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.

arXiv comment15 pages, 4 figures, 1 table

References in corpus (16)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Three qubits can be entangled in two inequivalent ways
• Scalable Quantum Simulation of Molecular Energies
• Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
• Quantum circuits for strongly correlated quantum systems
• Exact Ising model simulation on a quantum computer
• Efficient quantum algorithms for $GHZ$ and $W$ states, and implementation on the IBM quantum computer
• Polynomial-Time Simulation of Pairing Models on a Quantum Computer
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model
• The Lipkin-Meshkov-Glick model as a particular limit of the SU(1,1) Richardson-Gaudin integrable models
• Ultrafast Variational Simulation of Non-trivial Quantum States with Long Range Interactions
• A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer
• An application benchmark for fermionic quantum simulations
• Kitaev honeycomb tensor networks: exact unitary circuits and applications

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