[Paper Review] HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware

Nicolas P. D. Sawaya, Daniel Marti-Dafcik+14 more|arXiv (Cornell University)|Jun 22, 2023

Quantum Computing Algorithms and Architecture180 references4 citations

TL;DR

HamLib is a freely available, large-scale library of 2 to 1000 qubit quantum Hamiltonians spanning condensed matter physics, quantum chemistry, and classical optimization problems. It enables standardized benchmarking of quantum algorithms, hardware, and compilation stacks by providing pre-mapped, real-world problem instances, saving researchers time and improving reproducibility across studies.

ABSTRACT

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs. To this end, here we present a large dataset of qubit-based quantum Hamiltonians. The dataset, called HamLib (for Hamiltonian Library), is freely available online and contains problem sizes ranging from 2 to 1000 qubits. HamLib includes problem instances of the Heisenberg model, Fermi-Hubbard model, Bose-Hubbard model, molecular electronic structure, molecular vibrational structure, MaxCut, Max-$k$-SAT, Max-$k$-Cut, QMaxCut, and the traveling salesperson problem. The goals of this effort are (a) to save researchers time by eliminating the need to prepare problem instances and map them to qubit representations, (b) to allow for more thorough tests of new algorithms and hardware, and (c) to allow for reproducibility and standardization across research studies.

Motivation & Objective

• To address the lack of standardized, large-scale problem instances for benchmarking quantum algorithms and hardware.
• To reduce the time and expertise required to prepare quantum Hamiltonians for research, especially in electronic and vibrational structure calculations.
• To enable more rigorous and reproducible testing of quantum algorithms by providing a diverse, real-world dataset.
• To support hardware-software co-design by offering problem sets that reflect real-world complexity and parameterization.
• To promote standardization and fair comparison across quantum computing research through a shared, community-accessible dataset.

Proposed method

• The library compiles Hamiltonians from multiple domains: Heisenberg, Fermi-Hubbard, Bose-Hubbard, molecular electronic and vibrational structure, MaxCut, Max-k-SAT, Max-k-Cut, and TSP.
• Each Hamiltonian is mapped to a qubit representation using established quantum chemistry and optimization mapping techniques, such as Jordan-Wigner or Bravyi-Kitaev.
• Problem instances are generated with realistic physical parameters, including actual molecular geometries and vibrational frequencies.
• The dataset is structured in HDF5 format for efficient I/O and includes metadata for provenance, system size, and physical parameters.
• The library supports various problem types, including binary (qubit-based) and discrete-variable (d>2) optimization problems.
• It is hosted online and version-controlled to ensure reproducibility and facilitate community contributions and extensions.

Figure 1: The four categories of qubit Hamiltonians included in HamLib. In the area of chemistry we include real-world accurate Hamiltonians for both electronic and vibrational structure. The condensed matter dataset includes four commonly studied models defined on a variety of lattice topologies, w

Experimental results

Research questions

• RQ1 How can a standardized, large-scale dataset of quantum Hamiltonians improve reproducibility and fairness in quantum algorithm benchmarking?
• RQ2 To what extent can pre-mapped Hamiltonians reduce the time and expertise required to prepare test problems for quantum software and hardware evaluation?
• RQ3 How do diverse problem types—ranging from quantum chemistry to combinatorial optimization—contribute to more comprehensive benchmarking of quantum systems?
• RQ4 What role can such a dataset play in guiding hardware-software co-design, especially in optimizing gate scheduling and qubit connectivity?
• RQ5 How can real-world parameters in molecular and vibrational Hamiltonians enhance the industrial relevance of quantum computing research?

Key findings

• HamLib provides 2 to 1000 qubit Hamiltonians across 10 distinct problem classes, including electronic and vibrational structure for real molecules.
• The library includes 100+ molecular instances with accurate electronic structure data, enabling direct use in quantum chemistry algorithm testing.
• Vibrational structure Hamiltonians are generated with realistic anharmonic frequencies, including resonance effects, enhancing physical fidelity.
• The dataset supports both near-term variational algorithms (e.g., VQE, QAOA) and long-term simulation methods, enabling broad algorithmic evaluation.
• The library is available in a machine-readable HDF5 format with metadata, enabling automated benchmarking pipelines.
• HamLib reduces the barrier to entry for researchers by eliminating the need to generate Hamiltonians from scratch, accelerating algorithm and hardware development.