Quantum Simulations in Effective Model Spaces (I): Hamiltonian Learning-VQE using Digital Quantum Computers and Application to the Lipkin-Meshkov-Glick Model

Abstract

The utility of effective model spaces in quantum simulations of non-relativistic quantum many-body systems is explored in the context of the Lipkin-Meshkov-Glick model of interacting fermions. We introduce an iterative hybrid-classical-quantum algorithm, Hamiltonian learning variational quantum eigensolver (HL-VQE), that simultaneously optimizes an effective Hamiltonian, thereby rearranging entanglement into the effective model space, and the associated ground-state wavefunction. HL-VQE is found to provide an exponential improvement in Lipkin-Meshkov-Glick model calculations, compared to a naive truncation without Hamiltonian learning, throughout a significant fraction of the Hilbert space. Quantum simulations are performed to demonstrate the HL-VQE algorithm, using an efficient mapping where the number of qubits scales with the $\log$ of the size of the effective model space, rather than the particle number, allowing for the description of large systems with small quantum circuits. Implementations on IBM's QExperience quantum computers and simulators for 1- and 2-qubit effective model spaces are shown to provide accurate and precise results, reproducing classical predictions. This work constitutes a step in the development of entanglement-driven quantum algorithms for the description of nuclear systems, that leverages the potential of noisy intermediate-scale quantum (NISQ) devices.

30 pages, 17 figures, v3/v4: minor modifications

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Cited by in corpus (15)

• Nuclear shell-model simulation in digital quantum computers
• Multi-Body Entanglement and Information Rearrangement in Nuclear Many-Body Systems
• Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
• Quantum Simulations of SO(5) Many-Fermion Systems using Qudits
• Quantum Complexity Fluctuations from Nuclear and Hypernuclear Forces
• Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings
• Variational simulation of the Lipkin-Meshkov-Glick model on a neutral atom quantum computer
• A Quantum Simulation Approach to Implementing Nuclear Density Functional Theory via Imaginary Time Evolution
• A Quantum Annealing Protocol to Solve the Nuclear Shell Model
• Non-Markovian character and irreversibility of real-time quantum many-body dynamics
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
• Toward scalable quantum computations of atomic nuclei
• Detecting spacelike vacuum entanglement at all distances and promoting negativity to a necessary and sufficient entanglement measure in many-body regimes
• Entanglement-informed Construction of Variational Quantum Circuits
• A low-circuit-depth quantum computing approach to the nuclear shell model