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

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.

13 pages, 3 figures, v2 matches PRC version

References in corpus (21)

• A variational eigenvalue solver on a quantum processor
• The theory of variational hybrid quantum-classical algorithms
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices
• Symmetry restoration in mean-field approaches
• Preparing ground states of quantum many-body systems on a quantum computer
• Rodeo Algorithm for Quantum Computing
• Quantum computing of the ${}^6$Li nucleus via ordered unitary coupled clusters
• Variational approaches to constructing the many-body nuclear ground state for quantum computing
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Symmetry assisted preparation of entangled many-body states on a quantum computer
• Nuclear shell-model simulation in digital quantum computers
• Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers
• Spin-projection for quantum computation: A low-depth approach to strong correlation
• RPA vs. exact shell-model correlation energies
• An Alternative Approach to Quantum Imaginary Time Evolution
• Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective
• A constructive algorithm for the Cartan decomposition of SU(2^N)
• Projection algorithm for state preparation on quantum computers
• Deep Quantum Circuit Simulations of Low-Energy Nuclear States