# Unlocking the Potential of Quantum Machine Learning to Advance Drug Discovery

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## Abstract

**:**

## 1. Introduction

- Which QML models are used in drug discovery?
- Are QML versus ML algorithms more efficient in terms of time and accuracy in drug discovery?

## 2. Preliminaries—Background

#### 2.1. Drug Discovery

#### 2.2. Quantum Computing

**Qubit:**In a quantum processor, information is stored in qubits, which are the quantum counterparts of classical bits. A qubit can be either |0〉 or |1〉 or simultaneously in any state between them (superposition) denoted as |ψ〉 = a|0〉 + β|1〉, where α and β are complex probability amplitudes. The states mathematically can be represented as 2-d vectors:

_{1}= |β|

^{2}. Furthermore, P

_{0}+ P

_{1}= |α|

^{2}+ |β|

^{2}= 1, as claimed by the Born rule. The state after measuring the system can be $|{\mathsf{\psi}}^{\prime}\rangle =\frac{{\mathrm{M}}_{0}|\mathsf{\psi}\rangle}{\sqrt{{\mathrm{P}}_{0}}}=\frac{\mathsf{\alpha}}{|\mathsf{\alpha}|}|0\rangle =|0\rangle $, where we implicitly ignore the irrelevant global phase factors $\frac{\mathsf{\alpha}}{|\mathsf{\alpha}|}$ or $|{\mathsf{\psi}}^{\prime}\rangle =\frac{{\mathrm{M}}_{1}|\mathsf{\psi}\rangle}{\sqrt{{\mathrm{P}}_{1}}}=\frac{\mathsf{\beta}}{|\mathsf{\beta}|}|1\rangle =|1\rangle $. It is important to note that a single measurement of a qubit only provides information about one specific basis state. Due to the probabilistic nature of quantum measurements, subsequent measurements of the same qubit may yield different outcomes. To gain a more comprehensive understanding of the qubit’s state, multiple measurements need to be performed (Figure 2b).

**Superposition:**The fundamental principle of QC is based on the concept of superposition. This allows certain operations to be run in parallel rather than sequentially, resulting in an exponential reduction of the number of operations required for certain algorithms.

**Entanglement:**In addition to superposition, another fundamental principle of QC is quantum entanglement. When a qubit is correlated with other qubits, a change or alteration to it affects the rest of the qubits, even if they are physically separated. The measurement of one entangled qubit can affect the behavior of the same measurement in other entangled qubits, regardless of the distance between them. While particles do not communicate in the classical sense, there is a statistical correlation between the results of their measurements that cannot be explained using classical physics.

**Quantum Gate:**A quantum gate is a basic quantum circuit that operates on a small number of qubits. A program or algorithm consists of many quantum gates, similar to classical logic gates. In contrast to classical gates, quantum logic gates are reversible and operate simultaneously in all possible states of the qubit instead of operating in a state of either 0 or 1. The most common single-qubit quantum gates are the Hadamard (H), Identity or Pauli I gate (I), Bit flip or Pauli X gate (X), Pauli Y gate (Y), Pauli Z gate (Z), and Rotation gates (RX, RY, RZ). The Pauli gates are also sometimes notated as σ

_{x}, σ

_{y}, σ

_{z}, or with an index σ

_{i}, so that σ

_{0}= I, σ

_{1}= X, σ

_{2}= Y, σ

_{3}= Z. The most common two-qubit gate is the controlled-Not (CNOT or CX).

**Quantum Supremacy:**In many cases, analyzing the number of steps taken by quantum algorithms can show that they outperform classical algorithms for specific problems. This ability is known as quantum supremacy, where the number of steps taken by quantum algorithms is less than that taken by classical algorithms. The best-known examples of quantum acceleration include Shor’s algorithm for factorization, Grover search, and the simulation of quantum systems.

**NISQ:**NISQ (noisy intermediate-scale quantum) devices are quantum computers that implement logic operations using physical qubits and gates. Recent research has demonstrated that NISQ devices, which have a moderate number of qubits, can produce quantum states whose measurement results follow distributions that are difficult to produce by a classical computer [28]. While these devices will not be able to implement error correction, they are expected to provide computational advantages over classical supercomputers for certain problems [28]. It is important to note, however, that current quantum devices are still susceptible to noise and errors due to their interactions with the environment, which is a major obstacle to overcome to achieve scalable, fault-tolerant quantum computing (FTQC) devices.

**Quantum Algorithm/Circuit:**A quantum algorithm (QA), defined as a circuit, is composed of three essential parts (Figure 3a). The first part involves the conversion of classical data into quantum data, which is referred to as quantum embedding, state preparation, or feature mapping. The second part involves a sequence of quantum gates that are applied to the quantum data, resulting in a quantum computation. Finally, measurements are taken to extract classical information from the quantum system.

**Variational Quantum Algorithm/Circuit (VQA/VQC):**A variational quantum algorithm/circuit (VQA/VQC) is a type of hybrid quantum-classical optimization algorithm in which an objective function is evaluated by quantum computation [29]. The parameters of this function are then updated using classical optimization methods (Figure 3b). The terms “parameterized quantum circuit” (PQC) and “variational quantum algorithm” are used interchangeably.

#### 2.3. Quantum Machine Learning (QML)

**Dataset:**The initial step in the QML process involves choosing a dataset with specific characteristics. Apart from physicochemical properties that contribute to absorption, distribution, metabolism, excretion, and toxicity, the dataset must have characteristics that allow easy production and handling in the laboratory. This is because the pharmaceutical industry typically focuses on small molecules rather than large proteins or complex compounds. To simplify the handling and analysis of the compounds of these small molecules, formats such as SMILES [30,31] and Morgan Fingerprint [32] are commonly utilized to represent their sequence and structure. These representations aid in simplifying the handling and analysis of small molecules in the context of ML algorithms.

**Data Curation:**The increasing diversity and complexity of data in QML applications pose new challenges for data quality issues such as noise, data imbalance (overrepresentation of either active or inactive molecules), outliers, unlabeled data, no-normalized data, or data with missing values. Low-quality data can significantly affect the accuracy and reliability of QML analysis. Therefore, it is crucial to properly curate the data before analysis [32].

**Dimensionality Reduction:**As previously stated, the use of NISQ computers, which are considered to be near-term QC devices, is limited due to the small number of qubits available. As a result, encoding large molecules is a challenging task. To address this issue, several dimension reduction techniques have been employed, including principal component analysis (PCA) [30,32,35], linear discriminant analysis (LDA) [32], Autoencoder [35], and Anova [30]. A fundamental inquiry arises as to which of these methods provides the most effective data compression while retaining the necessary information for the development of efficient prediction models.

**QML Algorithm:**The selection of a QML algorithm is a crucial decision that requires careful consideration. Various QML algorithms exist, each with its own unique strengths and limitations. It is essential to evaluate the specific requirements of the drug discovery and the characteristics of the available quantum hardware or quantum simulator before choosing an algorithm. Thorough research and analysis should be conducted to determine which QML algorithm would be most effective for the drug discovery process and the type of data available.

**Experimental Environment:**The evaluation of QML techniques requires careful consideration of the platform on which the algorithms will be executed. The execution of QML models can occur either on quantum simulators, such as IBM’s Qiskit, Google’s Cirq, Tensorflow, and PennyLane, or on real quantum processors, such as those offered by IBM, Google, Rigetti, Xanadu, IonQ, and D-Wave. In recent times, Amazon and Microsoft have introduced cloud-based applications that enable researchers to run quantum algorithms on different quantum processors. Consequently, the choice of platform for executing QML algorithms is a crucial aspect that impacts the reliability and performance of QML techniques.

**Quantum Embedding:**Quantum embedding is a fundamental constituent of QML that entails the encoding of classical data into quantum states. It is of utmost importance, as all data present in natural phenomena and databases is classical. Therefore, quantum embedding serves as a bridge between classical data and quantum algorithms, enabling the use of QML techniques to address real-world problems. The computational cost of QML algorithms is directly affected by the choice of quantum embedding strategy. Despite the various strategies available, there is still much ongoing research regarding the transformation of classical data into a quantum circuit. Notably, amplitude embedding [35,36], angle embedding [31,36,37,38,39,40], and Hamiltonian [41] are the common encoding methods.

_{x}〉 as $\left|{\mathsf{\psi}}_{\mathrm{x}}\right.\u232a={\sum}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{x}}_{\mathrm{i}}\left|\mathrm{i}\right.\u232a$, where N = 2

^{n}, x

_{i}is the i-th element of x, and |i〉 is the i-th computational basis state. For instance, suppose we want to use amplitude encoding to encode the data point x, which has four dimensions (x

_{1}= 1.2, x

_{2}= 2.7, x

_{3}= 1.1, x

_{4}= 0.5). We require two qubits for these four features of x. The first step is to normalize the input ${\mathrm{x}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}=\frac{1}{\sqrt{10.19}}$ (x

_{1}= 1.2, x

_{2}= 2.7, x

_{3}= 1.1, x

_{4}= 0.5), where 10.19 = 1.2

^{2}+ 2.7

^{2}+ 1.1

^{2}+ 0.5

^{2}and the final quantum state is $\left|{\mathsf{\psi}}_{\mathrm{x}\mathrm{o}\mathrm{r}\mathrm{m}}\right.\u232a=\frac{1.2}{\sqrt{10.19}}\left|00\right.\u232a+\frac{2.7}{\sqrt{10.19}}\left|01\right.\u232a+\frac{1.1}{\sqrt{10.19}}\left|00\right.\u232a+\frac{0.5}{\sqrt{10.19}}\left|00\right.\u232a$.

_{i}is the i-th element of x, and R can be one of RX, RY, or RZ. The Hamiltonian encoding is a linear combination of the tensor product of Pauli operators $\mathrm{H}={\sum}_{\mathrm{j}}{\mathrm{C}}_{\mathrm{j}}{\u2a02}_{\mathrm{i}}{\mathsf{\sigma}}_{\mathrm{i}}^{\left(\mathrm{j}\right)}$, where C

_{j}is a scalar coefficient and σ

_{i}represents an element of the Pauli group {I, X, Y, Z}. An example of Hamiltonian encoding is H = 4.5I + 2.1X − 1.6ZZ.

**Training and Validation Model:**In order to ensure the validity of the model with unknown data, it is essential to avoid overtraining during the training phase of the algorithm. To accomplish this, multiple runs of the algorithm are performed using the training data. It is common practice to employ techniques such as cross-validation (CV) in such cases. Cross-validation provides a means to measure the degree of generalization of the model during training, assess its performance, and estimate its performance with unknown data. The cross-validation process involves the splitting of the original dataset into two subsets: the training set and the validation set. This procedure is repeated in each run of the experiment. The training set is used to train the model, while the validation set is used to assess its performance. By repeating this process, the algorithm can be trained and tested on different subsets of the data, which helps reduce the impact of any potential biases in the data. The performance of the model is evaluated by calculating metrics such as accuracy, precision, recall, and F1-score, which are commonly used in ML.

**Testing Model:**After training the model with the training set and tuning the parameters using the validation set, it is necessary to evaluate the model’s ability to generalize well to new and unseen data. The process of testing the model against the test set and assessing its performance using appropriate statistical measures is critical to determining the effectiveness of the model. If the test results demonstrate statistical significance, it can be concluded that a new and predictive drug model has been successfully developed. This approach ensures that the model’s performance is not limited to the data it was trained on and can be applied to real-world scenarios. Therefore, testing the model with the test set is a crucial step in validating the effectiveness of the model.

#### 2.4. Quantum Machine Learning (QML) Algorithms

#### 2.4.1. QNN

**Quantum Neural Network (QNN):**Neural networks (NNs) are algorithmic models that are inspired by the functioning of the human brain. They can be trained to recognize patterns in data and solve complex problems. The classical NNs are based on a series of interconnected nodes, or neurons, that are organized in a layered structure. These neurons have parameters that can be learned through the application of an ML algorithm. The implementation of QNNs does not rely on strict definitions of concepts such as “quantum neuron” or what constitutes the “quantum layer” of a classical NN. The architectural differences between classical NNs and quantum NNs can be observed in Figure 5a,b. One of the greatest challenges in QNNs is the disparity between the nonlinearity of classical NNs and the linearity of QC. Another significant challenge for optimizing QNNs is the initialization of their parameter space, as indicated in [42]. Several implementations of QNNs can be found in references [43,44,45].

**Quantum Convolutional Neural Network (QCNN):**A convolutional neural network (CNN) is a crucial category of NN designed for image classification. The architecture of a CNN typically includes several layers, each of which performs a specific type of computation. The first layer is usually a convolutional layer, which applies a set of filters to the input image to extract specific features. The second layer is typically a pooling layer, which downsamples the output of the convolutional layer to reduce the dimensionality of the feature map. Subsequent layers may include additional convolutional and pooling layers, followed by one or more fully connected layers that classify the input based on the extracted features (Figure 6). The primary goal of classical CNN and QCNN is to reduce the size of the matrices associated with images, which can be extensive. The first attempts to implement a QCNN were made in [46,47], where novel approaches were introduced. These pioneering works represent a significant step towards the development of efficient and effective QCNNs for image classification tasks and have inspired further research in this area.

**Quantum Long Short-Term Memory (QLSTM):**QLSTM is a type of quantum recurrent neural network (QRNN). Recurrent neural networks are designed to maintain the temporal storage of information. This is achieved using recurrent connections within the network, which allow the network to maintain previous states of information. In QLSTMs, variational quantum circuits are utilized to perform the recurrent computation within the network, replacing the traditional recurrent connections used in classical RNNs. These variational quantum circuits are designed to be trainable using techniques such as quantum gradient descent, which allows the network to learn from data. Initial attempts to implement hybrid QLSTMs were made by [31,48], both of which used variational quantum circuits in their QLSTM models.

**Quantum Radial Basis Function Neural Network (Q-RBFNN):**Q-RBFNN is a type of QNN architecture that shares similarities with the classical RBFNN. The RBFNN is composed of an input layer, a single hidden layer, and an output layer, and it utilizes radial basis functions as activation functions within the hidden layer.

**Quantum Boltzmann Machine (QB)/Quantum Restricted Boltzmann Machine (QRBM):**The Boltzmann machine (BM) is a stochastic neural network with two types of neurons—visible (inputs and outputs) and hidden—that are interconnected with one another. The quantum BM is represented as a set of interacting quantum spins that correspond to a tunable Ising model. In restricted Boltzmann machines (RBMs), visible neurons connect to hidden neurons without any synapses between identical neurons. In other words, visible neurons do not connect with other visible neurons, and hidden neurons do not connect with other hidden neurons. The analysis of QBMs conducted by Amin et al. [49] holds substantial significance and serves as a seminal study that has laid the groundwork for further research in the field.

#### 2.4.2. QGAN

#### 2.4.3. QVAE/AE

#### 2.4.4. QSVM

#### 2.4.5. Quantum Genetic Algorithms

#### 2.4.6. Quantum Linear and No-Linear Regression

## 3. Methodology

- “quantum machine learning” AND (“drug discovery” OR “drug design” OR “drug development”)

## 4. QML Applications in Drug Discovery

#### 4.1. QNN

^{pro}protein. Then, they applied HypaCADD to identify ligands that could bind with high affinity to SARS-CoV-2 virus proteins (3CL

^{pro}) and remain resilient against various mutations in the target protein. From a dataset of over 11 million compounds, the team subsampled 30,000 compounds and identified two lead compounds, ZINC000016020583 and ZINC000036707984, as potential inhibitors. They compared the performance of the above QML algorithms with classical neural networks and demonstrated that QC was on par with classical computing. Overall, the results indicate that HypaCADD is a promising hybrid approach that integrates classical and QC to address the challenges of CADD, particularly in the identification of ligands that can bind to target proteins while accounting for genetic mutations.

#### 4.2. QGAN

#### 4.3. QVAE/QAE

#### 4.4. QSVM

#### 4.5. Quantum Genetic Algorithms

#### 4.6. Quantum Linear and No-Linear Regression

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Carracedo-Reboredo, P.; Liñares-Blanco, J.; Rodríguez-Fernández, N.; Cedrón, F.; Novoa, F.J.; Carballal, A.; Maojo, V.; Pazos, A.; Fernandez-Lozano, C. A review on machine learning approaches and trends in drug discovery. Comput. Struct. Biotechnol. J.
**2021**, 19, 4538–4558. [Google Scholar] [CrossRef] - Sliwoski, G.; Kothiwale, S.; Meiler, J.; Lowe, E.W. Computational methods in drug discovery. Pharmacol. Res.
**2014**, 66, 334–395. [Google Scholar] [CrossRef] - Zinner, M.; Dahlhausen, F.; Boehme, P.; Ehlers, J.; Bieske, L.; Fehring, L. Quantum computing’s potential for drug discovery: Early stage industry dynamics. Drug Discov. Today
**2021**, 26, 1680–1688. [Google Scholar] [CrossRef] - Zinner, M.; Dahlhausen, F.; Boehme, P.; Ehlers, J.; Bieske, L.; Fehring, L. Toward the institutionalization of quantum computing in pharmaceutical research. Drug Discov. Today
**2022**, 27, 378–383. [Google Scholar] [CrossRef] - Feynman, R.P. Quantum mechanical computers. Found. Phys.
**1986**, 16, 507–532. [Google Scholar] [CrossRef] - Lloyd, S. Universal quantum simulators. Science
**1996**, 273, 1073–1078. [Google Scholar] [CrossRef] - Cao, Y.; Romero, J.; Aspuru-Guzik, A. Potential of quantum computing for drug discovery. IBM J. Res. Dev.
**2018**, 62, 6:1–6:20. [Google Scholar] [CrossRef] - Sajeev, V.; Vyshnavi, A.H.; Namboori, P.K. Thyroid Cancer Prediction Using Gene Expression Profile, Pharmacogenomic Variants and Quantum Image Processing in Deep Learning Platform-A Theranostic Approach. In Proceedings of the 2020 International Conference for Emerging Technology, Belgaum, India, 5–7 June 2020; pp. 1–5. [Google Scholar]
- Li, T.Y.; Mekala, V.R.; Ng, K.L.; Su, C.F. Classification of Tumor Metastasis Data by Using Quantum kernel-based Algorithms. In Proceedings of the IEEE 22nd International Conference on Bioinformatics and Bioengineering, Taichung, Taiwan, 7–9 November 2022; pp. 351–354. [Google Scholar]
- Houssein, E.H.; Abohashima, Z.; Elhoseny, M.; Mohamed, W.M. Hybrid quantum-classical convolutional neural network model for COVID-19 prediction using chest X-ray images. J. Comput. Des. Eng.
**2022**, 9, 343–363. [Google Scholar] [CrossRef] - Shahwar, T.; Zafar, J.; Almogren, A.; Zafar, H.; Rehman, A.U.; Shafiq, M.; Hamam, H. Automated detection of Alzheimer’s via hybrid classical quantum neural networks. Electronics
**2022**, 11, 721. [Google Scholar] [CrossRef] - Alam, M.; Ghosh, S. Qnet: A scalable and noise-resilient quantum neural network architecture for noisy intermediate-scale quantum computers. Front. Phys.
**2022**, 9, 702. [Google Scholar] [CrossRef] - Amin, J.; Sharif, M.; Fernandes, S.L.; Wang, S.H.; Saba, T.; Khan, A.R. Breast microscopic cancer segmentation and classification using unique 4-qubit-quantum model. Microsc. Res. Technol.
**2022**, 85, 1926–1936. [Google Scholar] [CrossRef] [PubMed] - Ullah, U.; Maheshwari, D.; Gloyna, H.H.; Garcia-Zapirain, B. Severity Classification of COVID-19 Patients Data using Quantum Machine Learning Approaches. In Proceedings of the 2022 International Conference on Electrical, Computer, Communications and Mechatronics Engineering, Male, Malvides, 16–18 November 2022; pp. 1–6. [Google Scholar]
- Sengupta, K.; Srivastava, P.R. Quantum algorithm for quicker clinical prognostic analysis: An application and experimental study using CT scan images of COVID-19 patients. BMC Med. Inform. Decis. Mak.
**2021**, 21, 227. [Google Scholar] [CrossRef] [PubMed] - Kumar, Y.; Koul, A.; Sisodia, P.S.; Shafi, J.; Kavita, V.; Gheisari, M.; Davoodi, M.B. Heart failure detection using quantum-enhanced machine learning and traditional machine learning techniques for internet of artificially intelligent medical things. Wirel. Commun. Mob. Comput.
**2021**, 2021, 1616725. [Google Scholar] [CrossRef] - Robert, A.; Barkoutsos, P.K.; Woerner, S.; Tavernelli, I. Resource-efficient quantum algorithm for protein folding. npj Quantum Inf.
**2021**, 7, 38. [Google Scholar] [CrossRef] - Outeiral, C.; Strahm, M.; Shi, J.; Morris, G.M.; Benjamin, S.C.; Deane, C.M. The prospects of quantum computing in computational molecular biology. Wiley Interdiscip. Rev. Comput. Mol. Sci.
**2021**, 11, e1481. [Google Scholar] [CrossRef] - Von Lilienfeld, O.A.; Müller, K.R.; Tkatchenko, A. Exploring chemical compound space with quantum-based machine learning. Nat. Rev. Chem.
**2020**, 4, 347–358. [Google Scholar] [CrossRef] - Singh, J.; Bhangu, K.S. Contemporary Quantum Computing Use Cases: Taxonomy, Review and Challenges. Arch. Comput. Methods Eng.
**2023**, 30, 615–638. [Google Scholar] [CrossRef] - Cordier, B.A.; Sawaya, N.P.; Guerreschi, G.G.; McWeeney, S.K. Biology and medicine in the landscape of quantum advantages. J. R. Soc. Interface
**2022**, 19, 20220541. [Google Scholar] [CrossRef] - Marchetti, L.; Nifosì, R.; Martelli, P.L.; Da Pozzo, E.; Cappello, V.; Banterle, F.; Trincavelli, M.L.; Martini, C.; D’Elia, M. Quantum computing algorithms: Getting closer to critical problems in computational biology. Brief. Bioinform.
**2022**, 23, bbac437. [Google Scholar] [CrossRef] - Sajjan, M.; Li, J.; Selvarajan, R.; Sureshbabu, S.H.; Kale, S.S.; Gupta, R.; Singh, V.; Kais, S. Quantum machine learning for chemistry and physics. Chem. Soc. Rev.
**2022**, 51, 6475–6573. [Google Scholar] [CrossRef] - McArdle, S.; Endo, S.; Aspuru-Guzik, A.; Benjamin, S.C.; Yuan, X. Quantum computational chemistry. Rev. Mod. Phys.
**2020**, 92, 015003. [Google Scholar] [CrossRef] - Avramouli, M.; Savvas, I.; Vasilaki, A.; Garani, G.; Xenakis, A. Quantum Machine Learning in Drug Discovery: Current State and Challenges. In Proceedings of the 26th Pan-Hellenic Conference on Informatics, Athens, Greece, 25–27 November 2022; pp. 394–401. [Google Scholar]
- Singh, D.B. (Ed.) Computer-Aided Drug Design; Springer: Singapore, 2020. [Google Scholar]
- Murray, C.W.; Verdonk, M.L.; Rees, D.C. Experiences in fragment-based drug discovery. Trends Pharmacol. Sci.
**2012**, 33, 224–232. [Google Scholar] [CrossRef] [PubMed] - Preskill, J. Quantum computing in the NISQ era and beyond. Quantum
**2018**, 2, 79. [Google Scholar] [CrossRef] - Cerezo, M.; Arrasmith, A.; Babbush, R.; Benjamin, S.C.; Endo, S.; Fujii, K.; McClean, J.R.; Mitarai, K.; Yuan, X.; Cincio, L.; et al. Variational quantum algorithms. Nat. Rev. Phys.
**2021**, 3, 625–644. [Google Scholar] [CrossRef] - Mensa, S.; Sahin, E.; Tacchino, F.; Barkoutsos, P.K.; Tavernelli, I. Quantum machine learning framework for virtual screening in drug discovery: A prospective quantum advantage. Mach. Learn. Sci. Technol.
**2023**, 4, 015023. [Google Scholar] [CrossRef] - Beaudoin, C.; Kundu, S.; Topaloglu, R.O.; Ghosh, S. Quantum Machine Learning for Material Synthesis and Hardware Security. In Proceedings of the 41st IEEE/ACM International Conference on Computer-Aided Design, San Diego, CA, USA, 30 October–3 November 2022; pp. 1–7. [Google Scholar]
- Batra, K.; Zorn, K.M.; Foil, D.H.; Minerali, E.; Gawriljuk, V.O.; Lane, T.R.; Ekins, S. Quantum machine learning algorithms for drug discovery applications. J. Chem. Inf. Model
**2021**, 61, 2641–2647. [Google Scholar] [CrossRef] - Lim, M.A.; Yang, S.; Mai, H.; Cheng, A.C. Exploring deep learning of quantum chemical properties for absorption, distribution, metabolism, and excretion predictions. J. Chem. Inf. Model.
**2022**, 62, 6336–6341. [Google Scholar] [CrossRef] - Isert, C.; Atz, K.; Jiménez-Luna, J.; Schneider, G. QMugs, quantum mechanical properties of drug-like molecules. Sci. Data
**2022**, 9, 273. [Google Scholar] [CrossRef] - Reddy, P.; Bhattacherjee, A.B. A hybrid quantum regression model for the prediction of molecular atomization energies. Mach. Learn. Sci. Technol.
**2021**, 2, 025019. [Google Scholar] [CrossRef] - Li, J.; Ghosh, S. Scalable variational quantum circuits for autoencoder-based drug discovery. In Proceedings of the 2022 Design, Automation and Test in Europe Conference and Exhibition (DATE), Antwerp, Belgium, 14–23 March 2022; pp. 340–345. [Google Scholar]
- Li, J.; Alam, M.; Congzhou, M.S.; Wang, J.; Dokholyan, N.V.; Ghosh, S. Drug discovery approaches using quantum machine learning. In Proceedings of the 58th ACM/IEEE Design Automation Conference, San Francisco, CA, USA, 5–9 December 2021; pp. 1356–1359. [Google Scholar]
- Suzuki, T.; Katouda, M. Predicting toxicity by quantum machine learning. J. Phys. Commun.
**2020**, 4, 125012. [Google Scholar] [CrossRef] - Li, J.; Topaloglu, R.O.; Ghosh, S. Quantum generative models for small molecule drug discovery. IEEE Trans. Autom. Sci. Eng.
**2021**, 2, 3103308. [Google Scholar] [CrossRef] - Darwish, S.M.; Shendi, T.A.; Younes, A. Chemometrics approach for the prediction of chemical compounds’ toxicity degree based on quantum inspired optimization with applications in drug discovery. Chemometr. Intell. Lab. Syst.
**2019**, 193, 103826. [Google Scholar] [CrossRef] - Jain, S.; Ziauddin, J.; Leonchyk, P.; Yenkanchi, S.; Geraci, J. Quantum and classical machine learning for the classification of non-small-cell lung cancer patients. SN Appl. Sci.
**2020**, 2, 1088. [Google Scholar] [CrossRef] - Khan, T.M.; Robles-Kelly, A. Machine learning: Quantum vs. classical. IEEE Access
**2020**, 8, 219275–219294. [Google Scholar] [CrossRef] - Tacchino, F.; Macchiavello, C.; Gerace, D.; Bajoni, D. An artificial neuron implemented on an actual quantum processor. npj Quantum Inf.
**2019**, 5, 26. [Google Scholar] [CrossRef] - Zhao, J.; Zhang, Y.H.; Shao, C.P.; Wu, Y.C.; Guo, G.C.; Guo, G.P. Building quantum neural networks based on a swap test. Phys. Rev. A
**2019**, 100, 012334. [Google Scholar] [CrossRef] - Zhao, C.; Gao, X.S. Qdnn: Deep neural networks with quantum layers. Quantum Mach. Intell.
**2021**, 3, 15. [Google Scholar] [CrossRef] - Cong, I.; Choi, S.; Lukin, M.D. Quantum convolutional neural networks. Nat. Phys.
**2019**, 15, 1273–1278. [Google Scholar] [CrossRef] - Henderson, M.; Shakya, S.; Pradhan, S.; Cook, T. Quanvolutional neural networks: Powering image recognition with quantum circuits. Quantum Mach. Intell.
**2020**, 2, 2. [Google Scholar] [CrossRef] - Chen, S.Y.; Yoo, S.; Fang, Y.L. Quantum long short-term memory. In Proceedings of the 2022 IEEE International Conference on Acoustics, Speech and Signal Processing, Singapore, 22–27 May 2022; pp. 8622–8626. [Google Scholar]
- Amin, M.H.; Andriyash, E.; Rolfe, J.; Kulchytskyy, B.; Melko, R. Quantum boltzmann machine. Phys. Rev. X
**2018**, 8, 021050. [Google Scholar] [CrossRef] - Ngo, T.A.; Nguyen, T.; Thang, T.C. A Survey of Recent Advances in Quantum Generative Adversarial Networks. Electronics
**2023**, 12, 856. [Google Scholar] [CrossRef] - Romero, J.; Olson, J.P.; Aspuru-Guzik, A. Quantum autoencoders for efficient compression of quantum data. Quantum Sci. Technol.
**2017**, 2, 045001. [Google Scholar] [CrossRef] - Khoshaman, A.; Vinci, W.; Denis, B.; Andriyash, E.; Sadeghi, H.; Amin, M.H. Quantum variational autoencoder. Quantum Sci. Technol.
**2018**, 4, 014001. [Google Scholar] [CrossRef] - Rebentrost, P.; Mohseni, M.; Lloyd, S. Quantum support vector machine for big data classification. Phys. Rev. Lett.
**2014**, 113, 130503. [Google Scholar] [CrossRef] - Lahoz-Beltra, R. Quantum genetic algorithms for computer scientists. Computers
**2016**, 5, 24. [Google Scholar] [CrossRef] - Moher, D.; Shamseer, L.; Clarke, M.; Ghersi, D.; Liberati, A.; Petticrew, M.; Shekelle, P.; Stewart, L.A. Preferred reporting items for systematic review and meta-analysis protocols (PRISMA-P) 2015 statement. Syst. Rev.
**2015**, 4, 1. [Google Scholar] [CrossRef] [PubMed] - Lau, B.; Emani, P.S.; Chapman, J.; Yao, L.; Lam, T.; Merrill, P.; Warrell, J.; Gerstein, M.B.; Lam, H.Y. Insights from incorporating quantum computing into drug design workflows. Bioinformatics
**2023**, 39, btac789. [Google Scholar] [CrossRef] - Wang, X.; Wang, X.; Zhang, S. Adverse Drug Reaction Detection from Social Media Based on Quantum Bi-LSTM with Attention. IEEE Access
**2022**, 11, 16194–16202. [Google Scholar] [CrossRef] - Smith, E.A.; Horan, W.P.; Demolle, D.; Schueler, P.; Fu, D.J.; Anderson, A.E.; Geraci, J.; Butlen-Ducuing, F.; Link, J.; Khin, N.A.; et al. Using Artificial Intelligence-based Methods to Address the Placebo Response in Clinical Trials. Innov. Clin. Neurosci.
**2022**, 19, 60–70. [Google Scholar] - Ganesh, R. Computational identification of inhibitors of MSUT-2 using quantum machine learning and molecular docking for the treatment of Alzheimer’s disease. Alzheimers Dement.
**2021**, 17, 1. [Google Scholar] [CrossRef]

**Figure 3.**Generic architecture of (

**a**) quantum algorithm/circuit; (

**b**) variational quantum algorithm/circuit—(U(x) is the quantum routine of encoding classical data x to the quantum state, V is the circuit block with quantum gates, and V(θ) is the variational circuit block with tunable parameters θ).

**Figure 8.**Architecture of (

**a**) AE (x: input data, z: latent vector, θ, φ: parameters); (

**b**) VAE (μ

_{x}: mean, σ

_{x}: standard deviation, θ, φ: parameters); (

**c**) quantum AE/VAE.

NN | LSTM | QBi-LSTM | LNS, CNNWEF, RNN, and ATT-RNN | |
---|---|---|---|---|

Weighted mQNN, cQNN, and qisQNN | [56] [≈] Precision [GenoDock, Platinum]/ [Rigetti, ibmq_bogota, PennyLane’s, Simulation]/ [AUC, F1, Sensitivity, Precision] | |||

QLSTM | [31] [−] Training accuracy [31] [+] Testing accuracy [USPTO-50k]/ [simulation PannyLane]/ [accuracy, Loss] | |||

QBi-LSTMA | [57] [+] Performance [TwiMed, TwitterADR]/ [simulation]/ [Precision, Recall rate, F1-score] | [57] [+] Performance [TwiMed, TwitterADR]/ [simulation]/ [Precision, Recall rate, F1-score] | [57] [+] Accuracy [57] [+] Training time [TwiMed, TwitterADR]/ [simulation]/ [Precision, Recall rate, F1-score] |

RBFNN | H-QFT-Based Hybrid QNN | Single-Layer CNN + MLP | Linear Regression/Logistic Regression/SVM Random Forest/XGBoost/Neural Network | |
---|---|---|---|---|

Q-RBFNN | [35] [≈] Accuracy [QM7]/ [simulation with noise]/ [MAE, RMSE, R2, Pearson correlation] | |||

H-QNN | [35] [−] Accuracy [QM7]/ [simulation with noise]/ [L1-Loss] | |||

single-layer QuanNN + MLP | [37] [+] Accuracy [TOUGH-C1]/ [simulation]/ [Cross Entropy] | |||

QRBM | [41] [≈] Accuracy [Kuner,Golumbic]/ [D-Wave]/ [accuracy] |

MolGAN | QGAN-HG | |
---|---|---|

QGAN-HG | [37,39] [+] Training epochs [37,39] [−] Training time [QM9, moderately reduced parameters]/ [Simulation,ibm_quito]/ [Fréchet Distance/training epochs/time] | |

QGAN-HG | [37,39] [−] Training epochs [37,39] [−] Training time [QM9, highly reduced parameters]/ [Simulation, ibm_quito]/ [Fréchet Distance/training epochs/time] | |

P-QGAN-HG | [39] [+] Learning accuracy [39] [+] Training time [37,39] [+] Training epochs [QM9, highly reduced parameters]/ [Simulation,ibm_quito]/ [Fréchet Distance/training epochs/time] |

VAE/AE | VAE | |
---|---|---|

BQ-VAE/AE | [36] [−] Accuracy [36] [≈] time training (epochs) [QM9] [non-normalized molecule]/ [simulation]/ [ accuracy, time training (epochs)] | |

BQ-VAE/AE | [36] [−] Accuracy [36] [+] time training (epochs) [QM9] [normalized molecule]/ [simulation]/ [accuracy, time training (epochs)] | |

SQ-VAE/AE | [36] [+] reconstruction accuracy [36] [+] sampling accuracy [PDBbind]/ [simulation]/ [accuracy, time training (epochs)] | |

Hybrid QVAE | [37] [−] Time learning [TOURCH1]/ [simulation]/ [L2 Loss, time] |

SVM | H-QSVM | Data Re-Uploading Classifier on CC | |
---|---|---|---|

QSVM | [32] [−] Accuracy [SARS-CoV-2 (Vero cell), small dataset]/ [ibmq_rochester]/ [Accuracy] | [32] [+] Accuracy [SARS-CoV-2 (Vero cell), small dataset]/ [ibmq_rochester]/ [Accuracy] | |

QSVM | [30] [+] ROC in cases [LIT-PCBA, COVID-19]/ [simulation]/ [ROC] [30] [+] ROC in cases [ADRB2, COVID-19]/ [IBM Quantum Montreal, IBM Quantum Guadalupe]/ [ROC] | ||

Data Re-uploading Classifier on QC | [32] [−] Accuracy [32] [+] Time [M. tuberculosis Inhibition -small dataset]/ [ ibmq_rochester]/ [accuracy, run time] [32] [−] Accuracy [32] [+] Time [cathepsin B(Pubchem)/ Krabbe disease (Pubchem)/ plague (Pubchem)/ M. tuberculosis (Pubchem)/ hERG]/ [simulation]/ [accuracy, run time] |

CGP and RBF-NN | |
---|---|

QIGP | [40] [+] Accuracy [40] [+] Τime [221 phenols]/ [simulation]/ [R, cosine similarities, MSE] |

Classical Linear Regression | MLR/RBF-NN | |
---|---|---|

Q Linear Regression | [35] [≈]Accuracy [QM7]/ [simulation with noise]/ [MAE, RMSE, R2, Pearson correlation] | |

PQC No Linear Regression | [38] [+] performance [221 phenols/ [simulation]/ [R _{train}^{2}, R_{val}^{2}, MSE_{train}, MSE_{val} RMS _{train}, RMS_{val}] |

Time | Accuracy/Precision | |
---|---|---|

QML superiority | 7 | 12 |

QML-ML equivalence | 2 | 4 |

ML superiority | 4 | 6 |

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## Share and Cite

**MDPI and ACS Style**

Avramouli, M.; Savvas, I.K.; Vasilaki, A.; Garani, G.
Unlocking the Potential of Quantum Machine Learning to Advance Drug Discovery. *Electronics* **2023**, *12*, 2402.
https://doi.org/10.3390/electronics12112402

**AMA Style**

Avramouli M, Savvas IK, Vasilaki A, Garani G.
Unlocking the Potential of Quantum Machine Learning to Advance Drug Discovery. *Electronics*. 2023; 12(11):2402.
https://doi.org/10.3390/electronics12112402

**Chicago/Turabian Style**

Avramouli, Maria, Ilias K. Savvas, Anna Vasilaki, and Georgia Garani.
2023. "Unlocking the Potential of Quantum Machine Learning to Advance Drug Discovery" *Electronics* 12, no. 11: 2402.
https://doi.org/10.3390/electronics12112402