Bang-bang algorithms for quantum many-body ground states: a tensor network exploration

Abstract

We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian $H=H_A+H_B$ in infinite systems. The first algorithm is a generalization of the quantum approximate optimization algorithm (QAOA) and uses a quantum computer to evolve an initial product state into an approximation of the ground state of $H$, by alternating between $H_A$ and $H_B$. We show for the 1D quantum Ising model that the accuracy in representing a gapped ground state improves exponentially with the number of alternations. The second algorithm is the variational imaginary time ansatz (VITA), which uses a classical computer to simulate the ground state via alternating imaginary time steps with $H_A$ and $H_B$. We find for the 1D quantum Ising model that an accurate approximation to the ground state is obtained with a total imaginary time $\tau$ that grows only logarithmically with the inverse energy gap $1/\Delta$ of $H$. This is much faster than imaginary time evolution by $H$, which would require $\tau \sim 1/\Delta$.

arXiv comment5+2 pages, 4+4 figures

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Cited by in corpus (4)

• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Quantum algorithm for one-quasiparticle excitations in the thermodynamic limit via cluster-additive block diagonalization