Divergences in classical and quantum linear response and equation of motion formulations

Abstract

Calculating molecular properties using quantum devices can be done through the quantum linear response (qLR) or, equivalently, the quantum equation of motion (qEOM) formulations. Different parameterizations of qLR and qEOM are available, namely naive, projected, self-consistent, and state-transfer. In the naive and projected parameterizations, the metric is not the identity, and we show that it depends on the redundant orbital rotations. This dependency may lead to divergences in the excitation energies for certain choices of the redundant orbital rotation parameters in an idealized noise-less setting. Further, this leads to significant variance when calculations include statistical noise from finite quantum sampling.

References in corpus (15)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• A variational eigenvalue solver on a quantum processor
• The theory of variational hybrid quantum-classical algorithms
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Automated construction of molecular active spaces from atomic valence orbitals
• Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Orbital optimized unitary coupled cluster theory for quantum computer
• A Quantum Algorithm to Calculate Band Structure at the EOM Level of Theory
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive
• Which options exist for NISQ-friendly linear response formulations?
• Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing
• Subspace methods for the simulation of molecular response properties on a quantum computer
• Reduced density matrix formulation of quantum linear response
• Estimating molecular thermal averages with the quantum equation of motion and informationally complete measurements

Cited by in corpus (2)

• Understanding and mitigating noise in molecular quantum linear response for spectroscopic properties on quantum computers
• Equation-of-motion internally contracted multireference unitary coupled-cluster theory