Predicting excited states from ground state wavefunction by supervised quantum machine learning

Abstract

Excited states of molecules lie in the heart of photochemistry and chemical reactions. The recent development in quantum computational chemistry leads to inventions of a variety of algorithms that calculate the excited states of molecules on near-term quantum computers, but they require more computational burdens than the algorithms for calculating the ground states. In this study, we propose a scheme of supervised quantum machine learning which predicts the excited-state properties of molecules only from their ground state wavefunction resulting in reducing the computational cost for calculating the excited states. Our model is comprised of a quantum reservoir and a classical machine learning unit which processes the measurement results of single-qubit Pauli operators with the output state from the reservoir. The quantum reservoir effectively transforms the single-qubit operators into complicated multi-qubit ones which contain essential information of the system, so that the classical machine learning unit may decode them appropriately. The number of runs for quantum computers is saved by training only the classical machine learning unit, and the whole model requires modest resources of quantum hardware that may be implemented in current experiments. We illustrate the predictive ability of our model by numerical simulations for small molecules with and without noise inevitable in near-term quantum computers. The results show that our scheme well reproduces the first and second excitation energies as well as the transition dipole moment between the ground states and excited states only from the ground state as an input. We expect our contribution will enhance the applications of quantum computers in the study of quantum chemistry and quantum materials.

arXiv comment26 pages, 7 figures, 2 tables

References in corpus (35)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Quantum algorithm for solving linear systems of equations
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• Machine learning and the physical sciences
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Quantum support vector machine for big data classification
• Quantum Circuit Learning
• Quantum Chemistry in the Age of Quantum Computing
• Quantum Convolutional Neural Networks
• Machine learning phases of matter
• Quantum principal component analysis
• Error mitigation for short-depth quantum circuits
• Extending the computational reach of a noisy superconducting quantum processor
• Quantum Computational Supremacy
• Learning phase transitions by confusion
• Machine Learning of Molecular Electronic Properties in Chemical Compound Space
• Quantum Data Fitting
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Variational Quantum Computation of Excited States
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Architectures for a quantum random access memory
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Subspace-search variational quantum eigensolver for excited states
• Prediction by linear regression on a quantum computer
• Electronic Spectra from TDDFT and Machine Learning in Chemical Space
• Variational quantum algorithms for discovering Hamiltonian spectra
• Quantum reservoir processing
• Machine Learning Exciton Dynamics
• Temporal Information Processing on Noisy Quantum Computers
• Machine Learning Phase Transitions with a Quantum Processor
• Quantum Template Matching

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