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

• URL: http://arxiv.org/abs/2410.02848v1
• Date: Thu, 3 Oct 2024 17:44:24 GMT
• Title: Simplified projection on total spin zero for state preparation on quantum computers
• Authors: Evan Rule, Ionel Stetcu, Joseph Carlson,
• Abstract summary: We introduce a simple algorithm for projecting on $J=0$ states of a many-body system. Our approach performs the necessary projections using the one-body operators $J_x$ and $J_z$. Given the reduced complexity in terms of gates, this approach can be used to prepare approximate ground states of even-even nuclei.
• Score: 0.5461938536945723
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $J^2$, 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 parameterized 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.

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