AGP-based unitary coupled cluster theory for quantum computers

Abstract

Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. The same goes for Ansätze on a quantum computer. We develop a unitary coupled cluster method on the antisymmetrized geminal power (AGP) -- a state formally equivalent to the number-projected Bardeen--Cooper--Schrieffer wavefunction. We demonstrate our method for the single-band Fermi--Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than $\mathcal{O}(\sqrt{M})$ in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry.

References in corpus (20)

• Hybrid quantum-classical algorithms and quantum error mitigation
• The Bitter Truth About Quantum Algorithms in the NISQ Era
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Is the Trotterized UCCSD Ansatz chemically well-defined?
• Symmetry broken and restored coupled-cluster theory I. Rotational symmetry and angular momentum
• A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers
• Solving Nuclear Structure Problems with the Adaptive Variational Quantum Algorithm
• Generalized swap networks for near-term quantum computing
• Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers
• Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
• Geminal replacement models based on AGP
• Exploring non-linear correlators on AGP
• Density Matrices of Seniority-Zero Geminal Wavefunctions
• Assessing the Accuracy of the Jastrow Antisymmetrized Geminal Power in the H4 Model System
• Construction of linearly independent non-orthogonal AGP states
• Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer
• Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation
• A Power Series Approximation in Symmetry Projected Coupled Cluster Theory
• Symmetry breaking slows convergence of the ADAPT Variational Quantum Eigensolver
• Transition density matrices of Richardson-Gaudin states

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• State preparation of AGP on a quantum computer without number projection
• Accurate and precise quantum computation of valence two-neutron systems
• Correlated pair ansatz with a binary tree structure
• A Quantum Algorithmic Approach to Multiconfigurational Valence Bond Theory: Insights from Interpretable Circuit Design
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions