Lipkin model on a quantum computer

TL;DR

This paper develops and tests variational quantum eigensolver circuits for the Lipkin model on quantum hardware, highlighting current limitations and potential improvements for quantum nuclear simulations.

Contribution

It introduces quantum circuits for VQE applied to the Lipkin model and analyzes error sources and mitigation strategies on current quantum hardware.

Findings

Error mitigation reduces quantum calculation errors

Initialization and two-qubit gates are primary error sources

Quantum hardware needs improvements for competitive accuracy

Abstract

Atomic nuclei are important laboratories for exploring and testing new insights into the universe, such as experiments to directly detect dark matter or explore properties of neutrinos. The targets of interest are often heavy, complex nuclei that challenge our ability to reliably model them (as well as quantify the uncertainty of those models) with classical computers. Hence there is great interest in applying quantum computation to nuclear structure for these applications. As an early step in this direction, especially with regards to the uncertainties in the relevant quantum calculations, we develop circuits to implement variational quantum eigensolver (VQE) algorithms for the Lipkin-Meshkov-Glick model, which is often used in the nuclear physics community as a testbed for many-body methods. We present quantum circuits for VQE for two and three particles and discuss the construction of circuits for more particles. Implementing the VQE for a two-particle system on the IBM Quantum Experience, we identify initialization and two-qubit gates as the largest sources of error. We find that error mitigation procedures reduce the errors in the results significantly, but additional quantum hardware improvements are needed for quantum calculations to be sufficiently accurate to be competitive with the best current classical methods.