Predicting toxicity by quantum machine learning

In recent years, parameterized quantum circuits have been regarded as machine learning models within the framework of the hybrid quantum-classical approach. Quantum machine learning (QML) has been applied to binary classification problems and unsupervised learning. However, practical quantum application to nonlinear regression tasks has received considerably less attention. Here, we develop QML models designed for predicting the toxicity of 221 phenols on the basis of quantitative structure activity relationship. The results suggest that our data encoding enhanced by quantum entanglement provided more expressive power than the previous ones, implying that quantum correlation could be beneficial for the feature map representation of classical data. Doubling the number of qubits had a positive impact on the performance, with the aid of the higher dimensionality in the feature map. Our QML models performed significantly better than the multiple linear regression method. Furthermore, our simulations indicate that the QML models were comparable to those obtained using radial basis function networks, while improving the generalization performance. The present study implies that QML could be an alternative approach for nonlinear regression tasks such as cheminformatics.

[1]  Tomás Babej,et al.  A quantum alternating operator ansatz with hard and soft constraints for lattice protein folding , 2018, 1810.13411.

[2]  Maria Schuld,et al.  Quantum Machine Learning in Feature Hilbert Spaces. , 2018, Physical review letters.

[3]  William J. Dunn,et al.  Quantitative structure—activity relationships (QSAR) , 1989 .

[4]  Peter D. Johnson,et al.  Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms , 2019, Advanced Quantum Technologies.

[5]  M. Sohaib Alam,et al.  Quantum Kitchen Sinks: An algorithm for machine learning on near-term quantum computers , 2018, 1806.08321.

[6]  Jos'e I. Latorre,et al.  Data re-uploading for a universal quantum classifier , 2019, Quantum.

[7]  Ivano Tavernelli,et al.  Resource-efficient quantum algorithm for protein folding , 2019, npj Quantum Information.

[8]  Keisuke Fujii,et al.  Quantum circuit learning , 2018, Physical Review A.

[9]  David J. Schwab,et al.  Supervised Learning with Tensor Networks , 2016, NIPS.

[10]  Dirk Oliver Theis,et al.  Input Redundancy for Parameterized Quantum Circuits , 2019, Frontiers in Physics.

[11]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[12]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[13]  H. Kubinyi,et al.  3D QSAR in drug design. , 2002 .

[14]  Hartmut Neven,et al.  Classification with Quantum Neural Networks on Near Term Processors , 2018, 1802.06002.

[15]  G. Rose,et al.  Finding low-energy conformations of lattice protein models by quantum annealing , 2012, Scientific Reports.

[16]  T. Monz,et al.  Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator , 2018, Physical Review X.

[17]  K. Nakajima,et al.  Universal Approximation Property of Quantum Feature Map , 2020, ArXiv.

[18]  D. Venturelli,et al.  Quantum Annealing Implementation of Job-Shop Scheduling , 2015, 1506.08479.

[19]  Harper R. Grimsley,et al.  An adaptive variational algorithm for exact molecular simulations on a quantum computer , 2018, Nature Communications.

[20]  Andrew W. Cross,et al.  Quantum optimization using variational algorithms on near-term quantum devices , 2017, Quantum Science and Technology.

[21]  David Von Dollen,et al.  Traffic Flow Optimization Using a Quantum Annealer , 2017, Front. ICT.

[22]  Marco Pistoia,et al.  Computational Investigations of the Lithium Superoxide Dimer Rearrangement on Noisy Quantum Devices. , 2019, The journal of physical chemistry. A.

[23]  The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size. , 2019, 1910.08187.

[24]  F. Petruccione,et al.  An introduction to quantum machine learning , 2014, Contemporary Physics.

[25]  Maxwell Henderson,et al.  Quanvolutional neural networks: powering image recognition with quantum circuits , 2019, Quantum Machine Intelligence.

[26]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[27]  M. Schuld,et al.  Circuit-centric quantum classifiers , 2018, Physical Review A.

[28]  Leo Zhou,et al.  Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices , 2018, Physical Review X.

[29]  Simone Severini,et al.  Hierarchical quantum classifiers , 2018, npj Quantum Information.

[30]  Ryan LaRose,et al.  Robust data encodings for quantum classifiers , 2020, Physical Review A.

[31]  Maria Schuld,et al.  Effect of data encoding on the expressive power of variational quantum-machine-learning models , 2020, Physical Review A.

[32]  Kristan Temme,et al.  Supervised learning with quantum-enhanced feature spaces , 2018, Nature.

[33]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[34]  M. Leib,et al.  Comparison of QAOA with Quantum and Simulated Annealing , 2019, 1901.01903.

[35]  Maliheh Aramon,et al.  A Novel Graph-based Approach for Determining Molecular Similarity , 2016, ArXiv.

[36]  Simone Severini,et al.  Quantum machine learning: a classical perspective , 2017, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[37]  Paola Gramatica,et al.  Principles of QSAR models validation: internal and external , 2007 .

[38]  L. A. Stone,et al.  Computer Aided Design of Experiments , 1969 .

[39]  Mark T. D. Cronin,et al.  Multivariate Discrimination between Modes of Toxic Action of Phenols , 2002 .

[40]  Scott N. Genin,et al.  Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer. , 2018, Journal of chemical theory and computation.

[41]  J. Gambetta,et al.  Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets , 2017, Nature.

[42]  Alán Aspuru-Guzik,et al.  Quantum Chemistry in the Age of Quantum Computing. , 2018, Chemical reviews.

[43]  Stefan Woerner,et al.  Quantum risk analysis , 2018, npj Quantum Information.

[44]  Haifeng Chen,et al.  Comparative Study of QSAR/QSPR Correlations Using Support Vector Machines, Radial Basis Function Neural Networks, and Multiple Linear Regression , 2004, J. Chem. Inf. Model..

[45]  Alán Aspuru-Guzik,et al.  The theory of variational hybrid quantum-classical algorithms , 2015, 1509.04279.

[46]  Alejandro Perdomo-Ortiz,et al.  Classical versus Quantum Models in Machine Learning: Insights from a Finance Application , 2019 .

[47]  Jack D. Hidary,et al.  Quantum Computing: An Applied Approach , 2019 .

[48]  Soonwon Choi,et al.  Quantum convolutional neural networks , 2018, Nature Physics.

[49]  Marcello Benedetti,et al.  Parameterized quantum circuits as machine learning models , 2019, Quantum Science and Technology.

[50]  Jacob biamonte,et al.  Quantum machine learning , 2016, Nature.

[51]  Jitender Verma,et al.  3D-QSAR in drug design--a review. , 2010, Current topics in medicinal chemistry.

[52]  Alexander Tropsha,et al.  Best Practices for QSAR Model Development, Validation, and Exploitation , 2010, Molecular informatics.

[53]  Daniel A. Lidar,et al.  Quantum annealing versus classical machine learning applied to a simplified computational biology problem , 2018, npj Quantum Information.

[54]  Thomas R. Bromley,et al.  Quantum computational finance: Monte Carlo pricing of financial derivatives , 2018, Physical Review A.

[55]  W. Dur,et al.  Concatenated tensor network states , 2009, 0904.1925.

[56]  K. Birgitta Whaley,et al.  Towards quantum machine learning with tensor networks , 2018, Quantum Science and Technology.

[57]  Alán Aspuru-Guzik,et al.  Potential of quantum computing for drug discovery , 2018, IBM J. Res. Dev..

[58]  Iordanis Kerenidis,et al.  Quantum Recommendation Systems , 2016, ITCS.

[59]  D Zhu,et al.  Training of quantum circuits on a hybrid quantum computer , 2018, Science Advances.

[60]  Dacheng Tao,et al.  The Expressive Power of Parameterized Quantum Circuits , 2018, ArXiv.

[61]  Shu-Hao Wu,et al.  Quantum generative adversarial learning in a superconducting quantum circuit , 2018, Science Advances.

[62]  Ievgeniia Oshurko Quantum Machine Learning , 2020, Quantum Computing.

[63]  Ryan Babbush,et al.  The theory of variational hybrid quantum-classical algorithms , 2015, 1509.04279.

[64]  Alán Aspuru-Guzik,et al.  A variational eigenvalue solver on a photonic quantum processor , 2013, Nature Communications.

[65]  Heinz Schmidli Quantitative Structure Activity Relationships (QSAR) , 1995 .

[66]  Haralambos Sarimveis,et al.  Prediction of toxicity using a novel RBF neural network training methodology , 2006, Journal of molecular modeling.