Curator's Take
AI Commentary
This article delivers one of the most extensive classical benchmarks for the Lipkin‑Meshkov‑Glick model, using DMRG on NERSC’s Perlmutter to obtain ground‑state energies for up to 1 400 spins—a scale far beyond current quantum hardware. By juxtaposing those results with VQE and Sample‑Based Quantum Diagonalization runs on an IBM Eagle processor, the authors show that subspace‑based methods like SQD can push NISQ accuracy farther than plain variational circuits while keeping circuit depth modest. The dataset and performance comparison give algorithm designers a concrete yardstick for evaluating when quantum approaches become competitive with state‑of‑the‑art tensor‑network simulations.
— Mark Eatherly
Summary
As quantum computing matures, it is critical to benchmark its real-world problem solving performance against competitive classical methods, such as tensor networks. In this work, we leverage the Density Matrix Renormalization Group (DMRG) algorithm to compute ground state energies of the Lipkin Meshkov Glick (LMG) model as a comparative benchmark against popular noisy intermediate-scale (NISQ) algorithms like the Variational Quantum Eigensolver (VQE) and Sample-Based Quantum Diagonalization (SQD) method. By running DMRG on the NERSC Perlmutter supercomputer, we provide one of the largest LMG ground state energy datasets in literature, containing accurate ground state energies for systems up to 1400 particles. We compare these results with VQE and SQD implementations on an IBM Eagle quantum computer for comparison. VQE achieved results within 1 percent error for 6 particles, while exceeding that threshold for all other values while SQD extended that range to 17 particles, suggesting that in a noisy intermediate scale quantum era, subspace-based approaches may strike the best balance between accuracy, circuit depth, and noise resilience.