Simplified projection on total spin zero for state preparation on quantum computers

Journal Article · 23 December 2024 · Physical Review. C

DOI: https://doi.org/10.1103/physrevc.110.064003 · OSTI ID:2496658

Rule, Evan Johnson  ^[1]; Stetcu, Ionel  ^[2]; Carlson, Joseph Allen  ^[2]

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1. University of California, Berkeley, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Here, we introduce a simple algorithm for projecting on J = 0 states of a many-body system by performing a series of rotations to remove states with angular momentum projections greater than zero. Existing methods rely on unitary evolution with the two-body operator J², which when expressed in the computational basis contains many complicated Pauli strings requiring Trotterization and leading to very deep quantum circuits. Our approach performs the necessary projections using the one-body operators J_x and J_z. By leveraging the method of Cartan decomposition, the unitary transformations that perform the projection can be parametrized as a product of a small number of two-qubit rotations, with angles determined by an efficient classical optimization. Given the reduced complexity in terms of gates, this approach can be used to prepare approximate ground states of even-even nuclei by projecting onto the J = 0 component of deformed Hartree-Fock states. We estimate the resource requirements in terms of the universal gate set {H,S,CNOT,T} and briefly discuss a variant of the algorithm that projects onto J = 1/2 states of a system with an odd number of fermions.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 2496658
• Report Number(s): LA-UR--24-20109
• Journal Information: Physical Review. C, Journal Name: Physical Review. C Journal Issue: 6 Vol. 110; ISSN 2469-9985
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English