Inverse iteration quantum eigensolvers assisted with a continuous variable. (1st April 2022)

• Record Type: Journal Article
• Authors: He, Min-Quan; Zhang, Dan-Bo; Wang, Z D
• Is Part Of: Quantum science and technology. Volume 7:Number 2(2022)
• Publication Date: 2022-04-01
• Subjects: quantum algorithm -- quantum many-body system -- hybrid-variable quantum computing; Quantum theory -- Periodicals; Quantum theory; Periodicals; 530
• DOI: 10.1088/2058-9565/ac5b30
• Languages: English
• ISSNs: 2058-9565

Abstract

Abstract: The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method. A key ingredient is constructing an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution. We first consider a continuous-variable quantum mode (qumode) for realizing such a linear combination as an integral, with weights being encoded into a qumode resource state. We demonstrate the quantum algorithm with numerical simulations under finite squeezing for various physical systems, including molecules and quantum many-body models. We also discuss a hybrid quantum–classical algorithm that directly sums up Hamiltonian evolution with different durations for comparison. It is revealed that continuous-variable resources are valuable for reducing the coherent evolution time of Hamiltonians in quantum algorithms.