Planted Solutions in Quantum Chemistry: Generating Non-Trivial Hamiltonians with Known Ground States

TL;DR

This paper introduces four classes of Hamiltonians with known ground states, inspired by planted-solution techniques, to generate realistic, tunable quantum chemistry problems for benchmarking electronic structure methods.

Contribution

It presents a novel framework for creating complex, realistic Hamiltonians with embedded solutions, enabling scalable benchmarking and analysis of electronic structure methods.

Findings

Hamiltonians support adjustable complexity and realistic electronic structure features.

Ground-state energies can be computed exactly from construction parameters.

Framework validated using DMRG to assess problem difficulty.

Abstract

Generating large, non-trivial quantum chemistry test problems with known ground-state solutions remains a core challenge for benchmarking electronic structure methods. Inspired by planted-solution techniques from combinatorial optimization, we introduce four classes of Hamiltonians with embedded, retrievable ground states. These Hamiltonians mimic realistic electronic structure problems, support adjustable complexity, and are derived from reference systems. Crucially, their ground-state energies can be computed exactly, provided the construction parameters are known. To obscure this structure and control perceived complexity, we introduce techniques such as killer operators, balance operators, and random orbital rotations. We showcase this framework using examples based on homogeneous catalysts of industrial relevance and validate tunable difficulty through density matrix renormalization group (DMRG) convergence behavior. Beyond enabling scalable, ground-truth benchmark generation, our approach offers a controlled setting to explore the limitations of electronic structure methods and investigate how Hamiltonian structure influences ground state solution difficulty.