Dimensionality reduction of many-body problem using coupled-cluster sub-system flow equations: classical and quantum computing perspective

Abstract

We discuss reduced-scaling strategies employing recently introduced sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to describe many-body systems. These strategies utilize properties of the SES-CC formulations where the equations describing certain classes of sub-systems can be integrated into a computational flows composed coupled eigenvalue problems of reduced dimensionality. Additionally, these flows can be determined at the level of the CC Ansatz by the inclusion of selected classes of cluster amplitudes, which define the wave function "memory" of possible partitionings of the many-body system into constituent sub-systems. One of the possible ways of solving these coupled problems is through implementing procedures, where the information is passed between the sub-systems in a self-consistent manner. As a special case, we consider local flow formulations where the so-called local character of correlation effects can be closely related to properties of sub-system embedding sub-algebras employing localized molecular basis. We also generalize flow equations to the time domain and to downfolding methods utilizing double exponential unitary CC Ansatz (DUCC), where reduced dimensionality of constituent sub-problems offer a possibility of efficient utilization of limited quantum resources in modeling realistic systems.

References in corpus (42)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Quantum Chemistry in the Age of Quantum Computing
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Extending the computational reach of a noisy superconducting quantum processor
• Schrieffer-Wolff transformation for quantum many-body systems
• Robust determination of molecular spectra on a quantum processor
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Coupled Cluster Theory for Molecular Polaritons: Changing Ground and Excited States
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Is the Trotterized UCCSD Ansatz chemically well-defined?
• Medium-mass nuclei from chiral nucleon-nucleon interactions
• Ab initio quantum dynamics using coupled-cluster
• Coupled cluster calculations of ground and excited states of nuclei
• A Non-Orthogonal Variational Quantum Eigensolver
• Coupled cluster approach to nuclear physics
• Exploiting locality in quantum computation for quantum chemistry
• On the difference between variational and unitary coupled cluster theories
• Downfolding of many-body Hamiltonians using active-space models: extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
• Time-dependent optimized coupled-cluster method for multielectron dynamics
• Hamiltonian simulation in the low-energy subspace
• Symplectic integration and physical interpretation of time-dependent coupled-cluster theory
• Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer
• Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian
• On the order problem in construction of unitary operators for the Variational Quantum Eigensolver
• Quantum simulations of excited states with active-space downfolded Hamiltonians
• Sub-system quantum dynamics using coupled cluster downfolding techniques
• The Interplay Between Lattice Topology, Frustration, and Spin Quantum Number in Quantum Antiferromagnets on Archimedean Lattices
• Improving the accuracy of quantum computational chemistry using the transcorrelated method
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation
• A Coupled-Cluster Formulation of Hamiltonian Lattice Field Theory: The Non-Linear Sigma Model
• The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUB$m$ Approximation Scheme for Lattice Models
• The coupled-cluster approach to quantum many-body problem in a three-Hilbert-space reinterpretation
• Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory
• Variational Quantum Eigensolver for Approximate Diagonalization of Downfolded Hamiltonians using Generalized Unitary Coupled Cluster Ansatz

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• The Variational Quantum Eigensolver: a review of methods and best practices
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