Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials

Abstract

Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However the discussion in all these recipes focus specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or on a predefined choice of the user. The work horse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs- Boltzmann distribution using a quantum circuit and the phase information obtained classically from the non-linear activation of a separate set of neurons. We show that the resource requirements of our algorithm is strictly quadratic. To demonstrate its efficacy, we use state-filtration in monolayer transition metal-dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring band-structures of exquisite materials to usual electronic structure methods or machine learning techniques which are implementable solely on a classical computer

References in corpus (84)

• Array Programming with NumPy
• Atomically thin MoS2: A new direct-gap semiconductor
• Quantum Computing in the NISQ era and beyond
• Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Quantum algorithm for solving linear systems of equations
• The density-matrix renormalization group
• Variational Quantum Algorithms
• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Machine learning and the physical sciences
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantum support vector machine for big data classification
• Perspective on density functional theory
• Quantum Chemistry in the Age of Quantum Computing
• Quantum Convolutional Neural Networks
• Simulated Quantum Computation of Molecular Energies
• Machine learning phases of matter
• Quantum principal component analysis
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides
• A high-bias, low-variance introduction to Machine Learning for physicists
• Many-body quantum state tomography with neural networks
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Towards Quantum Chemistry on a Quantum Computer
• Quantum algorithms for quantum chemistry and quantum materials science
• High Mobility Ambipolar MoS2 Field-Effect Transistors: Substrate and Dielectric Effects
• By-passing the Kohn-Sham equations with machine learning
• Finding Density Functionals with Machine Learning
• Quantum algorithms for supervised and unsupervised machine learning
• Quantum machine learning: a classical perspective
• Variational Quantum Computation of Excited States
• Quantum-enhanced machine learning
• Monolayer MoS2: trigonal warping, "Γ-valley", and spin-orbit coupling effects
• Exponential suppression of bit or phase flip errors with repetitive error correction
• Manipulation of the large Rashba spin splitting in polar two-dimensional transition metal dichalcogenides
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Quantum Boltzmann Machine
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Subspace-search variational quantum eigensolver for excited states
• Inverse statistical problems: from the inverse Ising problem to data science
• Machine Learning Phases of Strongly Correlated Fermions
• \textit{Ab-initio} Tight-Binding Hamiltonian for Transition Metal Dichalcogenides
• From transistor to trapped-ion computers for quantum chemistry
• Approximating quantum many-body wave-functions using artificial neural networks
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Is the Trotterized UCCSD Ansatz chemically well-defined?
• Tomography and Generative Data Modeling via Quantum Boltzmann Training
• Can single-reference coupled cluster theory describe static correlation?
• Excited states using semistochastic heat-bath configuration interaction
• Quantum Machine Learning for Electronic Structure Calculations
• Theory of second harmonic generation in few-layered MoS2
• Fast Semistochastic Heat-Bath Configuration Interaction
• Quantum singular value decomposition of non-sparse low-rank matrices
• Machine learning for many-body physics: The case of the Anderson impurity model
• A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
• Reducing qubit requirements for quantum simulation using molecular point group symmetries
• Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices
• A tight-binding model for MoS${}_2$ monolayers
• Quantum assisted Gaussian process regression
• High-temperature superfuidity of the two-component Bose gas in a TMDC bilayer
• Excitons and trions in monolayer transition metal dichalcogenides: A comparative study between the multiband model and the quadratic single-band model
• Valley-dependent spin transport in monolayer transition-metal dichalcogenides
• Penalty methods for variational quantum eigensolver
• Training a Large Scale Classifier with the Quantum Adiabatic Algorithm
• Strong Electron Correlation in Nitrogenase Cofactor, FeMoco
• Measurement Error Mitigation for Variational Quantum Algorithms
• Sensitivity and Entanglement in the Avian Chemical Compass
• Excited states in variational Monte Carlo using a penalty method
• Electrically tunable topological superconductivity and Majorana fermions in two dimensions
• Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations
• Approximating power of machine-learning ansatz for quantum many-body states
• Double-excitation manifold's effect on exciton transfer dynamics and the efficiency of coherent light harvesting
• Many-body calculations for periodic materials via quantum machine learning
• General error mitigation for quantum circuits
• Quantum Computational Method of Finding the Ground State Energy and Expectation Values
• Direct Application of the Phase Estimation Algorithm to Find the Eigenvalues of the Hamiltonians
• Quantum Machine Learning using Gaussian Processes with Performant Quantum Kernels
• Low-temperature thermal transport and thermopower of monolayer transition metal dichalcogenide semiconductors
• Using Restricted Boltzmann Machines to Model Molecular Geometries

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