Improving the Accuracy of the Variational Quantum Eigensolver for Molecular Systems by the Explicitly-Correlated Perturbative [2]-R12-Correction

Abstract

We provide an integration of the universal, perturbative explicitly correlated [2]${}_{\text{R12}}$-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources. Our proposed approach only requires knowledge of the one- and two-particle reduced density matrices (RDMs) of the reference wavefunction; these can be measured after having reached convergence in VQE. The RDMs are then combined with a set of molecular integrals. This computation comes at a cost that scales as the sixth power of the number of electrons. We explore the performance of the VQE+[2]${}_{\text{R12}}$ approach using both conventional Gaussian basis sets and our recently proposed directly determined pair-natural orbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbital and PNOs are investigated as a potential set of complementary basis functions in the computation of [2]${}_{\text{R12}}$. In particular the combination of MRA-PNOs with [2]${}_{\text{R12}}$ has turned out to be very promising -- persistently throughout our data, this allowed very accurate simulations at a quantum cost of a minimal basis set. Additionally, we found that the deployment of PNOs as complementary basis can greatly reduce the number of complementary basis functions that enter the computation of the correction at a cubic complexity.

References in corpus (34)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Quantum computational advantage using photons
• The theory of variational hybrid quantum-classical algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Hartree-Fock on a superconducting qubit quantum computer
• Variational ansatz-based quantum simulation of imaginary time evolution
• Hybrid quantum-classical algorithms and quantum error mitigation
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• A Quantum Computing View on Unitary Coupled Cluster Theory
• Efficient quantum measurement of Pauli operators in the presence of finite sampling error
• Is the Trotterized UCCSD Ansatz chemically well-defined?
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Decoding quantum errors with subspace expansions
• A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers
• Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer
• Tequila: A platform for rapid development of quantum algorithms
• Mutual information-assisted Adaptive Variational Quantum Eigensolver
• An explicitly correlated approach to basis set incompleteness in Full Configuration Interaction Quantum Monte Carlo
• Reducing qubit requirements while maintaining numerical precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach
• Chemistry on quantum computers with virtual quantum subspace expansion
• Optimized Low-Depth Quantum Circuits for Molecular Electronic Structure using a Separable Pair Approximation
• On the order problem in construction of unitary operators for the Variational Quantum Eigensolver
• Improving the accuracy of quantum computational chemistry using the transcorrelated method
• Assessment of Multireference Approaches to Explicitly Correlated Full Configuration Interaction Quantum Monte Carlo

Cited by in corpus (16)

• The Basics of Quantum Computing for Chemists
• Molecular Quantum Circuit Design: A Graph-Based Approach
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive
• Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data
• Nonunitary projective transcorrelation theory inspired by the F12 ansatz
• Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings
• Partitioning Quantum Chemistry Simulations with Clifford Circuits
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Shortcut to Chemically Accurate Quantum Computing via Density-based Basis-set Correction
• Coupled cluster method tailored with quantum computing
• Multireference error mitigation for quantum computation of chemistry
• Basis set generation and optimization in the NISQ era with Quiqbox.jl
• State Specific Measurement Protocols for the Variational Quantum Eigensolver
• Scaling up the transcorrelated density matrix renormalization group
• Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography
• Moments-based quantum computation of the electric dipole moment of molecular systems