Calculating nonadiabatic couplings and Berry's phase by variational quantum eigensolvers

Abstract

The variational quantum eigensolver (VQE) is an algorithm to find eigenenergies and eigenstates of systems in quantum chemistry and quantum many-body physics. The VQE is one of the most promising applications of near-term quantum devices to investigate such systems. Here we propose an extension of the VQE to calculate the nonadiabatic couplings of molecules in quantum chemical systems and Berry's phase in quantum many-body systems. Both quantities play an important role to understand the properties of a system beyond the naive adiabatic picture, e.g., nonadiabatic dynamics and topological phase of matter. We provide quantum circuits and classical post-processings to calculate the nonadiabatic couplings and Berry's phase. Specifically, we show that the evaluation of the nonadiabatic couplings reduces to that of expectation values of observables while that of Berry's phase also requires one additional Hadamard test. Furthermore, we simulate the photodissociation dynamics of a lithium fluoride molecule using the nonadiabatic couplings evaluated on a real quantum device. Our proposal widens the applicability of the VQE and the possibility of near-term quantum devices to study molecules and quantum many-body systems.

arXiv comment19 pages, 8 figures

References in corpus (59)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• Berry Phase Effects on Electronic Properties
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Quantum Circuit Learning
• Quantum Chemistry in the Age of Quantum Computing
• Quantum Convolutional Neural Networks
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Error mitigation for short-depth quantum circuits
• Quantum Algorithms Revisited
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Fermionic quantum computation
• Extending the computational reach of a noisy superconducting quantum processor
• Scalable Quantum Simulation of Molecular Energies
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Practical Quantum Error Mitigation for Near-Future Applications
• Hybrid quantum-classical algorithms and quantum error mitigation
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Quantum autoencoders for efficient compression of quantum data
• Variational Quantum Computation of Excited States
• Robust determination of molecular spectra on a quantum processor
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum chemistry calculations on a trapped-ion quantum simulator
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Layerwise learning for quantum neural networks
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Subspace-search variational quantum eigensolver for excited states
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• Variational quantum algorithms for discovering Hamiltonian spectra
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
• Noise Resilience of Variational Quantum Compiling
• Low rank representations for quantum simulation of electronic structure
• Quantized Berry Phases as Local Order Parameters of Quantum Liquids
• A general second order complete active space self-consistent-field solver for large-scale systems
• Methodology for replacing indirect measurements with direct measurements
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• On barren plateaus and cost function locality in variational quantum algorithms
• A Jastrow-type decomposition in quantum chemistry for low-depth quantum circuits
• Calculating energy derivatives for quantum chemistry on a quantum computer
• Calculation of the Green's function on near-term quantum computers
• When do we need to account for the geometric phase in excited state dynamics ?
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Theory of analytical energy derivatives for the variational quantum eigensolver
• Penalty methods for variational quantum eigensolver
• Experimental quantum kernel machine learning with nuclear spins in a solid
• Variational Quantum Algorithm for Non-equilibrium Steady States
• On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods
• $Z_N$ Berry Phases in Symmetry Protected Topological Phases
• An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry's phase and "magnetic" forces
• Berry Phase Estimation in Gate-Based Adiabatic Quantum Simulation

Cited by in corpus (10)

• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Analytical nonadiabatic couplings and gradients within the state-averaged orbital-optimized variational quantum eigensolver
• Probing many-body localization by excited-state VQE
• Training variational quantum algorithms with random gate activation
• A hybrid quantum algorithm to detect conical intersections
• Analytical formulation of the second-order derivative of energy for orbital-optimized variational quantum eigensolver: application to polarizability
• Non-adiabatic Quantum Wavepacket Dynamics Simulation Based on Electronic Structure Calculations using the Variational Quantum Eigensolver
• Quantum computing topological invariants of two-dimensional quantum matter
• Deep variational quantum eigensolver for excited states and its application to quantum chemistry calculation of periodic materials
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach