Benchmarking near-term quantum devices with the Variational Quantum Eigensolver and the Lipkin-Meshkov-Glick model

Abstract

The Variational Quantum Eigensolver (VQE) is a promising algorithm for Noisy Intermediate Scale Quantum (NISQ) computation. Verification and validation of NISQ algorithms' performance on NISQ devices is an important task. We consider the exactly-diagonalizable Lipkin-Meshkov-Glick (LMG) model as a candidate for benchmarking NISQ computers. We use the Bethe ansatz to construct eigenstates of the trigonometric LMG model using quantum circuits inspired by the LMG's underlying algebraic structure. We construct circuits with depth $\mathcal{O}(N)$ and $\mathcal{O}({\log }_{2}N)$ that can prepare any trigonometric LMG eigenstate of $N$ particles. The number of gates required for both circuits is $\mathcal{O}(N)$. The energies of the eigenstates can then be measured and compared to the exactly-known answers.

15 pages, 4 figures, 1 table

References in corpus (3)

• Quantum circuits for strongly correlated quantum systems
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• An application benchmark for fermionic quantum simulations

Cited by in corpus (6)

• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• Conserved charges in the quantum simulation of integrable spin chains
• Finite-size criticality in fully connected spin models on superconducting quantum hardware
• A Quantum Simulation Approach to Implementing Nuclear Density Functional Theory via Imaginary Time Evolution
• Quantum Simulation of Quantum Phase Transitions Using the Convex Geometry of Reduced Density Matrices
• Classically-Boosted Variational Quantum Eigensolver