response prediction

by   Asel Sagingalieva, et al.

Cancer is one of the leading causes of death worldwide. It is caused by a variety of genetic mutations, which makes every instance of the disease unique. Since chemotherapy can have extremely severe side effects, each patient requires a personalized treatment plan. Finding the dosages that maximize the beneficial effects of the drugs and minimize their adverse side effects is vital. Deep neural networks automate and improve drug selection. However, they require a lot of data to be trained on. Therefore, there is a need for machine-learning approaches that require less data. Hybrid quantum neural networks were shown to provide a potential advantage in problems where training data availability is limited. We propose a novel hybrid quantum neural network for drug response prediction, based on a combination of convolutional, graph convolutional, and deep quantum neural layers of 8 qubits with 363 layers. We test our model on the reduced Genomics of Drug Sensitivity in Cancer dataset and show that the hybrid quantum model outperforms its classical analog by 15 in predicting IC50 drug effectiveness values. The proposed hybrid quantum machine learning model is a step towards deep quantum data-efficient algorithms with thousands of quantum gates for solving problems in personalized medicine, where data collection is a challenge.


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I Introduction

Cancer is a leading cause of death worldwide, accounting for nearly 10 million deaths in 2020, or nearly one in six deaths Ferlay2021CancerSF . The main cause of death from cancer is widespread metastases formed as a result of the chaotic reproduction of corrupted cells. In any case of cancer, the normal regulation of cell division is disrupted due to a defect in one or more genes CancerNet . When the balance between old and new cells gets disrupted, a tumor, consisting of damaged cells with a propensity for unlimited cell division, develops. At some point, the presence of these cells begins to prevent the normal functioning of the cells and body tissues. The tumor becomes malignant or cancerous and spreads to nearby tissues. Usually, it takes many years for cells to build up enough damage to become cancerous. Sometimes, a defective gene is inherited from parents and in other cases, the mutation occurs due to the action of a toxic substance or penetrating radiation on the DNA of a single cell Gazdar2014HereditaryLC . Each new case is different from the others due to the diversity of cell mutations, which gives us many treatment options. The selection of medicines is not an easy task when it comes to cancer, so the approach to treating each patient should be personalized Vogenberg2010PersonalizedMP . The focus of personalized medicine in oncology is, therefore, to focus on the most efficient and efficacious treatment.

Artificial intelligence can help develop personalized medicine by making the determination of diagnoses and disease-appropriate therapy faster and less costly since machine learning algorithms have proven themselves capable of guaranteeing high accuracy of predictions, learning from patient data collected over years of clinical research Awwalu2015ArtificialII . The successes of artificial intelligence in the past decade have been numerous and fascinating. Machine learning models have been applied to problems varying in purpose and structure, from complicated object detection models yolo to impressive stable diffusion models dalle2

. A specific use case of machine learning with high potential yield is in the pharmaceutical industry, where innovations could dramatically affect people’s well-being. In this work, we specifically focus on the applications of machine learning algorithms to understanding and predicting the drug response of patients with tumors. It is worth noting that modern machine learning algorithms, namely deep learning models, solve problems better having lots of data since they can learn from a large dataset and extract structures and hidden dependencies from them. But when it comes to personalized medicine, including predicting drug responses, collecting data is a challenge 

Hekler2019WhyWN .

Quantum technologies can greatly help classical machine learning. Since the existing classical models require significant computational resources, this limits their performance. Quantum computing models have the potential to improve the training process of existing classical models dunjko2018machine ; Neven2012QBoostLS ; PhysRevLett.113.130503 ; saggio2021experimental , allowing for better target function prediction accuracy with fewer iterations. These methods provide a polynomial speedup, which is critical for large and complex problems where small improvements can make a big difference. Quantum computing can offer unique advantages over classical computing in many areas such as, chemistry simulation, machine learning, optimization and, of course, medicine biamonte2017quantum ; McArdle2020QuantumCC ; Nannicini . For example, in Ref. Yogesh , it was shown that already existing machine learning algorithms, being quantum-enhanced, significantly contribute to medical science and healthcare. The authors have also shown that the prediction of heart failure as the cause of death can be effectively and more precisely be predicted with the help of quantum machine learning algorithms instead of the usage of classical ones. Among many existing quantum methods, quantum neural networks Broughton2020TensorFlowQA ; Farhi ; mcclean2018barren ; PhysRevA.98.042308 are one of the most promising. For instance, in Ref. Li2021QuantumGM , the authors use quantum generative adversarial neural network (GAN) with hybrid generator for discovery of new drug molecules. The results of the article show that classical GAN cannot properly learn molecule distribution. However, the proposed QGAN-HG (with only 15 extra quantum gate parameters) can learn molecular tasks much more effectively. In addition, hybrid quantum neural networks (HQNN) find optima with fewer iterations and with higher accuracy compared to classical neural networks, especially for a small amount of data asel1 . The previous examples show that hybrid quantum methods can have an advantage over purely classical approaches. They also indicate that quantum neural networks have the potential to solve pharmacological problems, such as the task of predicting the response of patients to different medications.

In this article, we propose a HQNN to solve the problem of predicting values. The dataset that we use is called GDSC and contains information on mutations in genomes that can be matched with different types of cancer, as well as the chemical formula of drug molecules. Our goal is to predict how the mutation will respond to the drug, how effective the drug will be and the value of . Sec. III.1 details the dataset. Sec. III.2 describes in detail what preprocessing we perform and the architecture of the network used to solve the prediction task, which is a combination of classical and quantum layers. The classical part of the hybrid network consists of several subnets, which are graph convolutional networks and convolutional networks for extracting information about drugs and cancer cell lines, respectively. The quantum layer of 8 qubits consists of an encoding layer, Variational Quantum Circuit (VQC) of 363 layers and a measurement layer. The result of measuring one qubit is a classical bit, which is the drug response prediction value for a given drug/cell line pair. Sec. III.3 describes the training process and presents the comparison of the HQNN and a classical one where the quantum layer is replaced by classical fully connected layers. The hybrid quantum approach showed a 15% better result in predicting the values compared to its classical counterpart.

Ii Machine learning for drug response prediction

In this section, we showcase existing Machine Learning approaches that led up to this paper. All the models mentioned below had experiments set using the Genomics of Drug Sensitivity in Cancer (GDSC) Yang2013GenomicsOD dataset, including drug-specific description, cancer cells and calculated value.

The metric is an important measure of drug response that is used to evaluate the effectiveness of a therapy against different types of cancer. It represents the half maximal inhibitory concentration. The of a drug can be determined by constructing a dose-response curve while examining the effect of different concentrations of the drug on the response of the disease. The larger the value is, the higher the drug concentration that is needed to destroy cells by 50%. In other words, the drug is less effective and the response of the disease to this medicine is low. Similarly, the smaller the value is, the lower the concentration of the drug that is required to suppress cells by 50% and the more effective the drug is.

Among the first approaches to solving the problem of predicting drugs using sensitivity to cancer cells was the one implemented in 2012 Garnett2012SystematicIO

. Using the elastic net model, it was possible to identify complex biomarkers and match them with sensitive cancer cells. The elastic net model uses coordinate descent to predict with a linear model and uses the determination coefficient to set the parameters for the estimator. Elastic Net adopted genomic features to reproduce the tumor environment and thus considered only part of features which was rather small to reach high accuracy and universality concerning the larger set of drugs and diseases.

Random Forest is a classification model that applies a sequence of queries to a set of data samples in order to linearly restrict and split it into classes genomics . It was shown that the model considered cancer cells and drug features performed well as multi-drug yet left space for increasing the model’s robustness by taking into account more input features of the cell lines.

Ridge regression, in a similar way to linear regression, follows a path of coordinate descent. It then changes the cost function in a way so that it could regain the regression model’s stability and avoid overfitting. A model that had an additional quadratic term in its loss function Geeleher and that consisted of baseline gene expression only managed to perform better than several existing biomarkers, though the model is believed to be improved by being more specific in expressing other levels of gene structure.

When a Convolutional Neural Network (CNN) gets a picture as an input, it assigns weights to a filter and does convolution to an existing layer of pixels. A filter or kernel extracts the dominating features and the pooling layer is implemented to reduce the volume of the object. After going through the series of convolutional and pooling layers, the resulting features are processed by the fully connected (FC) layers and then are distributed into classes. The proposed approach

Chang2018CancerDR employed an ensemble of five models that gave an average predicted value for cancer cell lines (instead of cancer types). Along with genomic fingerprints, the models used selected mutation positions.

Figure 1: In each case, the drug response is calculated for a pair of chemical formula of the medication/cell line. The drug response is evaluated using the 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.

Since the first deep learning models emerged, their application in the field of personalized medicine increased with their development. In 2019, a deep learning multi-layered model was proposed starting with an input layer, followed by nonlinearity layers and a classification layer at the end deep_learning_framework . The pathways to each drug were analysed to increase the efficiency of the neural net performance. The accuracy of the predictions increases as the training datasets become larger so it is believed that it is possible to improve the model with larger datasets.

Another deep learning-based model applies the method of late integration of mutation, aberration number and omics-data, DL MOLI SharifiNoghabi2019MOLIML

. The model performs preprocessing of the data to send the result through three encoder neural sub-networks to extract features. Then the model connects the features into one representation of the given tumor sample and follows the classifier structure with the cost function considering triplet loss to separate responder samples from non-responders.

Visual neural networks (VNN) applied to the given cluster of problems represent models of the human cancer cell. In the VNN model, considering both drug and genotype features, their embedding was performed in parallel human_cancer_cells

. The drug branch was built as an artificial network of three hidden FC layers, where each drug was described as a fingerprint at the input. Genotypes were binary-encoded and passed through the VNN, which was constructed as cell subsystems, each assigned its number of neurons.

In the presented variety of approaches to solving the problem of personalized medicine, each classical neural network tried to integrate data into the model and, in its way, tried to reproduce the conditions of real life as best as possible. However, until now, previous approaches not only did not take into account the possible factors influencing the study to the maximum, but also an architecture capable of taking into account the influence of all these factors could not be built, leaving alone the problem of small datasets and overfitting. Consequently, the result was given for some special cases.

In this article, we present a method for solving the problem of predicting the values using a hybrid quantum neural network. To date, we have not found studies that would solve the problem of predicting the values using quantum or hybrid quantum neural networks. Our approach allows solving the drug response prediction problem more accurately than its classical counterpart on a small dataset. In the next section, hybrid quantum method and results will be described in detail.

Iii Results

This paper explores the use of hybrid quantum models in drug response prediction. The proposed model is a combination of graph convolutional, convolutional, and quantum layers. We tested our model on a small part of the dataset, taken using GDSC database (Sec. III.1). Hybrid quantum-classical model can provide higher learning efficiency, requiring fewer iterations, and can show lower prediction error in the values on a 15% compared to the classical analogue as will be shown below.

Figure 2:

HQNN architecture. The cell-line is fed to the network as a vector with 735 elements to a 1-dimensional convolutional network and 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 the schematic above to reach a fully connected layer of 128 neurons. Then, they are combined into a single layer of 256 (2x128) neurons. Classical information from every 8 classical neurons of 256 neurons is encoded into encoded into rotation angles

around the Z-axis into each of 8 qubits of the 32 quantum circuits forming a quantum layer, the total number of variational parameters is 1320. The measurement result of the first qubit is a prediction of the value.

iii.1 Description of dataset

The dataset known as the Genomics of Drug Sensitivity in Cancer (GDSC) Yang2013GenomicsOD is considered to be the largest database keeping information about cancer cell line sensitivity on prescribed anti-cancer drugs and genetic correlations.

The GDSC database consists of cell line drug sensitivity data, generated from ongoing high-throughput screening, genomic datasets for cell lines and the analysis of genomic features, or systematic integration of large-scale genomic and drug sensitivity datasets, for example see Fig. 1. The compounds selected for the screening of cancer are anticancer therapeutics. They are comprised of approved drugs used in the clinic, drugs undergoing clinical development, drugs in clinical trials and tool compounds in early phase development. They cover a wide range of targets and processes implicated in cancer biology. Cell line drug sensitivity is measured using fluorescence-based cell viability assays following 72 hours of drug treatment. Values from the dataset include the value, the slope of the dose-response curve and the area under the curve for each experiment. In this study, we used version 6.0 of the dataset.

iii.2 Hybrid quantum neural network architecture

The principle of operation of the neural network as shown in Fig. 1 is the distribution of drugs, represented in the form of a chemical formula in the dataset, and cancer cells encoded in a binary chain over two parallel working neural networks and placing all the results in a quantum neural network for analysis and prediction of the value.

In this section, we present a solution to the problem of prediction, describe in detail the architecture of the network used. The architecture of a hybrid quantum neural network (HQNN) is illustrated in Fig. 2 and consists of 3 subnetworks: Neural network for cell line representations (Sec. III.2.1), Neural network for drug representations (Sec. III.2.2) and Quantum neural network (Sec. III.2.3). It is worth noting that we were inspired to use such a classical part of our hybrid model Ref. nguyen .

iii.2.1 Cell line representation

In biology, a cell line is a population of human cells that normally would not multiply indefinitely, however, because of the gene mutation these cells avoided cellular aging and instead continue to divide infinitely. Thus, in our studies, the cell line represents the tumor itself as a binary vector, where 1 indicated the presence of genomic mutation and 0, its absence as one can see at the Fig. 2

. A one-dimensional convolutional layer was used to encode the cell line’s genomic features which are represented in the form of one-hot encoding namely 735 dimensional binary vector. Then the feature map was passed through the Max Pooling layer in order to reduce the spatial volume of the map. After three repetitions of the convolutional layers, the final fully connected layer flattens the output into a vector of 128 dimensions.

iii.2.2 Drug representation

The drug is represented as a graph in the format of SMILES, using the PubChem library Yang2013GenomicsOD . In this format, the drug is written in a line. Each node of the graph contains information describing its graphical and chemical representation, including the atom type, the chemical bonds, the branching of the molecule, its configuration and its isotopes. The atom type is encoded with the standard abbreviation of the chemical elements, the bonds are represented with special symbols, branches are described with parentheses, and isotopes are specified with a number equal to the integer isotopic mass preceding the atomic symbol. Then the drug data transformed into a molecular graphs using RDKit software Landrum2016RDKit2016_09_4 . Each of 223 drug has its unique chemical structure which can be naturally represented as a graph where the vertices and edges denote chemical atoms and bonds, respectively. Thus, each graph obtained from one line of SMILES contains information about one specific drug and has a number of vertices equal to the number of atoms in the molecule of this drug, and the edges in the graph are responsible for the bonds between atoms in the molecule. Representing drugs in graphs is more suitable than in strings since it conserves the nature of chemical structures of drugs. Since drugs were represented in the forms of graphs, Graph Convolutional Network Kipf2017SemiSupervisedCW was used to learn its features.

A Graph Convolutional Layer was taken 2 matrices as an input: feature matrix and adjacency matrix , which displays the connections between atoms, where - number of atoms in a molecule, - atomic features, 78 dimensional binary feature vector, and then produced a node-level output with features each node.

In the used sub-network there were three graph convolutional layers after each of them an activation function ReLU

Agarap2018DeepLU was used, after the last graph convolutional layer a global max pooling was applied. The obtained output was turned into a 128-dimensional vector by the sequence of two fully connected layers with sizes 312, 1024 and 128 respectively.

iii.2.3 Quantum neural network

The resulting combination of both cell and drug data, constituting a vector of 256 nodes, was transformed into a quantum layer of the HQNN. In this work, we employ a large and deep quantum neural network. This size arises from a need to propagate uncompressed data (256 neurons) through from the classical preparation networks to the quantum layer. Commonly-used QNN architectures normally encode each feature on a separate qubit IQP ; asel1 ; asel2 , but for 256 neurons this is not accessible to today’s quantum engineers for two main reason: 1) this qubit count is far beyond the fault-tolerant readily-accessible quantum simulator or hardware, and 2) the noise-free barren plateau problem bp affects this region with high potency, rendering the model impossible to train. Instead, we take inspiration from the data re-uploading method introduced in data_reuploading and developed further in schuld_fourier to create a lattice of features: we use 8 qubits, and create a lattice of length 32, where the first 8 features are encoded on the first length using the rotations gates around Z-axis, features 9-16 on the second, and this pattern is continued for all the 256 features produced by the classical lead up to the quantum layer. Entangling variational layers are placed between each layer of feature encoding to allow for highest Fourier accessibility schuld_fourier to the feature encoding. In the final layer, all qubits but the first make a CNOT operation on the first qubit so that the Z-measurement is propagated to all qubits. The Z-measurement is then augmented using an multiplicative and an additive trainable parameter to fit the requirements of the value. Thus, the output of the HQNN is the prediction of the value of the particular chemical/cell line pair.

It is noteworthy that a quantum circuit of this depth would be far too difficult a challenge for today’s noisy quantum devices and it is likely that this architecture in its current form will stay on a quantum simulator for the foreseeable future. However, it is possible to create mathematically identical circuits to it with much shallower depth but higher qubit counts. This means that by increasing the number of qubits, we get the same model but much shallower and thus with higher potential for being run on a noisy quantum device.

The HQNN was compared with its classical counterpart, the architecture of differs only in the last part: instead of a quantum layer, the classical network has 2 fully connected layers, the numbers of neurons in which are 8 and 1. In terms of the number of parameters, these two models also differ only in the last part: the HQNN has 1320 variational parameters, while the classical model has 2056.

iii.3 Training and results

In our experiment, the hybrid quantum model was evaluated on drug/cell line pairs provided by the GDSC database with known values. The used data consisted of

pairs of drugs and cell lines. The corresponding received response values were normalized in the range of (0,1). The data were shuffled and distributed into training and testing sets. Since it is difficult to collect data in tasks related to the pharmaceutical industry and personal medicine, and hybrid quantum neural networks performed well in solving problems on a small dataset, the dataset was redused to 5000 samples for training and 1000 for testing procedure. To increase the representativeness of the dataset and prevent accidental skewness, the data was shuffled in the training set at each epoch. As an optimizer, Adam 

kingma2014adam was used with learning rate equals .

Figure 3: Dependence of the MSE loss on the number of epochs. The hybrid model outperforms the classical counterpart by 15%.

To estimate the model’s efficiency, we used the mean square error (MSE) metric. It measures the difference between and , where denotes the ground-truth for each of the sample, in our case drug/cell line pair and denotes the predicted value .

The successful performance of the model is determined by small values of the MSE - the lower, the better.

All machine learning simulations were carried out in the QMware cloud, on which the classical part was implemented with the PyTorch library 

PyTorch and the quantum part was implemented with the PennyLane framework. PennyLane offers a variety of qubit devices. We used the 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 backprop was used and for the quantum part, the adjoint method ; Luo2020yaojlextensible was used. The results of the simulations are shown in Fig. 3.

Thus the network with the deep quantum layer demonstrates a better result than the classical one and the improvement in the loss of the hybrid model is more than 15% compared to the classical model with the same architecture.

Iv Conclusion

In this study, we present a novel hybrid quantum neural network consists of deep quantum circuit with 1320 trainable gates for anticancer drug response prediction. In our model, drugs were represented as molecular graphs, while cell lines were represented as binary vectors. To learn the features of drugs and cell lines, graph convolutional and convolutional layers with fully connected layers, respectively, were used, then a deep quantum neural network predicted the response values for the drug/cell line pairs. We were able to encode information from 256 neurons into just 8 qubits. As far as we know, this is the first work in which hybrid neural networks are used to predict the value of .

In addition, we have demonstrated that our hybrid model is 15 % better than its classical counterpart, in which the quantum layer is replaced by a fully connected classical layer with 8 neurons. We tested our models on a reduced dataset presented by GDSC and consisting of 5000 and 1000 training and test drugs/cell line pairs, respectively. The results of this experiment show that hybrid neural networks may significantly help in personal medicine tasks where data collection is a difficult task, also in anticancer drug design and understanding cancer biology.

In future work, we are planning to calculate a list of the values for certain drug/cell line pairs using the models produced in this work as well as increase the complexity and performance of the HQNN.


  • (1) J. Ferlay, M. Colombet, I. Soerjomataram, D. M. Parkin, M. Piñeros, A. Znaor, and F. Bray, “Cancer statistics for the year 2020: An overview,” International Journal of Cancer, vol. 149, pp. 778 – 789, 2021.
  • (2) “Cancer net.”
  • (3) A. F. Gazdar, L. Robinson, D. Oliver, C. Xing, W. D. Travis, J. Soh, S. Toyooka, L. M. Watumull, Y. Xie, K. H. Kernstine, and J. H. Schiller, “Hereditary lung cancer syndrome targets never smokers with germline egfr gene t790m mutations,” Journal of Thoracic Oncology, vol. 9, p. 456–463, 2014.
  • (4) F. R. Vogenberg, C. I. Barash, and M. Pursel, “Personalized medicine: part 1: evolution and development into theranostics.,” P & T : a peer-reviewed journal for formulary management, vol. 35 10, pp. 560–76, 2010.
  • (5) J. Awwalu, A. G. Garba, A. Ghazvini, and R. Atuah, “Artificial intelligence in personalized medicine application of ai algorithms in solving personalized medicine problems,” International Journal of Computer Theory and Engineering, vol. 7, pp. 439–443, 2015.
  • (6) J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, “You only look once: Unified, real-time object detection,” arXiv:1506.02640, 2015.
  • (7) A. Ramesh, P. Dhariwal, A. Nichol, C. Chu, and M. Chen, “Hierarchical text-conditional image generation with clip latents,” arXiv:2204.06125, 2022.
  • (8) E. B. Hekler, P. V. Klasnja, G. Chevance, N. M. Golaszewski, D. M. Lewis, and I. Sim, “Why we need a small data paradigm,” BMC Medicine, vol. 17, 2019.
  • (9) V. Dunjko and H. J. Briegel, “Machine learning & artificial intelligence in the quantum domain: a review of recent progress,” Reports on Progress in Physics, vol. 81, no. 7, p. 074001, 2018.
  • (10) H. Neven, V. S. Denchev, G. Rose, and W. G. Macready, “QBoost: Large scale classifier training withadiabatic quantum optimization,” in Proc. Asian Conf. Mach. Learn. (S. C. H. Hoi and W. Buntine, eds.), vol. 25 of Proceedings of Machine Learning Research, pp. 333–348, PMLR, 2012.
  • (11)

    P. Rebentrost, M. Mohseni, and S. Lloyd, “Quantum support vector machine for big data classification,”

    Physical Review Letters, vol. 113, p. 130503, Sep 2014.
  • (12) V. Saggio, B. E. Asenbeck, A. Hamann, T. Strömberg, P. Schiansky, V. Dunjko, N. Friis, N. C. Harris, M. Hochberg, D. Englund, et al.

    , “Experimental quantum speed-up in reinforcement learning agents,”

    Nature, vol. 591, no. 7849, pp. 229–233, 2021.
  • (13) J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learning,” Nature, vol. 549, no. 7671, p. 195, 2017.
  • (14) S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, “Quantum computational chemistry,” Reviews of Modern Physics, 2020.
  • (15)

    G. Nannicini, “Performance of hybrid quantum-classical variational heuristics for combinatorial optimization,”

    Physical Review E, vol. 99, 2019.
  • (16) Y. Kumar, A. Koul, P. Singh Sisodia, J. Shafi, K. Verma, M. Gheisari, and M. B. Davoodi, “Heart failure detection using quantum-enhanced machine learning and traditional machine learning techniques for internet of artificially intelligent medical things,” Wireless Communications and Mobile Computing, p. 16, 2021.
  • (17) M. Broughton, G. Verdon, T. McCourt, A. J. Martinez, J. H. Yoo, et al., “TensorFlow Quantum: A software framework for quantum machine learning,” arXiv:2003.02989, 2020.
  • (18) E. Farhi and H. Neven, “Classification with quantum neural networks on near term processors,” arXiv:1802.06002, 2018.
  • (19) J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,” Nature Communications, vol. 9, no. 1, pp. 1–6, 2018.
  • (20) P. Rebentrost, T. R. Bromley, C. Weedbrook, and S. Lloyd, “Quantum Hopfield neural network,” Physical Review A, vol. 98, p. 042308, 2018.
  • (21) J. Li, R. O. Topaloglu, and S. Ghosh, “Quantum generative models for small molecule drug discovery,” IEEE Transactions on Quantum Engineering, vol. 2, pp. 1–8, 2021.
  • (22) M. Perelshtein, A. Sagingalieva, K. Pinto, V. Shete, A. Pakhomchik, A. Melnikov, F. Neukart, G. Gesek, A. Melnikov, and V. Vinokur, “Practical application-specific advantage through hybrid quantum computing,” arXiv:2205.04858, 2022.
  • (23) W. Yang, J. Soares, P. Greninger, E. J. Edelman, H. Lightfoot, S. A. Forbes, N. Bindal, D. Beare, J. A. Smith, I. R. Thompson, S. Ramaswamy, P. A. Futreal, D. A. Haber, M. R. Stratton, C. H. Benes, U. McDermott, and M. J. Garnett, “Genomics of drug sensitivity in cancer (gdsc): a resource for therapeutic biomarker discovery in cancer cells,” Nucleic Acids Research, vol. 41, pp. D955 – D961, 2013.
  • (24) M. J. Garnett, E. J. Edelman, S. J. Heidorn, C. D. Greenman, A. Dastur, K. W. Lau, P. Greninger, I. R. Thompson, X. Luo, J. Soares, Q. Liu, F. Iorio, D. Surdez, L. Chen, R. J. Milano, G. Bignell, A. T. Tam, H. Davies, J. A. Stevenson, S. Barthorpe, S. R. Lutz, F. Kogera, K. Lawrence, A. McLaren-Douglas, X. Mitropoulos, T. Mironenko, H. Thi, L. Richardson, W. Zhou, F. Jewitt, T. Zhang, P. O’Brien, J. L. Boisvert, S. Price, W. Hur, W. Yang, X. Deng, A. P. Butler, H. G. Choi, J. W. Chang, J. Baselga, I. Stamenkovic, J. A. Engelman, S. V. Sharma, O. Delattre, J. Saez-Rodriguez, N. S. Gray, J. Settleman, P. A. Futreal, D. A. Haber, M. R. Stratton, S. Ramaswamy, U. McDermott, and C. H. Benes, “Systematic identification of genomic markers of drug sensitivity in cancer cells,” Nature, vol. 483, pp. 570 – 575, 2012.
  • (25) M. P. Menden, F. Iorio, M. Garnett, U. McDermott, C. H. Benes, P. J. Ballester, and J. Saez-Rodriguez, “Machine learning prediction of cancer cell sensitivity to drugs based on genomic and chemical properties,” PLOS ONE, vol. 8, pp. 1–7, 04 2013.
  • (26) H. R. Geeleher P., Cox N.J., “Clinical drug response can be predicted using baseline gene expression levels and in vitro drug sensitivity in cell lines,” Genome Biology, vol. 15, 2014.
  • (27) Y. Chang, H. Park, H. jin Yang, S. Lee, K.-Y. Lee, T. S. Kim, J. Jung, and J.-M. Shin, “Cancer drug response profile scan (cdrscan): A deep learning model that predicts drug effectiveness from cancer genomic signature,” Scientific Reports, vol. 8, 2018.
  • (28) T. Sakellaropoulos, K. Vougas, S. Narang, F. Koinis, A. Kotsinas, A. Polyzos, T. J. Moss, S. Piha-Paul, H. Zhou, E. Kardala, E. Damianidou, L. G. Alexopoulos, I. Aifantis, P. A. Townsend, M. I. Panayiotidis, P. Sfikakis, J. Bartek, R. C. Fitzgerald, D. Thanos, K. R. Mills Shaw, R. Petty, A. Tsirigos, and V. G. Gorgoulis, “A deep learning framework for predicting response to therapy in cancer,” Cell Reports, vol. 29, no. 11, pp. 3367–3373.e4, 2019.
  • (29) H. Sharifi-Noghabi, O. I. Zolotareva, C. C. Collins, and M. Ester, “Moli: multi-omics late integration with deep neural networks for drug response prediction,” Bioinformatics, vol. 35, pp. i501 – i509, 2019.
  • (30) B. M. Kuenzi, J. Park, S. H. Fong, K. S. Sanchez, J. Lee, J. F. Kreisberg, J. Ma, and T. Ideker, “Predicting drug response and synergy using a deep learning model of human cancer cells,” Cancer Cell, vol. 38, no. 5, pp. 672–684.e6, 2020.
  • (31) T. Nguyen, G. T. T. Nguyen, T. Nguyen, and D.-H. Le, “Graph convolutional networks for drug response prediction,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 19, pp. 146–154, 01 2022.
  • (32)

    G. Landrum, “RDKit: Open-source cheminformatics software,” 2016.

  • (33) T. Kipf and M. Welling, “Semi-supervised classification with graph convolutional networks,” arXiv:1609.02907, 2017.
  • (34) A. F. Agarap, “Deep learning using rectified linear units (ReLU),” arXiv:1803.08375, 2018.
  • (35) T. Douce, D. Markham, E. Kashefi, E. Diamanti, T. Coudreau, P. Milman, P. van Loock, and G. Ferrini, “Continuous-variable instantaneous quantum computing is hard to sample,” Physical Review Letters, vol. 118, no. 7, 2017.
  • (36) A. Sagingalieva, A. Kurkin, A. Melnikov, D. Kuhmistrov, M. Perelshtein, A. Melnikov, A. Skolik, and D. Von Dollen, “Hyperparameter optimization of hybrid quantum neural networks for car classification,” arXiv:2205.04878, 2022.
  • (37) J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,” Nature Communications, vol. 9, 11 2018.
  • (38) A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, “Data re-uploading for a universal quantum classifier,” Quantum, vol. 4, p. 226, 2020.
  • (39) M. Schuld, R. Sweke, and J. J. Meyer, “Effect of data encoding on the expressive power of variational quantum-machine-learning models,” Physical Review A, vol. 103, no. 3, 2021.
  • (40) D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv:1412.6980, 2014.
  • (41) “PyTorch.”, 2022.
  • (42) D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, pp. 533–536, 10 1986.
  • (43) T. Jones and J. Gacon, “Efficient calculation of gradients in classical simulations of variational quantum algorithms,” arXiv:2009.02823, 2020.
  • (44) X.-Z. Luo, J.-G. Liu, P. Zhang, and L. Wang, “Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design,” Quantum, vol. 4, p. 341, Oct. 2020.