International Journal of Quantum Chemistry

Entanglement of angular momenta of atoms and molecules

Kenji Mishima, Koichi Yamashita

Published Jan 1, 2008• 3 citations

Abstract

Abstract In this article, we investigate the entanglement degrees of angular momenta of atoms and molecules. We demonstrate theoretically and numerically the guidelines, how to prepare maximally entangled states and how the entanglement of the angular momenta changes by changing the quantum numbers of atoms and molecules. We show that the entanglement degree reduces to the Clebsch–Gordan coefficients frequently encountered in angular momentum theory. The maximally entangled states found in this manner are useful for quantum computers and quantum information science. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

DOI: 10.1002/qua.21644

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International Journal of Quantum Chemistry

Entanglement of angular momenta of atoms and molecules

Kenji Mishima, Koichi Yamashita

Published Jan 1, 2008• 3 citations

Publisher

Abstract

DOI: 10.1002/qua.21644

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Nov 1, 20151 citation

Coupled angular-momentum eigenstates are widely used in atomic and nuclear physics calculations and are building blocks for spin networks and the Schur transform. To combine two angular momenta

{\mathbf{J}}_{1}

and

{\mathbf{J}}_{2}

, forming eigenstates of their total angular momentum

\mathbf{J}={\mathbf{J}}_{1}+{\mathbf{J}}_{2}

, we develop a quantum-walk scheme that does not require inputting

O({j}^{3})

nonzero Clebsch--Gordan (CG) coefficients classically. In fact, our scheme may be regarded as a unitary method for computing CG coefficients on quantum computers with a typical complexity of

O(j)

and a worst-case complexity of

O({j}^{3})

. Equivalently, our scheme provides decompositions of the dense CG unitary into sparser unitary operations. Our scheme prepares angular-momentum eigenstates using a sequence of Hamiltonians to move an initial state deterministically to desired final states, which are usually highly entangled states in the computational basis. In contrast with usual quantum walks, whose Hamiltonians are prescribed, we engineer the Hamiltonians in $\text{su}(2)\ifmmode\times\else\texttimes\fi{}\text{su}(2)$, which are inspired by, but different from, Hamiltonians that govern magnetic resonances and dipole interactions. To achieve a deterministic preparation of both ket and bra states, we use projection and destructive interference to double pinch the quantum walks, such that each step is a unit-probability population transfer within a two-level system. We test our state preparation scheme on classical computers, reproducing tables of CG coefficients. We also implement small test problems on current quantum hardware.