Spin-projection for quantum computation: A low-depth approach to strong correlation

Tsuchimochi, Takashi; Mori, Yuto; Ten‐no, Seiichiro

doi:10.1103/physrevresearch.2.043142

Cited by 30 publications

(31 citation statements)

References 50 publications

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“…As this may turn out to lead to poor chemical properties other than the energy, this conundrum has sparked recent approaches toward symmetry restoration. [40][41][42][43][44][45] In the following sections, we explore the theory of second quantization in terms of spinors and contrast it with the simplifications that arise when using a spin-orbital basis. The distinctions that appear in these formalisms are discussed at the level of the orbitals, one-and two-electron operators and density matrices, in order to prepare the discussion of the semantic design of GQCP's reusable software objects in Sec.…”

Section: Theoretical Conceptsmentioning

confidence: 99%

GQCP: The Ghent Quantum Chemistry Package

Lemmens

Vriendt

Hende

et al. 2021

The Journal of Chemical Physics

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The Ghent Quantum Chemistry Package (GQCP) is an open-source electronic structure software package that aims to provide an intuitive and expressive software framework for electronic structure software development. Its high-level interfaces (accessible through C++ and Python) have been specifically designed to correspond to theoretical concepts, while retaining access to lower-level intermediates and allowing structural run-time modifications of quantum chemical solvers. GQCP focuses on providing quantum chemical method developers with the computational "building blocks" that allow them to flexibly develop proof of principle implementations for new methods and applications up to the level of two-component spinor bases.

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Section: Theoretical Conceptsmentioning

confidence: 99%

GQCP: The Ghent Quantum Chemistry Package

Lemmens

Vriendt

Hende

et al. 2021

The Journal of Chemical Physics

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“…So far, a wide variety of theoretical developments have been made in VQE. For example, development of new ansatzes, [16][17][18][19][20][21][22][23][24] qubit reductions by utilizing natural orbitals, 25,26 extension of ansatzes for larger systems, [27][28][29][30] introduction of error mitigation techniques, [31][32][33] spatial and spin symmetry adaptations, [34][35][36][37] reduction of the number of qubit measurements, [38][39][40][41] applications for electronic excited states, [42][43][44][45] and so on. Proof-of-principle demonstrations on quantum devices were also reported.…”

Section: ⟩ = |0⟩ + |1⟩ ≐mentioning

confidence: 99%

Towards Accurate Description of Chemical Reaction Energetics by Using Variational Quantum Eigensolver: A Case Study of the C2v Quasi-Reaction Pathway of Beryllium Insertion to H2 Molecule

Sugisaki

Kato²,

Minato³

et al. 2021

Preprint

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Variational quantum eigensolver (VQE)-based quantum chemical calculations of atoms and molecules have been extensively studied as a computational model using noisy intermediate-scale quantum devices. VQE uses a parametrized quantum circuit defined through an "ansatz" to generate the approximated wave functions, and thus appropriate choice of an ansatz is the most important step. Because most of chemistry problems focus on the energy difference between two electronic states or structures, calculating the total energies in different molecular structures with the same accuracy is essential to correctly understand chemistry and chemical processes. Here we applied numerical simulations of VQE to the quasi-reaction pathway of Be insertion to H2 molecule, which is the representative systems of both dynamical and static electron correlation effects are prominent. Our numerical simulations revealed that the energy calculated using the conventional unitary coupled cluster (UCC) ansatz exhibits large discrepancy from the full-configuration interaction (CI) value around the point where an avoided crossing occurs. We demonstrated that the multireference unitary coupled cluster with partially generalized singles and doubles (MR-UCCpGSD) ansatz can give more reliable results in respect of total energy and the overlap with the full-CI solution, insisting importance of multiconfigurational treatments in the calculations of strongly correlated systems.

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“…[44]. Moreover, related schemes have been employed to restore symmetry in a continuous group such as the SU(2) total-spin conservation [45,46] and the U(1) particle-number conservation [47,48], where the integral over continuous parameters of the group in the projection operator is properly discretized.…”

Section: Introductionmentioning

confidence: 99%

Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer

Seki,

Yunoki

2021

Preprint

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We propose an extended version of the symmetry-adapted variational-quantum-eigensolver (VQE) and apply it to a two-component Fermi-Hubbard model on a bipartite lattice. In the extended symmetry-adapted VQE method, the Rayleigh quotient for the Hamiltonian and a parametrized quantum state in a properly chosen subspace is minimized within the subspace and is optimized among the variational parameters implemented on a quantum circuit to obtain variationally the ground state and the ground-state energy. The corresponding energy derivative with respect to a variational parameter is expressed as a Hellmann-Feynman-type formula of a generalized eigenvalue problem in the subspace, which thus allows us to use the parameter-shift rules for its evaluation. The natural-gradient-descent method is also generalized to optimize variational parameters in a quantum-subspace-expansion approach. As a subspace for approximating the ground state of the Hamiltonian, we consider a Krylov subspace generated by the Hamiltonian and a symmetry-projected variational state, and therefore the approximated ground state can restore the Hamiltonian symmetry that is broken in the parametrized variational state prepared on a quantum circuit. We show that spatial symmetry operations for fermions in an occupation basis can be expressed as a product of the nearest-neighbor fermionic swap operations on a quantum circuit. We also describe how the spin and charge symmetry operations, i.e., rotations, can be implemented on a quantum circuit. By numerical simulations, we demonstrate that the spatial, spin, and charge symmetry projections can improve the accuracy of the parametrized variational state, which can be further improved systematically by expanding the Krylov subspace without increasing the number of variational parameters.

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Spin-projection for quantum computation: A low-depth approach to strong correlation

Cited by 30 publications

References 50 publications

GQCP: The Ghent Quantum Chemistry Package

GQCP: The Ghent Quantum Chemistry Package

Towards Accurate Description of Chemical Reaction Energetics by Using Variational Quantum Eigensolver: A Case Study of the C2v Quasi-Reaction Pathway of Beryllium Insertion to H2 Molecule

Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer

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