Quantum Eigenvector Continuation for Chemistry Applications

Abstract

A typical task for classical and quantum computing in chemistry is finding a potential energy surface (PES) along a reaction coordinate, which involves solving the quantum chemistry problem for many points along the reaction path. Developing algorithms to accomplish this task on quantum computers has been an active area of development, yet finding all the relevant eigenstates along the reaction coordinate remains a difficult problem, and determining PESs is thus a costly proposal. In this paper, we demonstrate the use of a eigenvector continuation -- a subspace expansion that uses a few eigenstates as a basis -- as a tool for rapidly exploring potential energy surfaces. We apply this to determining the binding PES or torsion PES for several molecules of varying complexity. In all cases, we show that the PES can be captured using relatively few basis states; suggesting that a significant amount of (quantum) computational effort can be saved by making use of already calculated ground states in this manner.

arXiv comment13 pages, 8 figures, 3 pages of appendix

References in corpus (30)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Barren plateaus in quantum neural network training landscapes
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Recent developments in the PySCF program package
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Quantum Spin Liquids
• The Variational Quantum Eigensolver: a review of methods and best practices
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Hartree-Fock on a superconducting qubit quantum computer
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Training variational quantum algorithms is NP-hard
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Emerging quantum computing algorithms for quantum chemistry
• A Non-Orthogonal Variational Quantum Eigensolver
• Eigenvector continuation with subspace learning
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
• Adiabatic state preparation study of methylene
• Surrogate models for quantum spin systems based on reduced order modeling
• Simulation of adiabatic quantum computing for molecular ground states
• Volume extrapolation via eigenvector continuation

Cited by in corpus (5)

• Eigenvector Continuation and Projection-Based Emulators
• Interpolating many-body wave functions for accelerated molecular dynamics on the near-exact electronic surface
• Cheaper and more noise-resilient quantum state preparation using eigenvector continuation
• Controlled Gate Networks: Theory and Application to Eigenvalue Estimation
• Linear Foundation Model for Quantum Embedding: Data-Driven Compression of the Ghost Gutzwiller Variational Space