Reduced Density Matrix Sampling: Self-consistent Embedding and Multiscale Electronic Structure on Current Generation Quantum Computers

Abstract

We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum chemistry and condensed matter physics. In both of these contexts, a strongly correlated quantum region of the extended system is isolated and self-consistently coupled to its environment via the sampling of reduced density matrices. We analyze the viability of current generation quantum devices to provide the required fidelity of these objects for a robust and efficient optimization of this subspace. We show that with a simple error mitigation strategy and optimization of compact tensor product bases to minimize the number of terms to sample, these self-consistent algorithms are indeed highly robust, even in the presence of significant noises on quantum hardware. Furthermore, we demonstrate the use of these density matrices for the sampling of non-energetic properties, including dipole moments and Fermi liquid parameters in condensed phase systems, achieving a reliable accuracy with sparse sampling. It appears that uncertainties derived from the iterative optimization of these subspaces is smaller than variances in the energy for a single subspace optimization with current quantum hardware. This boosts the prospect for routine self-consistency to improve the choice of correlated subspaces in hybrid quantum-classical approaches to electronic structure for large systems in this multiscale fashion.

References in corpus (50)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• 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
• The theory of variational hybrid quantum-classical algorithms
• Quantum Cluster Theories
• Recent developments in the PySCF program package
• Fermionic quantum computation
• Quantum algorithms for quantum chemistry and quantum materials science
• Elucidating Reaction Mechanisms on Quantum Computers
• Hartree-Fock on a superconducting qubit quantum computer
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Practical Quantum Error Mitigation for Near-Future Applications
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• Zero temperature metal-insulator transition in the infinite-dimensional Hubbard model
• Quantum embedding theories
• Automated construction of molecular active spaces from atomic valence orbitals
• Hybrid quantum-classical approach to correlated materials
• Accelerated Variational Quantum Eigensolver
• Cheap and near exact CASSCF with large active spaces
• Structure optimization for parameterized quantum circuits
• Pushing Configuration-Interaction to the Limit: Towards Massively Parallel MCSCF Calculations
• Quantum simulations of materials on near-term quantum computers
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• CASSCF with Extremely Large Active Spaces using the Adaptive Sampling Configuration Interaction Method
• Quantum Machine Learning for Electronic Structure Calculations
• A general second order complete active space self-consistent-field solver for large-scale systems
• Orbital entanglement in bond-formation processes
• Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
• Accuracy and Resource Estimations for Quantum Chemistry on a Near-term Quantum Computer
• A state-averaged orbital-optimized hybrid quantum-classical algorithm for a democratic description of ground and excited states
• Efficient evaluation of quantum observables using entangled measurements
• Quantum HF/DFT-Embedding Algorithms for Electronic Structure Calculations: Scaling up to Complex Molecular Systems
• Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory
• Rigorous wave function embedding with dynamical fluctuations
• Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware
• Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: a study with an auxiliary-field quantum Monte Carlo solver
• Efficient and Stochastic Multireference Perturbation Theory for Large Active Spaces within a Full Configuration Interaction Quantum Monte Carlo Framework
• Gutzwiller Hybrid Quantum-Classical Computing Approach for Correlated Materials
• Energy-weighted density matrix embedding of open correlated chemical fragments
• Quantum computed moments correction to variational estimates
• Fully Algebraic and Self-consistent Effective Dynamics in a Static Quantum Embedding
• Generalization of the output of variational quantum eigensolver by parameter interpolation with low-depth ansatz
• Orbital Optimization in the Active Space Decomposition Model
• Improved Stochastic Multireference Perturbation Theory for Correlated Systems with Large Active Spaces
• Frequency-dependent and algebraic bath states for a Dynamical Mean-Field Theory with compact support
• Construction of a dispersion relation from an arbitrary density of states

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• Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding
• On the effective reconstruction of expectation values from ab initio quantum embedding
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive
• Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach
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